",isbn:"978-1-83969-591-9",printIsbn:"978-1-83969-590-2",pdfIsbn:"978-1-83969-592-6",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"e39a567d9b6d2a45d0a1d927362c9005",bookSignature:"Dr. Umar Zakir Abdul Hamid and Associate Prof. Ahmad 'Athif Mohd Faudzi",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10778.jpg",keywords:"Model-Based Control, Optimal Control, Industrial Automation, Linear Actuator, Nonlinear Actuator, System Identification, Soft Robotics, Service Robots, Unmanned Aerial Vehicle, Autonomous Vehicle, Process Engineering, Chemical Engineering",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 25th 2021",dateEndSecondStepPublish:"March 25th 2021",dateEndThirdStepPublish:"May 24th 2021",dateEndFourthStepPublish:"August 12th 2021",dateEndFifthStepPublish:"October 11th 2021",remainingDaysToSecondStep:"16 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,biosketch:"Umar Zakir Abdul Hamid, Ph.D. is an autonomous vehicle expert, and with more than 30 scientific publications under his belt, Umar actively participates in global automotive standardization efforts and is a Secretary for a Society of Automotive Engineers (SAE) Committee.",coeditorOneBiosketch:"Associate Professor Dr. Ahmad 'Athif Mohd Faudzi has more than 100 scientific publications as of 2021 and is currently leading a team of 18 researchers in UTM doing research works on control, automation, and actuators.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"268173",title:"Dr.",name:"Umar Zakir Abdul",middleName:null,surname:"Hamid",slug:"umar-zakir-abdul-hamid",fullName:"Umar Zakir Abdul Hamid",profilePictureURL:"https://mts.intechopen.com/storage/users/268173/images/system/268173.jpg",biography:"Umar Zakir Abdul Hamid, PhD has been working in the autonomous vehicle field since 2014 with various teams in different countries (Malaysia, Singapore, Japan, Finland). 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1. Introduction
The chapter goal is focused to introduce the concept of fractional delay filters (FDF), as well as a concise description of most of the existing design techniques. For this purpose, several illustrative examples are presented, where each design method is implemented by MATLAB programs.
A fractional delay filter is a filter of digital type having as main function to delay the processed input signal a fractional of the sampling period time. There are several applications where such signal delay value is required, examples of such systems are: timing adjustment in all-digital receivers (symbol synchronization), conversion between arbitrary sampling frequencies, echo cancellation, speech coding and synthesis, musical instruments modelling etc. (Laakson et al., 1996).
In order to achieve the fractional delay filter function, two main frequency-domain specifications must be met by the filter. The filter magnitude frequency response must have an all-pass behaviour in a wide frequency range, as well as its phase frequency response must be linear with a fixed fractional slope through the bandwidth.
Several FIR design methods have been reported during the last two decades. There are two main design approaches: time-domain and frequency-domain design methods. In first one, the fractional delay filter coefficients are easily obtained through classical mathematical interpolation formulas, but there is a small flexibility to meet frequency-domain specifications. On the other hand, the frequency-domain methods are based on frequency optimization process, and a more frequency specification control is available. One important result of frequency-domain methods is a highly efficient implementation structure called Farrow structure, which allows online fractional value update.
The chapter is organized as follows. Next section gives the formal definition of fractional delay filter. In the third section, some design methods are briefly described. Two efficient implementation structures for wideband fractional delay filter, as well as description of recently reported design methods for such structures, are illustrated in fourth section. MATLAB designed examples and concluding remarks are presented in fifth and sixth sections, respectively.
2. Fractional delay filter definition
The continuous-time output signal ya(t) of a general signal delay system is defined by:
ya(t)=x(t−tl)E1
where x(t) is the continuous-time input signal and tl the obtained time delay value. In a discrete-time system, the input-output relationship of a signal delay system is expressed as:
y(lT)=x(nT−DT)E2
where the delay value is given by DT, y(lT) and x(nT) are the discrete-time versions of output and input signals, respectively, and T is the sampling period time.
A signal delay value equal to a multiple of the sampling period, D as an integer N, can be easily implemented in a discrete-time system by memory elements storing the signal value for a time of NT:
y(lT)=x(nT−NT)E3
In this case, the signal delay value is limited to be only N time the sampling period, tl=NT. For instance in telephone quality signals, with a sampling frequency of 8 KHz, only delays values multiple of 125μseconds are allowed.
Let us introduce the FDF function using time-domain signals sketched in Fig 1. The FDF output y(lT), squared samples, is obtained a delay time tl after input x(nl), with a delay value μlT given as a fraction of the sampling period time, 0<μl<1. As shown in Fig. 1, the fractional delay value μl may be variable; this way, it can be changed at any desired time.
The fundamental design problem of a FDF is to obtain the FDF unit impulse response hFD(n,μ), in such a way that the obtained output value y(lT) = ya(DT) be as close as possible to ya(tl) for 0<μl <1. The simplified block diagram for a FDF is shown in Fig. 2, which output for a no causal FIR FDF filter is given by the discrete-time convolution:
y(lT)=∑k=−NFD/2NFD/2−1x(nl−k)hFD(k,μl)E4
where NFD is the even length of the FDF. The system function H(z) of the FDF can be expressed as:
H(z)=z−DE5
Figure 1.
FDF time-domain behaviour.
Figure 2.
Simplified block diagram for a FDF.
where the delay value is given as: D = Dfix+μl, Dfix is a fixed delay value and μl is the desired fractional delay value. As a consequence, the ideal frequency response of a FDF Hid(ω,μl) is:
Hid(ω,μl)=e−j(Dfix+μl)ωE6
Hence the ideal FDF frequency response has an all-band unity magnitude response:
|Hid(ω,μl)|=1,|ω|≤πE7
and a linear frequency phase response with a constant phase delay given, respectively, by:
θid(ω,μl)=−DωE8
τpid(ω,μl)=DE9
The main goal of all existing FDF design methods, based on a frequency design approach, is to obtain the FDF filter coefficients through approximating this ideal frequency performance.
Applying inverse discrete Fourier transform to the ideal FDF frequency response, the ideal FDF filter unit impulse response hid(n,μ) is obtained as:
hid(n,μ)=sin[π(n−D)]π(n−D)=sinc(n−D)E10
Given a desired factional delay value, the FDF coefficients can be easily obtained with this infinite length delayed sinc function. Due to this infinite length, it is evident that an FIR FDF will be always an approximation to the ideal case.
As an illustrative example, the ideal FDF unit impulse responses for two delay values D= 3.0 (Dfix=3.0 and μ = 0) and D=3.65 (Dfix=3.0 and μ = 0.65) are shown in Fig. 3 and 4, respectively. The unit impulse responses were obtained using MATLAB function sinc. The FDF unit impulse responses are shown as solid lines, and the delayed sinc function as dot line. In the first case, only one three-sample delay is needed, which can be easily implemented with memory components as described above. However, the FDF unit impulse response for the second case has an infinite number of nonzero coefficients (IIR) and it is a no causal sequence, which makes it impractical for implementing in real-time applications.
Figure 3.
Ideal FDF unit impulse response for D=3.0.
Figure 4.
Ideal FDF unit impulse response for D=3.65.
3. FDF Design methods
The existing design methods for FIR FDF use a large range of strategies to approximate as close as possible the ideal FDF unit impulse response hid(n,μ). It is possible to highlight three main strategies:
Magnitude frequency response approximation: The FDF unit impulse response is obtained such that its frequency magnitude response is as close as possible to the ideal FDF one, accordingly to some defined error criterion.
Interpolation design method: The design approach is based on computing FDF coefficients through classical mathematical interpolation methods, such as Lagrange or B-spline. The design is a completely time-domain approach.
Hybrid analogue-digital model approach: The FDF design is accomplished through the use of an analogue-digital model. The design methods using this strategy are based on a frequency-domain approach.
A concise description of each one of these strategies is presented in the following.
3.1. Magnitude frequency response approximation
The design method goal is to obtain the FDF unit impulse response hFD(n,μ) based on comparing its magnitude frequency response with the ideal one. The frequency response of the designed FDF with even-length NFD is given by:
HFD(ω,μ)=∑k=−NFD/2+1NFD/2hFD(k,μ)e−jωkE11
One of the criterions used for the magnitude frequency response comparison is the least squares magnitude error defined as:
e2(ω)=1π∫0ωp|HDF(ω,μ)−Hid(ω,μ)|2dωE12
The error function e2(ω) is minimized by truncating the ideal unit impulse response to NFD samples, which can be interpreted as applying a delayed M-length window w(n) to the ideal IIR FDF unit impulse response:
hFD(n,μ)=hid(n−D,μ)w(n−D)E13
where ω(n) is equal to unity in the interval 0≤n≤NFD-1 and zero otherwise.
The windowing process on the ideal unit impulse response causes not-desired effects on the FDF frequency response, in particular the Gibbs phenomenon for rectangular window (Proakis & Manolakis, 1995).
In general, the performance of a FDF obtained by truncating the sinc function is usually not acceptable in practice. As a design example, the FDF frequency magnitude and phase responses for D=3.65, using a rectangular window with NFD=50, are shown in Fig 5. We can see that the obtained FDF bandwidth is less than 0.9π and although the IIR sinc function has been truncated up to 50 taps, neither its frequency magnitude nor its phase response are constant.
The windowed unit impulse response hFD(n,μ) has a low-pass frequency response, in this way it can be modified to approximate only a desired pass-band interval (0,απ) as follows:
hFD(n,μ)={αsinc[α(n−D)]for0≤n≤NFD−10otherwiseE14
Figure 5.
FDF frequency response for D=3.65 with rectangular window, NFD=50.
The magnitude and phase responses of a FDF with NFD= 8 and α=0.5 are shown in Fig. 6, which were obtained using MATLAB. The phase delay range is from D=3.0 to 3.5 samples with an increment of 0.1. More constant phase delay responses and narrower bandwidth is achieved.
Figure 6.
FDF frequency responses using windowing method for D=3.0 to 3.5 with ΝFD = 8 and α =0.5.
In principle, window-based design is fast and easy. However, in practical applications it is difficult to meet a desired magnitude and phase specifications by adjusting window parameters. In order to meet a variable fractional delay specification, a real-time coefficient update method is required. This can be achieved storing the window values in memory and computing the values of the sinc function on line, but this would require large memory size for fine fractional delay resolution (Vesma, 1999).
The smallest least squares error can be achieved by defining its response only in a desired frequency band and by leaving the rest as a “don’t care” band. This can be done using a frequency-domain weighting as follows (Laakson et al., 1996):
e3(ω)=1π∫0ωpW(ω)|HDF(ω,μ)−Hid(ω,μ)|2E15
where ωp is the desired pass-band frequency and W(ω) represents the weighting frequency function, which defines the corresponding weight to each band. In this way, the error is defined only in the FDF pass-band, hence the optimization process is applied in this particular frequency range.
In Fig. 7 are shown the FDF frequency responses designed with this method using W(ω)=1, ΝFD = 8 and α =0.5. We can see a notable improvement in the resulting FDF bandwidth compared with the one obtained using the least square method, Fig. 6.
There is another design method based on the magnitude frequency response approach, which computes the FDF coefficients by minimizing the error function:
e4(ω)=max0≤ω≤ωp|HFD(ω,μ)−Hid(ω,μ)|E16
The solution to this optimization problem is given by the minimax method proposed by (Oetken, 1979). The obtained FDF has an equiripple pass-band magnitude response. As an illustrative example, the frequency response of an FDF designed through this minimax method is shown in Fig. 8, where NFD=20 and ωp=0.9π.
Figure 7.
FDF frequency responses using weighted least square method for D=3.0 to 3.5 with ΝFD = 8 and α =0.5.
Figure 8.
FDF Frequency responses using minimax method for D=9.0 to 9.5 with ΝFD = 20 and α =0.9.
3.2. Interpolation design approach
Instead of minimizing an error function, the FDF coefficients are computed from making the error function maximally-flat at ω=0. This means that the derivatives of an error function are equal to zero at this frequency point:
∂nec(ω)∂ωn|ω=0=0,n=0,1,2,....NFD−1E17
the complex error function is defined as:
ec(ω)=HFD(ω,μl)−Hid(ω,μl)E18
where HFD(ω,μl) is the designed FDF frequency response, and Hid(ω,μl) is the ideal FDF frequency response, given by equation (Eq. 6). The solution of this approximation is the classical Lagrange interpolation formula, where the FDF coefficients are computed with the closed form equation:
hL(n)=∏k=0k≠nNFDD−kn−kn=0,1,2,....NFDE19
where NFD is the FDF length and the desired delayD=⌊NFD/2⌋+μl. We can note that the filter length is the unique design parameter for this method.
The FDF frequency responses, designed with Lagrange interpolation, with a length of 10 are shown in Fig. 9. As expected, a flat magnitude response at low frequencies is presented; a narrow bandwidth is also obtained.
Figure 9.
FDF Frequency responses using Lagrange interpolation for D=4.0 to 4.5 with ΝFD = 10.
The use of this design method has three main advantages (Laakson et al., 1994): 1) the ease to compute the FDF coefficients from one closed form equation, 2) the FDF magnitude frequency response at low frequencies is completely flat, 3) a FDF with polynomial-defined coefficients allows the use of an efficient implementation structure called Farrow structure, which will be described in section 3.3.
On the other hand, there are some disadvantages to be taken into account when a Lagrange interpolation is used in FDF design: 1) the achieved bandwidth is narrow, 2) the design is made in time-domain and then any frequency information of the processed signal is not taken into account; this is a big problem because the time-domain characteristics of the signals are not usually known, and what is known is their frequency band, 3) if the polynomial order is NFD; then the FDF length will be NFD, 4) since only one design parameter is used, the design control of FDF specifications in frequency-domain is limited.
The use of Lagrange interpolation for FDF design is proposed in (Ging-Shing & Che-Ho, 1990, 1992), where closed form equations are presented for coefficients computing of the desired FDF filter. A combination of a multirate structure and a Lagrange-designed FDF is described in (Murphy et al., 1994), where an improved bandwidth is achieved.
The interpolation design approach is not limited only to Lagrange interpolation; some design methods using spline and parabolic interpolations were reported in (Vesma, 1995) and (Erup et al., 1993), respectively.
3.3. Hybrid analogue-digital model approach
In this approach, the FDF design methods are based on the hybrid analogue-digital model proposed by (Ramstad, 1984), which is shown in Fig. 10. The fractional delay of the digital signal x(n) is made in the analogue domain through a re-sampling process at the desired time delay tl. Hence a digital to analogue converter is taken into account in the model, where a reconstruction analog filter ha(t) is used.
Figure 10.
Hybrid analogue-digital model.
An important result of this modelling is the relationship between the analogue reconstruction filer ha(t) and the discrete-time FDF unit impulse response hFD(n,μ), which is given by:
hFD(n,μ)=ha((n+μl)T)E20
where n=-NFD/2,-NFD/2+1,…., NFD/2-1, and T is the signal sampling frequency. The model output is obtained by the convolution expression:
y(l)=∑k=0NFD−1x(nl−k+NFD/2)ha((k+μl−NFD/2)T)E21
This means that for a given desired fractional value, the FDF coefficients can be obtained from a designed continuous-time filter.
The design methods using this approach approximate the reconstruction filter ha(t) in each interval of length T by means of a polynomial-based interpolation as follows:
ha((n+μl)T)=∑m=0Mcm(n)μlmE22
for k=-NFD/2,-NFD/2+1,…., NFD/2-1. The cm(k)’s are the unknown polynomial coefficients and M is the polynomials order.
If equation (Eq. 22) is substituted in equation (Eq. 21), the resulted output signal can be expressed as:
y(l)=∑m=0Mvm(nl)μlmE23
where:
vm(nl)=∑k=0NFD−1x(nl−k+NFD/2)cm(k−NFD/2)E24
are the output samples of the M+1 FIR filters with a system function:
Cm(z)=∑k=0NFD−1cm(k−NFD/2)z−kE25
The implementation of such polynomial-based approach results in the Farrow structure, (Farrow, 1988), sketched in Fig. 11. This implementation is a highly efficient structure composed of a parallel connection of M+1 fixed filters, having online fractional delay value update capability. This structure allows that the FDF design problem be focused to obtain each one of the fixed branch filters cm(k) and the FDF structure output is computed from the desired fractional delay given online μl.
The coefficients of each branch filter Cm(z) are determined from the polynomial coefficients of the reconstruction filter impulse response ha(t). Two mainly polynomial-based interpolation filters are used: 1) conventional time-domain design such as Lagrange interpolation, 2) frequency-domain design such as minimax and least mean squares optimization.
Figure 11.
Farrow structure.
As were pointed out previously, Lagrange interpolation has several disadvantages. A better polynomial approximation of the reconstruction filter is using a frequency-domain approach, which is achieved by optimizing the polynomial coefficients of the impulse response ha(t) directly in the frequency-domain. Some of the design methods are based on the optimization of the discrete-time filter hFD(n,μl)) and others on making the optimization of the reconstruction filter ha(t). Once that this filter is obtained, the Farrow structure branch filters cm(k) are related to hFD(n,ml) using equations (Eq. 20) and (Eq. 22). One of main advantages of frequency-domain design methods is that they have at least three design parameters: filter length NFD, interpolation order M, and pass-band frequency ωp.
There are several methods using the frequency design method (Vesma, 1999). In (Farrow, 1988) a least-mean-squares optimization is proposed in such a way that the squared error between HFD(ω,μl) and the ideal response Hid(ω,μl) is minimized for 0≤ω≤ωp and for 0≤μl<1. The design method reported in (Laakson et al., 1995) is based on optimizing cm(k) to minimize the squared error between ha(t) and the hFD(n,μl) filters, which is designed through the magnitude frequency response approximation approach, see section 3.1. The design method introduced in (Vesma et al., 1998) is based on approximating the Farrow structure output samples vm(nl) as an mth order differentiator; this is a Taylor series approximation of the input signal. In this sense, Cm(ω) approximates in a minimax or L2 sense the ideal response of the mth order differentiator, denoted as Dm(ω), in the desired pass-band frequencies. In (Vesma & Saramaki, 1997) the designed FDF phase delay approximates the ideal phase delay value μl in a minimax sense for 0≤ω≤ωp and for 0≤μl<1 with the restriction that the maximum pass-band amplitude deviation from unity be smaller than the worst-case amplitude deviation, occurring when μ=0.5.
4. FDF Implementation structures
As were described in section 3.3, one of the most important results of the analogue-digital model in designing FDF filters is the highly efficient Farrow structure implementation, which was deduced from a piecewise approximation of the reconstruction filter through a polynomial based interpolation. The interpolation process is made as a frequency-domain optimization in most of the existing design methods.
An important design parameter is the FDF bandwidth. A wideband specification, meaning a pass-band frequency of 0.9π or wider, imposes a high polynomial order M as well as high branch filters length NFD. The resulting number of products in the Farrow structure is given by NFD(M+1)+M, hence in order to reduce the number of arithmetic operations per output sample in the Farrow structure, a reduction either in the polynomial order or in the FDF length is required.
Some design approaches for efficient implementation structures have been proposed to reduce the number of arithmetic operations in a wideband FDF. A modified Farrow structure, reported in (Vesma & Samaraki, 1996), is an extension of the polynomial based interpolation method. In (Johansson & Lowerborg, 2003), a frequency optimization technique is used a modified Farrow structure achieving a lower arithmetic complexity with different branch filters lengths. In (Yli-Kaakinen & Saramaki, 2006a, 2006a, 2007), multiplierless techniques were proposed for minimizing the number of arithmetic operations in the branch filters of the modified Farrow structure. A combination of a two-rate factor multirate structure and a time-domain designed FDF (Lagrange) was reported in (Murphy et al., 1994). The same approach is reported in (Hermanowicz, 2004), where symmetric Farrow structure branch filters are computed in time-domain with a symbolic approach. A combination of the two-rate factor multirate structure with a frequency-domain optimization process was firstly proposed in (Jovanovic-Docelek & Diaz-Carmona, 2002). In subsequence methods (Hermanowicz & Johansson, 2005) and (Johansson & Hermanowicz &, 2006), different optimization processes were applied to the same multirate structure. In (Hermanowicz & Johansson, 2005), a two stage FDF jointly optimized technique is applied. In (Johansson & Hermanowicz, 2006) a complexity reduction is achieved by using an approximately linear phase IIR filter instead of a linear phase FIR in the interpolation process.
Most of the recently reported FDF design methods are based on the modified Farrow structure as well as on the multirate Farrow structure. Such implementation structures are briefly described in the following.
4.1. Modified Farrow structure
The modified Farrow structure is obtained by approximating the reconstruction filter with the interpolation variable 2μl -1 instead of μl in equation (Eq. 22):
ha((n+μl)T)=∑m=0Mcm\'(k)(2μl−1)mE26
for k=-NFD/2,-NFD/2+1,…., NFD/2-1. The first four basis polynomials are shown in Fig. 12. The symmetry property ha(-t)= ha(t) is achieved by:
cm\'(n)=(−1)mcm\'(−n−1)E27
for m= 0, 1, 2,…,M and n=0, 1,….,NFD/2. Using this condition, the number of unknowns is reduced to half.
The reconstruction filter ha(t) can be now approximated as follows:
ha(t)=∑n=0NFD/2∑m=0Mcm\'(n)g(n,m,t)E28
where cm(n) are the unknown coefficients and g(n,m,t)’s are basis functions reported in (Vesma & Samaraki, 1996).
Figure 12.
Basis polynomials for modified Farrow structure for 0≤ m ≤ 3.
The modified Farrow structure has the following properties: 1) polynomial coefficients cm(n) are symmetrical, according to equation (Eq. 27); 2) The factional value μl is substituted by 2μl -1, the resulting implementation of the modified Farrow structure is shown in Fig. 13; 3) the number of products per output sample is reduced from NFD(M+1)+M to NFD(M+1)/2+M.
The frequency design method in (Vesma et al., 1998) is based on the following properties of the branch digital filters Cm(z):
The FIR filter Cm(z), 0≤m≤M, in the original Farrow structure is the mth order Taylor approximation to the continuous-time interpolated input signal.
In the modified Farrow structure, the FIR filters C’m(z) are linear phase type II filters when m is even and type IV when m is odd.
Each filter Cm(z) approximates in magnitude the function Kmwm, where Km is a constant. The ideal frequency response of an mth order differentiator is (jω)m, hence the ideal response of each Cm(z) filter in the Farrow structure is an mth order differentiator.
In same way, it is possible to approximate the input signal through Taylor series in a modified Farrow structure for each C’m(z), (Vesma et al., 1998). The mth order differential approximation to the continuous-time interpolated input signal is done through the branch filter C’m(z), with a frequency response given as:
Figure 13.
Modified Farrow structure.
C\'m(ω)=ejω(NFD−1)/2(−jω)m2mm!E29
The input design parameters are: the filter length NFD, the polynomial order M, and the desired pass-band frequency ωp.
The NFD coefficients of the M+1\n\t\t\t\t\tC’m(z) FIR filters are computed in such a way that the following error function is minimized in a least square sense through the frequency range [0,ωp]:
From this equation it can be observed that the design of a wide bandwidth FDF requires an extensive computing workload. For high fractional delay resolution FDF, high precise differentiator approximations are required; this imply high branch filters length, NFD, and high polynomial order, M. Hence a FDF structure with high number of arithmetic operations per output sample is obtained.
4.2. Multirate Farrow structure
A two-rate-factor structure in (Murphy et al., 1994), is proposed for designing FDF in time-domain. The input signal bandwidth is reduced by increasing to a double sampling frequency value. In this way Lagrange interpolation is used in the filter coefficients computing, resulting in a wideband FDF.
The multirate structure, shown in Fig. 14, is composed of three stages. The first one is an upsampler and a half-band image suppressor HHB(z) for incrementing twice the input sampling frequency. Second stage is the FDF HDF(z), which is designed in time-domain through Lagrange interpolation. Since the signal processing frequency of HDF(z) is twice the input sampling frequency, such filter can be designed to meet only half of the required bandwidth. Last stage deals with a downsampler for decreasing the sampling frequency to its original value. Notice that the fractional delay is doubled because the sampling frequency is twice. Such multirate structure can be implemented as the single-sampling-frequency structure shown in Fig. 15, where H0(z) and H1(z) are the first and second polyphase components of the half-band filter HHB(z), respectively. In the same way HFD0(z) and HFD1(z) are the polyphase components of the FDF HFD(z) (Murphy et al, 1994).
The resulting implementation structure for HDF(z) designed as a modified Farrow structure and after some structure reductions (Jovanovic-Dolecek & Diaz-Carmona, 2002) is shown in Fig. 16. The filters Cm,0(z) and Cm,1(z) are the first and second polyphase components of the branch filter Cm(z), respectively.
Figure 14.
FDF Multirate structure.
Figure 15.
Single-sampling-frequency structure.
Figure 16.
Equivalent single-sampling-frequency structure.
The use of the obtained structure in combination with a frequency optimization method for computing the branch filters Cm(z) coefficients was exploited in (Jovanovic-Dolecek & Diaz-Carmona, 2002). The approach is a least mean square approximation of each one of the mth differentiator of input signal, which is applied through the half of the desired pass-band. The resulting objective function, obtained this way from equation (Eq. 32), is:
The decrease in the optimization frequency range allows an abrupt reduction in the coefficient computation time for wideband FDF, and this less severe condition allows a resulting structure with smaller length of filters Cm(z).
The half-band HHB(z) filter plays a key role in the bandwidth and fractional delay resolution of the FDF filter. The higher stop-band attenuation of filter HHB(z), the higher resulting fractional delay resolution. Similarly, the narrower transition band of HHB(z) provides the wider resulting bandwidth.
In (Ramirez-Conejo, 2010) and (Ramirez-Conejo et al., 2010a), the branch filters coefficients cm(n) are obtained approximating each mth differentiator with the use of another frequency optimization method. The magnitude and phase frequency response errors are defined, for 0≤w≤wp and 0≤μl≤1, respectively as:
emag(ω)=|HFD(ω)|−1,E34
epha(ω)=−ϕ(ω)ω−(Dfix+μl),E35
where HFD(ω) and ϕ(ω) are, respectively, the frequency and phase responses of the FDF filter to be designed. In the same way, this method can also be extended for designing FDF with complex specifications, where the complex error used is given by equation (Eq. 18).
The coefficients computing of the resulting FDF structure, shown in Fig. 16, is done through frequency optimization for global magnitude approximation to the ideal frequency response in a minimax sense. The objective function is defined as:
Δm=max0≤μl≤1[max0≤ω≤ωp|em(ω)|]E36
The objective function is minimized until a magnitude error specification δm is met. In order to meet both magnitude and phase errors, the global phase delay error is constrained to meet the phase delay restriction:
Δp=max0≤μl≤1[max0≤ω≤ωp|ep(ω)|]≤δpE37
where δp is the FDF phase delay error specification. The minimax optimization can de performed using the function fminmax available in the MATLAB Optimization Toolbox.
As is well known, the initial solution plays a key role in a minimax optimization process, (Johansson & Lowenborg, 2003), the proposed initial solution is the individual branch filters approximations to the mth differentiator in a least mean squares sense, accordingly to (Jovanovic-Delecek & Diaz-Carmona, 2002):
Em=∫0ωp2[em(ω)]2dωE38
The initial half-band filter HHB(z) to the frequency optimization process can be designed as a Doph-Chebyshev window or as an equirriple filter. The final hafband coefficients are obtained as a result of the optimization.
The fact of using the proposed optimization process allows the design of a wideband FDF structure with small arithmetic complexity. Examples of such designing are presented in section 5.
An implementation of this FDF design method is reported in (Ramirez-Conejo et al., 2010b), where the resulting structure, as one shown in Fig. 16, is implemented in a reconfigurable hardware platform.
The design example is based on the method described in (Diaz-Carmona et al., 2010). The desired FDF bandwidth is 0.9π, and a fractional delay resolution of 1/10000.
A half-band filter HHB(z) with 241 coefficients was used, which was designed with a Dolph-Chebyshev window, with a stop-band attenuation of 140 dBs. The design parameters are: M=12 and NFD=10 with a resulting structure arithmetic of 202 products per output sample.
The frequency optimization is applied up to only ωp=0.45π, causing a notably computing workload reduction, compared with an optimization on the whole desired bandwidth (Vesma et al., 1998). As a matter of comparison, the MATLAB computing time in a PC running at 2GHz for the optimization on half of the desired pass-band is 1.94 seconds and 110 seconds for the optimization on the whole pass-band. The first seven differentiator approximations for both cases are shown in Fig. 17 and Fig. 18.
The frequency responses of the resulted FDF from μ=0.008 to 0.01 samples for the half pass-band and for the whole pass-band optimization process, are shown in Fig. 19 and Fig. 20, respectively.
The use of the optimization process (Vesma et al., 1998) with design parameters of M=12 and NFD=104 results in a total number of 688 products per output sample. Accordingly to the described example in (Zhao & Yu, 2006), using a weighted least squares design method, an implementation structure with NFD=67 and M=7 is required to meet ωp=0.9π, which results in arithmetic complexity of 543 products per output sample.
Figure 17.
Frequency responses of the first seven ideal differentiators (dotted line) and the obtained approximations (solid line) in 0≤ω≤0.45π with NFD=10 and M=12.
Figure 18.
First seven differentiator ideal frequency responses (dotted line) and obtained approximations (solid line) in 0≤ω≤0.9π with NFD=104 and M=12.
Figure 19.
FDF frequency responses using half band frequency optimization method for μl=0.0080 to 0.0100 with ΝFD = 10 and M=12.
Figure 20.
FDF frequency responses, using all-bandwidth frequency optimization method for μl=0.0080 to 0.0100 with NFD=104 and M=12.
In order to compare the frequency-domain approximation achieved by the described method with existing design methods results, the frequency-domain absolute error e(ω,μ), the maximum absolute error emax, and the root mean square error erms are defined, like in (Zhao & Yu, 2006), by:
e(ω,μ)=|HFD(ω,μ)−Hid(ω,μ)|E39
emax=max{e(ω,μ)},0≤ω≤ωp,0≤μ≤1E40
erms=[∫0ωp∫01e2(ω,μ)dμdω]1/2E41
The maximum absolute magnitude error and the root mean square error obtained are shown in Table 1, reported in (Diaz-Carmona et al., 2010), as well as the results reported by some design methods.
Method
emax(dBs)
erms
(Tarczynski et al., 1997)
-100.0088
2.9107x10-6
(Wu-Sheng, & Tian-Bo, 1999)
-100.7215
2.7706x10-6
(Tian-Bo, 2001)
-99.9208
4.931x10-4
(Zhao & Yu, 2006)
-99.3669
2.8119x10-6
(Vesma et al., 1998)
-93.69
4.81x10-4
(Diaz-Carmona et al., 2010)
-86.17
2.78x10-4
Table 1.
Magnitude frequency response error comparison.
Example 2:
The FDF is designed using the explained minimax optimization approach applied on the single-sampling-frequency structure, Fig. 16, according to (Ramirez et al., 2010a). The FDF specifications are: ωp = 0.9π, δm = 0.01 and δp =0.001, the same ones as in the design example of (Yli-Kaakinen & Saramaki, 2006a). The given criterion is met with NFD = 7 and M = 4 and a half-band filter length of 55. The overall structure requires Prod = 32 multipliers, Add = 47 adders, resulting in a Δm = 0.0094448 and Δp = 0.00096649. The magnitude and phase delay responses obtained for μl = 0 to 0.5 with 0.1 delay increment are depicted in Fig. 21. The results obtained, and compared with those reported by other design methods, are shown in Table 2. The design described requires less multipliers and adders than (Vesma & Saramaki, 1997), (Johansson & Lowenborg, 2003), the same number of multipliers and nine less adders than (Yli-Kaakinen & Saramaki, 2006a), one more multiplier and three less adders than (Yli-Kaakinen & Saramaki, 2006b), and two more multipliers than (Yli-Kaakinen, & Saramaki, 2007).
Method
Arithmetic complexity
NFD
M
Prod
Add
Δm
Δp
(Vesma & Saramaki, 1997)
26
4
69
91
0.006571
0.0006571
(Johansson, & Lowenborg, 2003)
28
5
57
72
0.005608
0.0005608
(Yli-Kaakinen & Saramaki, 2006a)
28
4
32
56
0.009069
0.0009069
(Yli-Kaakinen & Saramaki, 2006b)
28
4
31
50
0.009742
0.0009742
(Yli-Kaakinen & Saramaki, 2007)
28
4
30
-
0.009501
0.0009501
(Ramirez-Conejo et al.,2010)
7
4
32
47
0.0094448
0.0009664
Table 2.
Arithmetic complexity results for example 2.- Not reported
Figure 21.
FDF frequency responses, using minimax optimization approach in example 2.
Figure 22.
FDF frequency response errors, using minimax optimization approach in example 2.
Example 3:
This example shows that the same minimax optimization approach can be extended for approximating a global complex error. For this purpose, the filter design example described in (Johansson & Lowenborg 2003) is used, which specifications are ωp = 0.9π, and maximum global complex error of δc = 0.0042. Such specifications are met with NFD = 7 and M = 4 and a half-band filter length of 69. The overall structure requires Prod = 35 multipliers with a resulting maximum complex error Δc = 0.0036195. The results obtained are compared in Table 3 with the reported ones in existing methods. The described method requires less multipliers than (Johansson & Lowenborg 2003), (Hermanowicz, 2004) and case A of (Hermanowicz & Johansson, 2005). Reported multipliers of (Johansson & Hermanowicz, 2006) and case B of (Hermanowicz & Johansson, 2005) are less than the obtained with the presented design method. It should be pointed out that in (Johansson & Hermanowicz, 2006) an IIR half-band filter is used and in case B of (Hermanowicz & Johansson, 2005) and (Johansson & Hermanowicz, 2006) a switching technique between two multirate structures must be implemented. The resulted complex error magnitude is shown in Fig. 23 for fractional delay values from D =17.5 to 18.0 with 0.1 increment, magnitude response of the designed FDF is shown in Fig. 24 and errors of magnitude and phase frequency responses are presented in Fig 25.
Method
Arithmetic complexity
NFD
M
Prod
(Johansson & Lowenborg 2003)
39
6
73
(Johansson & Lowenborg 2003)a
31
5
50
(Hermanowicz, 2004)
11
6
60(54)
(Hermanowicz & Johansson, 2005)
7
5
36
(Hermanowicz & Johansson, 2005)b
7
3
26
(Johansson & Hermanowicz, 2006)
-
6
32
(Johansson & Hermanowicz, 2006)b
-
3
22
(Ramirez-Conejo et al., 2010)
7
4
35
Table 3.
Arithmetic complexity results for example 3.a. Minimax design with subfilters jointly optimized.
Figure 23.
FDF frequency complex error, using minimax optimization approach in example 3.
Figure 24.
FDF frequency response using minimax optimization approach in example 3.
Figure 25.
FDF frequency response errors using minimax optimization approach in example 3.
6. Conclusion
The concept of fractional delay filter is introduced, as well as a general description of most of the existing design methods for FIR fractional delay filters is presented. Accordingly to the explained concepts and to the results of recently reported design methods, one of the most challenging approaches for designing fractional delay filters is the use of frequency-domain optimization methods. The use of MATLAB as a design and simulation platform is a very useful tool to achieve a fractional delay filter that meets best the required frequency specifications dictated by a particular application.
Acknowledgments
Authors would like to thank to the Technological Institute of Celaya at Guanajuato State, Mexico for the facilities in the project development, and CONACYT for the support.
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Introduction ",level:"1"},{id:"sec_2",title:"2. Fractional delay filter definition",level:"1"},{id:"sec_3",title:"3. FDF Design methods",level:"1"},{id:"sec_3_2",title:"3.1. Magnitude frequency response approximation",level:"2"},{id:"sec_4_2",title:"3.2. Interpolation design approach",level:"2"},{id:"sec_5_2",title:"3.3. Hybrid analogue-digital model approach",level:"2"},{id:"sec_7",title:"4. FDF Implementation structures",level:"1"},{id:"sec_7_2",title:"4.1. Modified Farrow structure",level:"2"},{id:"sec_8_2",title:"4.2. Multirate Farrow structure",level:"2"},{id:"sec_10",title:"5. FDF Design examples",level:"1"},{id:"sec_11",title:"6. Conclusion",level:"1"},{id:"sec_12",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Diaz-CarmonaJ.Jovanovic-DolecekG.Ramirez-AgundisA.2010Frequency-based optimization design for fractional delay FIR filters. 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Springer Circuits, syst., Signal Processing,\n\t\t\t\t\t25April 2006), 265294'},{id:"B29",body:'Yli-KaakinenJ.SaramakiT.2006bAn efficient structure for FIR filters with an adjustable fractional delay, Proceedings of Digital Signal Processing Applications, 617623Moscow, Russia, March 29-31, 2006.'},{id:"B30",body:'Yli-KaakinenJ.SaramakiT.2007A simplified structure for FIR filters with an adjustable fractional delay, Proceedings of IEEE Int. Symp. Circuits and Systems, 34393442New Orleans, USA, May 27-30, 2007.'},{id:"B31",body:'ZhaoH.YuJ.2006A simple and efficient design of variable fractional delay FIR filters. IEEE Trans. On Circuits and Systems-II: Express Brief,\n\t\t\t\t\t53February 2006), 157160'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Javier Diaz-Carmona",address:"",affiliation:'
Institute ITC Celaya, Institute INAOE Puebla,, Mexico
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Oriols",authors:[{id:"22644",title:"Dr.",name:"Guillermo",middleName:null,surname:"Albareda",fullName:"Guillermo Albareda",slug:"guillermo-albareda"},{id:"22645",title:"Dr.",name:"Fabio",middleName:null,surname:"Traversa",fullName:"Fabio Traversa",slug:"fabio-traversa"},{id:"22646",title:"Dr.",name:"Abdelilah",middleName:null,surname:"Benali",fullName:"Abdelilah Benali",slug:"abdelilah-benali"},{id:"22647",title:"Dr.",name:"Xavier",middleName:null,surname:"Oriols",fullName:"Xavier Oriols",slug:"xavier-oriols"}]},{id:"14013",title:"Monte-Carlo Simulation in Electron Microscopy and Spectroscopy",slug:"monte-carlo-simulation-in-electron-microscopy-and-spectroscopy",signatures:"Vladimír Stary",authors:[{id:"23253",title:"Prof.",name:"Vladimir",middleName:null,surname:"Stary",fullName:"Vladimir Stary",slug:"vladimir-stary"}]},{id:"14014",title:"Monte Carlo Simulation of SEM and SAM Images",slug:"monte-carlo-simulation-of-sem-and-sam-images",signatures:"Y.G. Li, S.F. Mao and Z.J. 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Trohidou and M. Vasilakaki",authors:[{id:"21966",title:"Dr.",name:"Kalliopi",middleName:null,surname:"Trohidou",fullName:"Kalliopi Trohidou",slug:"kalliopi-trohidou"},{id:"22714",title:"Dr.",name:"Marianna",middleName:null,surname:"Vasilakaki",fullName:"Marianna Vasilakaki",slug:"marianna-vasilakaki"}]},{id:"14024",title:"Monte Carlo Simulation for Magnetic Domain Structure and Hysteresis Properties",slug:"monte-carlo-simulation-for-magnetic-domain-structure-and-hysteresis-properties",signatures:"Katsuhiko Yamaguchi, Kenji Suzuki and Osamu Nittono",authors:[{id:"22402",title:"Dr.",name:"Katsuhiko",middleName:null,surname:"Yamaguchi",fullName:"Katsuhiko Yamaguchi",slug:"katsuhiko-yamaguchi"},{id:"22659",title:"Prof.",name:"Kenji",middleName:null,surname:"Suzuki",fullName:"Kenji Suzuki",slug:"kenji-suzuki"},{id:"22660",title:"Prof.",name:"Osamu",middleName:null,surname:"Nittono",fullName:"Osamu Nittono",slug:"osamu-nittono"}]},{id:"14025",title:"Monte Carlo Simulations of Grain Growth in Polycrystalline Materials Using Potts Model",slug:"monte-carlo-simulations-of-grain-growth-in-polycrystalline-materials-using-potts-model",signatures:"Miroslav Morháč and Eva Morháčova",authors:[{id:"22290",title:"Dr.",name:"Miroslav",middleName:null,surname:"Morhac",fullName:"Miroslav Morhac",slug:"miroslav-morhac"},{id:"22408",title:"Dr.",name:"Eva",middleName:null,surname:"Morhacova",fullName:"Eva Morhacova",slug:"eva-morhacova"}]},{id:"14026",title:"Monte Carlo Simulations of Grain Growth in Metals",slug:"monte-carlo-simulations-of-grain-growth-in-metals",signatures:"Sven K. Esche",authors:[{id:"19228",title:"Prof.",name:"Sven K.",middleName:null,surname:"Esche",fullName:"Sven K. Esche",slug:"sven-k.-esche"}]},{id:"14027",title:"Monte Carlo Simulations on Defects in Hard-Sphere Crystals Under Gravity",slug:"monte-carlo-simulations-on-defects-in-hard-sphere-crystals-under-gravity",signatures:"Atsushi Mori",authors:[{id:"20749",title:"Dr.",name:"Atsushi",middleName:null,surname:"Mori",fullName:"Atsushi Mori",slug:"atsushi-mori"}]},{id:"14028",title:"Atomistic Monte Carlo Simulations in Steelmaking: High Temperature Carburization and Decarburization of Molten Steel",slug:"atomistic-monte-carlo-simulations-in-steelmaking-high-temperature-carburization-and-decarburization-",signatures:"R. Khanna, R. Mahjoub and V. Sahajwalla",authors:[{id:"19010",title:"Associate Prof.",name:"Rita",middleName:null,surname:"Khanna",fullName:"Rita Khanna",slug:"rita-khanna"}]},{id:"14029",title:"GCMC Simulations of Gas Adsorption in Carbon Pore Structures",slug:"gcmc-simulations-of-gas-adsorption-in-carbon-pore-structures",signatures:"Maria Konstantakou, Anastasios Gotzias, Michael Kainourgiakis, Athanasios K. Stubos and Theodore A. Steriotis",authors:[{id:"22788",title:"Dr.",name:"Theodore A.",middleName:null,surname:"Steriotis",fullName:"Theodore A. Steriotis",slug:"theodore-a.-steriotis"},{id:"22800",title:"Dr.",name:"Maria",middleName:null,surname:"Konstantakou",fullName:"Maria Konstantakou",slug:"maria-konstantakou"},{id:"22801",title:"Mr.",name:"Anastasios",middleName:null,surname:"Gotzias",fullName:"Anastasios Gotzias",slug:"anastasios-gotzias"},{id:"22802",title:"Dr.",name:"Michael",middleName:null,surname:"Kainourgiakis",fullName:"Michael Kainourgiakis",slug:"michael-kainourgiakis"},{id:"22803",title:"Dr.",name:"Athanasios",middleName:null,surname:"Stubos",fullName:"Athanasios Stubos",slug:"athanasios-stubos"}]},{id:"14030",title:"Effect of the Repulsive Interactions on the Nucleation and Island Growth: Kinetic Monte Carlo Simulations",slug:"effect-of-the-repulsive-interactions-on-the-nucleation-and-island-growth-kinetic-monte-carlo-simulat",signatures:"Hu Juanmei and Wu Fengmin",authors:[{id:"19969",title:"Dr.",name:"Fengmin",middleName:null,surname:"Wu",fullName:"Fengmin Wu",slug:"fengmin-wu"},{id:"33150",title:"Prof.",name:"Juanmei",middleName:null,surname:"Hu",fullName:"Juanmei Hu",slug:"juanmei-hu"}]},{id:"14031",title:"Monte Carlo Methodology for Grand Canonical Simulations of Vacancies at Crystalline Defects",slug:"monte-carlo-methodology-for-grand-canonical-simulations-of-vacancies-at-crystalline-defects",signatures:"Döme Tanguy",authors:[{id:"22170",title:"Dr.",name:"Döme",middleName:null,surname:"Tanguy",fullName:"Döme Tanguy",slug:"dome-tanguy"}]},{id:"14032",title:"Frequency-Dependent Monte Carlo Simulations of Phonon Transport in Nanostructures",slug:"frequency-dependent-monte-carlo-simulations-of-phonon-transport-in-nanostructures",signatures:"Qing Hao and Gang Chen",authors:[{id:"20961",title:"Prof.",name:"Gang",middleName:null,surname:"Chen",fullName:"Gang Chen",slug:"gang-chen"},{id:"20962",title:"Dr.",name:"Qing",middleName:null,surname:"Hao",fullName:"Qing Hao",slug:"qing-hao"}]},{id:"14033",title:"Performance Analysis of Adaptive GPS Signal Detection in Urban Interference Environment using the Monte Carlo Approach",slug:"performance-analysis-of-adaptive-gps-signal-detection-in-urban-interference-environment-using-the-mo",signatures:"V. Behar, Ch. Kabakchiev, I. Garvanov and H. Rohling",authors:[{id:"2768",title:"Dr.",name:"Christo",middleName:null,surname:"Kabakchiev",fullName:"Christo Kabakchiev",slug:"christo-kabakchiev"},{id:"18669",title:"Dr.",name:"Vera",middleName:null,surname:"Behar",fullName:"Vera Behar",slug:"vera-behar"},{id:"18671",title:"Dr.",name:"Ivan",middleName:null,surname:"Garvanov",fullName:"Ivan Garvanov",slug:"ivan-garvanov"},{id:"18672",title:"Prof.",name:"Hermann",middleName:null,surname:"Rohling",fullName:"Hermann Rohling",slug:"hermann-rohling"}]},{id:"14034",title:"Practical Monte Carlo Based Reliability Analysis and Design Methods for Geotechnical Problems",slug:"practical-monte-carlo-based-reliability-analysis-and-design-methods-for-geotechnical-problems",signatures:"Jianye Ching",authors:[{id:"19783",title:"Prof.",name:"Jianye",middleName:null,surname:"Ching",fullName:"Jianye Ching",slug:"jianye-ching"}]},{id:"14035",title:"A Monte Carlo Framework to Simulate Multicomponent Droplet Growth by Stochastic Coalescence",slug:"a-monte-carlo-framework-to-simulate-multicomponent-droplet-growth-by-stochastic-coalescence",signatures:"Lester Alfonso, Graciela Raga and Darrel Baumgardner",authors:[{id:"18046",title:"Prof.",name:"Lester",middleName:null,surname:"Alfonso",fullName:"Lester Alfonso",slug:"lester-alfonso"},{id:"22501",title:"Dr.",name:"Graciela",middleName:null,surname:"Raga",fullName:"Graciela Raga",slug:"graciela-raga"},{id:"22502",title:"Dr.",name:"Darrel",middleName:null,surname:"Baumgardner",fullName:"Darrel Baumgardner",slug:"darrel-baumgardner"}]},{id:"14036",title:"Monte Carlo Simulation of Room Temperature Ballistic Nanodevices",slug:"monte-carlo-simulation-of-room-temperature-ballistic-nanodevices",signatures:"Ignacio Íñiguez-de-la-Torre, Tomás González, Helena Rodilla, Beatriz G. Vasallo and Javier Mateos",authors:[{id:"22253",title:"Dr.",name:"Tomas",middleName:null,surname:"Gonzalez",fullName:"Tomas Gonzalez",slug:"tomas-gonzalez"},{id:"22450",title:"Dr.",name:"Javier",middleName:null,surname:"Mateos",fullName:"Javier Mateos",slug:"javier-mateos"},{id:"22451",title:"Dr.",name:"Ignacio",middleName:null,surname:"Iñiguez-de-la-Torre",fullName:"Ignacio Iñiguez-de-la-Torre",slug:"ignacio-iniguez-de-la-torre"},{id:"22452",title:"Prof.",name:"Helena",middleName:null,surname:"Rodilla",fullName:"Helena Rodilla",slug:"helena-rodilla"},{id:"22453",title:"Dr.",name:"Beatriz",middleName:null,surname:"Garcia Vasallo",fullName:"Beatriz Garcia Vasallo",slug:"beatriz-garcia-vasallo"}]},{id:"14037",title:"Estimation of Optical Properties in Postharvest and Processing Technology",slug:"estimation-of-optical-properties-in-postharvest-and-processing-technology",signatures:"László Baranyai",authors:[{id:"19663",title:"Dr.",name:"Laszlo",middleName:null,surname:"Baranyai",fullName:"Laszlo Baranyai",slug:"laszlo-baranyai"}]},{id:"14038",title:"MATLAB Programming of Polymerization Processes using Monte Carlo Techniques",slug:"matlab-programming-of-polymerization-processes-using-monte-carlo-techniques",signatures:"Mamdouh A. Al-Harthi",authors:[{id:"22395",title:"Prof.",name:"Mamdouh A.",middleName:null,surname:"Al-Harthi",fullName:"Mamdouh A. Al-Harthi",slug:"mamdouh-a.-al-harthi"}]},{id:"14039",title:"Monte Carlo Simulations in Solar Radio Astronomy",slug:"monte-carlo-simulations-in-solar-radio-astronomy",signatures:"G. Thejappa and R. J. MacDowall",authors:[{id:"21608",title:"Dr.",name:"Thejappa",middleName:null,surname:"Golla",fullName:"Thejappa Golla",slug:"thejappa-golla"}]},{id:"14040",title:"Using Monte Carlo Simulation for Prediction of Tool Life",slug:"using-monte-carlo-simulation-for-prediction-of-tool-life",signatures:"Sayyad Zahid Qamar, Anwar Khalil Sheikh, Tasneem Pervez and Abul Fazal M. Arif",authors:[{id:"21687",title:"Dr.",name:"Sayyad Zahid",middleName:null,surname:"Qamar",fullName:"Sayyad Zahid Qamar",slug:"sayyad-zahid-qamar"},{id:"21688",title:"Prof.",name:"Anwar Khalil",middleName:null,surname:"Sheikh",fullName:"Anwar Khalil Sheikh",slug:"anwar-khalil-sheikh"},{id:"21689",title:"Prof.",name:"Abul Fazal M.",middleName:null,surname:"Arif",fullName:"Abul Fazal M. Arif",slug:"abul-fazal-m.-arif"},{id:"21690",title:"Prof.",name:"Tasneem",middleName:null,surname:"Pervez",fullName:"Tasneem Pervez",slug:"tasneem-pervez"}]},{id:"14041",title:"Loss of Load Expectation Assessment in Electricity Markets using Monte Carlo Simulation and Neuro-Fuzzy Systems",slug:"loss-of-load-expectation-assessment-in-electricity-markets-using-monte-carlo-simulation-and-neuro-fu",signatures:"H. Haroonabadi",authors:[{id:"20037",title:"Dr.",name:"Hossein",middleName:null,surname:"Haroonabadi",fullName:"Hossein Haroonabadi",slug:"hossein-haroonabadi"}]},{id:"14042",title:"Automating First- and Second-order Monte Carlo Simulations for Markov Models in TreeAge Pro",slug:"automating-first-and-second-order-monte-carlo-simulations-for-markov-models-in-treeage-pro",signatures:"Benjamin P. Geisler",authors:[{id:"19631",title:"Dr.",name:"Benjamin",middleName:"Peter",surname:"Geisler",fullName:"Benjamin Geisler",slug:"benjamin-geisler"}]},{id:"14043",title:"Monte Carlo Simulations of Adsorbed Molecules on Ionic Surfaces",slug:"monte-carlo-simulations-of-adsorbed-molecules-on-ionic-surfaces",signatures:"Abdulwahab Khalil Sallabi",authors:[{id:"22986",title:"Prof.",name:"A",middleName:null,surname:"Slabi",fullName:"A Slabi",slug:"a-slabi"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"75303",title:"Households’ Adaptation to Climate Change Hazards in Semi-Arid Region of Mopani, South Africa",doi:"10.5772/intechopen.94759",slug:"households-adaptation-to-climate-change-hazards-in-semi-arid-region-of-mopani-south-africa",body:'
1. Introduction
Adaptation to climate change hazard is attracting growing international attention as confidence in forecasts for climate change is rising [1]. Developing countries have unique adaptation needs because of high vulnerabilities and the tendencies to bear a significant share of global climate change costs [2]. The Intergovernmental Panel on Climate Change\'s (IPCC) Fourth Assessment Report noted that public recognition and concern about the global environmental issue of human-induced climate change has reached unprecedented heights. Research into the drivers, both natural and anthropogenic, the character and magnitude, their impact on human living conditions and ecosystems, and possible approaches to adaptation and mitigation, as well-as understanding of the complex relationships with ecosystems interacting with them, has also increased in recent years [3].
While anthropogenic greenhouse gas emissions, which aggravates climate change are mainly from rich industrialized countries, the consequences of which are projected to be relatively acute and more serious in developing countries particularly in semi-arid region of Africa, where, for instance, rise in temperature and reduction in precipitation are likely to result in high evaporation, with serious health related consequences [4, 5]. South Africa like many developing countries’ national economies and employment heavily rely on climate-fed activities [6], coupled with high poverty levels, limited technological and weak institutional ability to adapt to climate change qualifies for classical case in which urban populations (children, elderly, persons with disabilities and women) are more susceptible to climate change adversities [7].
Nonetheless, climate change adaptation strategies and projects on one hand, still focus mainly on sustainable rural adaptation, without much attention on urban areas, especially small and medium towns, where there is increasing household vulnerability and climate change pressures [8]. Current literature on adaptation to climate change in urban areas are largely coastal and big city biased [9, 10, 11]. On the other hand the early years of international climate change studies’ attention on adaptation as a strategy was compromised by mitigation and impacts [12]. In recent years, several models incorporate mitigation, as an anthropogenic intervention to the changing climate [3] and has rapidly escalated, while models that incorporate adaptation are still in their various stages of development, advancement and yet to reach maturity [13].
Inherently, it has become urgent to focus on approaches and instruments that assist with the reduction and reversal of the prevailing and unescapable climate change hazards, coupled with the need to maximize the immediate manifestation of the net benefits of adaptation [14]. As an essential policy response, local level and individual (including private) households’ adaptation strategies to climate change needs to be apportioned the desired priority in climate change policy agendas at all levels and scales of governance.
This chapter aims through a holistic approach, to provide the highlights of the South African governments at several levels and scales of governance to advance adaption and mitigation urban household practices and interventions. This analysis and discussion is conducted within the global context of existing adaptation framework that incorporate the local level and individual households’ (private) adaptive practices, efforts and initiatives. Furthermore, the chapter also identifies some of the key issues hindering the success of urban adaptation policies and interventions in the region.
In brief, the chapter places in perspective, the basic steps necessary for a more participatory urban management for sustainable households’ adaptation to climate-related hazards in the semi-arid region of Mopani, South Africa.
2. Literature review
2.1 Adaptation, a fundamental component of climate change vulnerability
The new climate is no longer a doubtful global reality, but a phenomenon that we need to learn to live with for years to come [11]. Its disposition to leaving no facet of human endeavor immune from its negative externalities are unpredictable and presents very worrisome realities for the contemporary society and urban communities [15] largely manifesting beyond alterations in temperature and precipitation threatening the existence of humanity, particularly in Africa, and other developing countries [3, 16].
Adaptive ability to climate change hazard is considered a new field of endeavor, serving as a converging point for several experts, ranging from development experts, climate scientists, planners, disaster managers, and a host of other experts and disciplines/fields [17]. This has brought about divergent conceptual models to the study of vulnerability and adaptation, though addressing similar issues and emphasizing similar processes, but rather with different vocabularies [18]. The growth in the body of literature on the conceptual issue has brought about a confusing set of terminologies with unclear relationship [16, 19, 20]. However, notwithstanding the differences, the recognitions and understanding of the need to curtail the adversities of the phenomenon is the most crucial.
The frustrations from the present context of failure to successfully mitigate greenhouse gas emissions and curtail its associate developmental issues has resulted in adaptation becoming not only an inevitable strategy to frustrate vulnerability but also an integral social components for vulnerability assessment [16, 21]. However, this course of action is still in the trial periods of being considered relevant, particularly within science and policy contexts [22, 23].
Adaptation to climate change, is the “adjustment in natural or human systems in response to actual or expected climatic stimuli or their effects, which moderates harm or exploits beneficial opportunities” [24] as cited in [25]. It can take various dimensions from being reactive or anticipatory, private or public, and autonomous or planned [24], it can equally either be active or passive [26], spontaneous or prompted by alteration in conditions [27]. It is however a phenomenon that its success is hinges on the adoption of several co-and interdependent factors, including but not limited to human, technological y and policy matters.
However, many regions of the world, particularly Africa currently have limited access to these technologies, appropriate information and financial resources [28]. The cost-effective use of adaptation strategies will therefore depend upon the availability of financial resources, technology transfer, and cultural, educational, managerial, institutional, legal and regulatory practices, both applicable domestically and internationally [29, 30]. Hence “the need to consider indigenous knowledge system-based support and intervention”, for effective climate change adaptation strategies as one of the under-studied and utilized adaptation and mitigation strategy especially in Africa and developing countries in general [31].
In this chapter we further argue that like all other cultures, in Mopani District people are essentially adaptive, while exposed to environmental variability and risky circumstances in the past. These events called to question the local people’s adaptive capacity in respect to environmental variability and risk within the resources and technologies available options to them [32]. Therefore, to efficiently and adequately confront the prevailing and the potential climate change hazards, indigenous knowledge (IK) must be embraced, but be enhanced particularly beyond peoples’ experienced coping option ranges [33, 34]. The development and adoption of IK notion has necessitated the paradigm shift from organic adaptation approach to scientific adaptation framework models that attempt to respond to gaps ranging from adaptation needs determination, to adaptation assessment and interventions. The ensuing section of this chapter attempts at the identification of some existing adaptation models from a historical lens perspective, to typologies of these models and gaps that characterized them as well-as offering suggestions for improvements.
2.2 Climate change adaptation models
Adaptation modeling field is wide, varied and is punctuated with largely unclear disciplinary/field boundaries [35]. The definition of what are its constituents is equally open to numerous interpretations, with tagging of several models as adaptation models added another confusing layer to the identity and boundaries controversies [36]. In several contexts of science, models are considered very essential and key in different fields, disciplines and specialties. For instance, Evolutionary models are very important in the biological sciences disciplines while the agent-based models are a dominant feature in the social sciences [37]. Models are painstakingly built, tested, compared and revised in light of practice and feed-back loop for future lessons [36].
On a general note a classification of models on climate change adaptation was further made in line with the existing ones by [36] who identified two distinct typologies or categories of adaptation models, these include:
Adaptation Centered Models (ACMs); and
Impact Centered Models (ICMs);
Over time, advancement in understanding the consequences of climate change and policy interpretations and the associated challenges has occasioned a shift in global priority in climate change policy [37, 38, 39, 40]. At the onset, an undeviating cause–effect style prevailed, then climate situations forms the foundation upon which future climate impacts is estimated, which then outlines the needs for adaptation. With this linear concept, on one hand, adaptation to climate change is divorced from social activities and processes where needs are informed by scientific manipulations [41, 42] on one hand. On the other hand, a more comprehensive approach where the risk assessment is guided by management of past climatic hazards experience, and adaptation recommendation are determined by the option’s probability to reduce the prevailing and future climate risks while synergizing with other policy objectives, and existing management activity [43]. The later concept is currently in vogue and has enjoyed patronage from researchers, academics and policy makers, informed by its openness and comprehensiveness. Upon the determination and assessment of the needs, the choice of the form of adaptation will be made from the following identified three adaptation options:
No-regrets adaptation options;
Proactive anticipatory adaptation; and
Win-win adaptation
These options are not new, but the policies in various forms of decision models about them in Mopani District like other municipalities is currently characterized by limited attention and priorities [44]. Thus, making the success of the municipal adaptation efforts to appear unsuccessful.
However, a probe into the available literature and survey analysis with respect to climate change adaptation and the various adopted models in the study area, revealed some essential issues. These are policy related issues; Climate change issue; and adaptation issues. These issues form the fundamentals upon which the following identified gaps are considered critical in the existing models. These include:
With respect to climate change adaptation and the various adopted models, survey revealed some essential issues related to policy; Climate change issue; and adaptation issues. These issues form the fundamentals upon which the following identified gaps are considered critical in the existing models. These include:
2.2.1.1 Gaps in relations to the current climate change adaptation models
Our findings revealed that many models on climate change adaptation, apart from being highly mathematical in nature, are based on methodological ideas that originate from the advanced economies [45], limiting their applicability in local African communities’ context. This is because the assumptions upon which the models are largely based are alien to the prevailing realities in the region particularly in Semi-arid region of Mopani District in South Africa. In addition, several of these models are largely rural biased [46], or centered on metropolitan, big and coastal cities [47]. Similarly, some are rather infrastructure or sector-specific adaptation framework such as water, transport agriculture and energy sectors [48, 49, 50, 51, 52], while rather than local community based adaptation models, other models have focused on macro level postulations [53]. Hence the need for a flexible household-based conceptual framework model that is participatory and applicable at all levels of policy and decision making.
2.2.1.2 Gaps related to policies
Several studies have advocated for household-based climate change adaptation strategy to be anchored by municipal planning agency [54, 55, 56]. The study acknowledges that most local municipalities in the district are still relying on macro level climate change adaptation formulated policies from the national government. Despite that the impacts of climate change on both human and environment are well acknowledged in the various municipalities’ planning instruments (Integrated Development Plans, Spatial Development Framework etc.), yet, little evidence exist to indicate the efforts to pragmatically and coherently address the challenges [44].
2.2.1.3 Gaps related to reporting climate change events
During data collection, our interactions with the community members, revealed that municipal governments were rather relying on reactive adaptation procedure rather than proactive. The delay in reporting of incidence of hazards have resulted in more costly, more devastating and sometimes unrepairable situations. Due to the devastating consequences often occasioned by late reporting of climate change emergencies, the climate change adaptation challenges are complex, dynamic and contextual, thereby requiring urgent attention by stakeholders.
For adaptation to be beneficial and cost effective, it should not be solely reactionary but rather proactive and anticipatory [57]. Changing climate is no longer in doubt so also is the likelihood of the trend to proceed to the coming century at an unprecedented rate in history, as projected [20, 58] with strong signals to a rising hazards for regions of such countries that are already water-stressed, like Mopani District, Limpopo province [5, 59] and other semi-arid regions of Africa are also projected.
Hence for effective communities adaptation, government at all levels have pivotal roles to play, particularly within the global context of adaptation framework as guided by the current regime. On this basis the chapter highlights the various steps taken by the South African governments (National, Provincial, District and Local Municipalities) with regard to adaptation needs of the citizens, through policies, program and projects interventions.
2.3 Efforts of South African governments within the global context of adaptation framework
In order to understand the roles of the various levels of government in South Africa in combatting the menace occasioned by climate change across the country, activities of government (National, Provincial, District as well-as local municipalities) regarding climate change adaptation were reviewed. This was assessed through the policies, strategies and legislations (Acts), and it was equally further done within the global context. The Republic of South Africa, being a signatory to Kyoto Protocol and a part of the United Nations Framework Convention on Climate Change (UNFCCC), has taken several initiatives (past and present) in striving to fulfil the expected obligations as regards the protection of citizens and the regional territory against the aggressiveness of climate change and its associated adversities. Some of these efforts as regards adaptation are highlighted in different eras in this section, and these include the following:
2.3.1 Apartheid era
The legal framework for managing disaster in South Africa preceding democratic rule, were largely administered by the Civil Protection Act No. 67 of 1977 [60]. The National Disaster Management Framework (NDMF) was initiated but was characterized by inadequacies following over a hundred lives lost to Lainsburg floods in the year 1981 alone [61]. In reaction to this incidence, out of various legislative and structural reforms that were put together to overhaul the system for proper integration of disaster management was the South Africa Constitution of 1996.
2.3.2 Post-apartheid era
The South Africa Constitution of 1996 marked the beginning of a prominent legislative and structural reforms of disaster management, by specifying the roles of the government at all levels in Part A Schedule 4 [62]. This necessitated the extension of the Civil Protection Act, the pioneer integrated policy on the management of disaster, called “the Green Paper on Disaster Management” [63].
The same era has witnessed active participation in various fora and conventions with respect to dealing with the challenges and opportunities that climate change presents since 1994. Commitment have been shown by the country to sustainable development with both active international participation and institutionalizing national frameworks. The frameworks include out of others: the Kyoto Protocol, the United Nations Framework Convention on Climate Change, the Cancun Agreement, the Convention on International Trade in Endangered Species of Wild Fauna and Flora, the Ramsah Convention on Wetlands of International Importance, the Basel Convention on the Control of Transboundary Movement of Hazardous Wastes and Their Disposal, and the Montreal Protocol for the Protection of the Ozone Layer [64] cit. in [65]. This suggests an involving participation of the country on climate change issues at the global realm.
Similarly, South Africa has at various times successfully instituted some climate change related legal frameworks that are either sector-prone (e.g. waste management, carbon tax, transport, energy efficiency, renewable energy and several others). Other related planning instrument is the Integrated Development Planning (IDP), through which short and medium-terms development objectives, strategies and programs are prepared as strategic plans for municipalities. It is a key instrument for guiding and informing fiscal allocation (budget), administration and decision making for service delivery and development within municipal’s jurisdiction [66]. Subsequently, White Paper on Disaster Management was produced, emphasizing proactive and integrated approach in the management of disaster through public (stakeholders) participation and capacity building [67]. Targeting the creation of National Disaster Management Centre, enhance disaster prevention among the poor and disadvantaged zones, ensure adequate funding system and facilitate access to information (South African Government Gazette).
In 2002 Disaster Management Act 57 of 2002 was institutionalized, highlighting the guiding philosophies for disaster management and defined tasks [68]. The Act provides for the establishment of Intergovernmental Committee on Disaster Management, with powers to the Premier of the concerned Province and Local Government to select members. While at national level, the Minister of Cooperative Governance and Traditional Affairs is empowered to establish a National Disaster Management Advisory Forum with several governmental and non-governmental organizational representatives, traditional institutions and various professional, Sec 5. (1). Section 8. (1) Establishes a National Disaster Management Centre (NDMF) to form part of, at the same time functions within the control of the Minister under a state department of the public service. Provincial disaster management framework is instituted in Section 28. (1) of the Act not only to be established but also implement a disaster management framework aligned to the NDMF objectives and in consistent with the provisions of Act (No. 57,2002) and the NDMF, 33 (I). The local government is empowered under chapter 5 to appoint a disaster officer [62]. This gave birth to the establishment of Mopani District Disaster Management Centre at District Municipal level and the appointment of disaster manager in the five local municipalities in Mopani District as gathered during our field survey, they equally had plans for disaster management framework [69].
In 2011, the parliaments of South Africa adopted the National Climate Change Response Strategy (NCCRS). The policy document is generally anchored on some strategic priorities such as risk reduction and management; mitigation actions (with significant targeted outcomes); sectoral responses; policy and regulatory alignment.
The establishment of the National Climate Change Monitoring and Evaluation System came with the objectives of tracking South Africa’s transition to a climate resilient society, by following-up on the country’s transition to a lower carbon economy and by tracking climate finance. The benefits of the system include out of others, the provision of an evidence-based impacts and the vulnerabilities to climate change, and providing learning for the workability and otherwise of climate change response. This will inform the future responses to climate change as well-as facilitate the assessment of the impact and need for climate finance and institutionalizing national communication and biennial update reports. As promising as these objectives are, the M&E system has till now been struggling to find its rightful place, because of the disconnect between the municipalities and the grassroots where the data (for national communication and biennial reports) ought to be generated. Although the M&S system is substantially mitigation-focused not adaptation oriented, it still remains a viable too and mechanism for managing adaptation if well captured and harnessed.
The specific urban policy and planning that was institutionalized that “seek to influence the distributions and operations of investment and consumption processes in cities for the common good” [70] was the South African Integrated Urban Development Framework (IUDF) as approved in 2016 by Cabinet. Although attempt by various Government’s Departments have in different ways attempted to address the challenges of urban areas since 1994 with significant achievements in areas such as service extension, municipal reform, urban renewal and economic infrastructure development, these efforts are largely viewed as inadequate [71]. Not so much achievements have been recorded in the mainstreaming of climate change to urban planning. The municipalities in Mopani District are still relying on the National Urban Policy without plans (currently) to have theirs that embrace the economic, political, social and environmental peculiarities of their respective areas. However, the adoption of the Paris Agreement as well as the New Urban Agenda, signaled a renewed motivation for action, particularly to mainstreaming climate change in Urban Policy.
The Mopani District Municipality in line with the National Disaster Management Act 2005 acknowledges the current and the potential climate change threats to both human and the environment. It equally recognizes the need for actions to mitigate, as well as prepare for the projected changes (adaptation) in the District. Consequent upon this, the district municipality in 2016 developed Vulnerability Assessment and Climate Change Response Plan to prioritize the development of Climate Change Response strategies. The Plan recognizes several numbers of ways that climate change will impact on human settlements across the district and thus identifies related indicators, sub-projects and actions for inclusion in the service delivery and the plans for budget implementation [72]. Our field survey revealed that the identified projects are held for paucity of funds.
The frustrations from the failure of municipalities to guarantee the protection of households through the implementation of a pragmatic actions have prompted private adaptation initiatives across the selected towns in the district to curtail the impacts of climate change. The section of this chapter succeeding the description of the study area and methods, addresses the various initiatives of households towards coping with climate change in the selected towns.
3. Study area and methods
3.1 Description of the study area
Located in the semi-arid region, the northern-most province (Limpopo) of South Africa, Mopani District Municipality is a category C municipality (Figure 1).
Figure 1.
Mopani District municipality showing the five local Municipalities within the context of Limpopo Province and South Africa Context.
The district consist of five local Municipalities, including: Greater Giyani, (the district administrative seat), Maruleng, Greater Letaba, Ba-Phalaborwa and Greater Tzaneen. The municipality is situated on Longitudes: 29° 52´E to 31° 52´E and Latitudes: 23° 0´S to 24° 38´S, with 31° E as the central meridian. It covers 13,948.418 ha (10.2%) of the surface area of South Africa. It shares boundaries in the east with Mozambique, in the north, with Vhembe District Municipality through Thulamela & Makhado municipalities, while bordered in the south, by Mpumalanga province through Ehlanzeni District Municipality and, by Capricorn District Municipality to the west [72].
3.2 Climate of Mopani District
Being within the semi-arid region, the district is characterized by temperature that ranges from a high average of 21°C in the Mountainous areas with a very high average of 25°C in the dry low-veld areas of Kruger National Park. In the district Frost rarely occurs, while the monthly distribution of the average daily maximum temperatures indicates that the average midday temperatures for Mopani Rest Camp (Kruger) range from 23.7°C in June to 30°C in January. The region is the coldest during June when the mercury drops to 8°C on average during the night. The District falls within the Letaba Catchment area, which is 13 779 km2 and has a mean annual precipitation of 612mm (Environmental Management Framework for the Olifants and Letaba river catchment areas, Report, 2009).
Mopani Rest Camp (Kruger) receives about 520 mm of rain per year, with most proportion (85%) of precipitation in Mopani District is received in mid-summer, while with the lowest (3 mm) is received in June and the highest (96 mm) in January [72]. The rainfall varies from the mountainous zones in the Drakensberg Mountains (2000 mm/a) and the dry low-veld in the Kruger National Park (400 mm/a). The district is situated within the Letaba Catchments area which has a 612 mm Mean annual precipitation.
Climate is recognized by the municipality to be changing, altering and resulting to rising temperature and reduced and erratic rainfall across the district, which is a reflection of the regional climate [58, 75]. The new climate pattern according to the district Integrated Development Plan has caused reduction of access to potable water, food security threats and increase health effects to poverty stricken communities [72]. Part of the strategies identified in the planning instrument for the mitigation of the emission of global warming causing-gases include: utilizing every space for plants, using alternative forms of energy and strict control against deforestation.
3.3 Methods
Consequent upon climate change challenges, households in Mopani have consistently adopted several private and individual strategies to adapt with the varying climate change extreme events. In line with this, we examine the individual household coping strategies to climate change related extreme events and hazards in six purposively selected small and medium-sized towns (Tzaneen, Nkowankowa, Hoedspruit, Modjadjiskloof, Phalaborwa and Giyani) in Mopani District. Sample size of 500 were estimated and drawn using multistage random sampling method, with proportional share to each towns. Guided by the focus of this chapter, data collection methods emphasizes direct/personal interviews, questionnaire and visual inspection/ transect walk in order to ensure a high rate of response. Though the study adopts mixed method, open-ended questions were minimized, and well-ordered, where necessary. Review of existing literature was used to complement the current research findings. The investigated variables were isolated because of their being the direct location-specific effects occasioned by climate change. These variables are categorized into three, these include: those strategies related to increased temperature; reduced water level (rainfalls); and incidence of flood. These variables were cross tabulated against the selected towns of respondents and are discussed as follow.
4. Result and discussion
4.1 Households’ efforts towards adapting to climate change in the semi-arid region of Mopani District
Although efforts are on-going globally, regionally and nationally to reverse the trend in climate variability through research, treaties, collaborations, dialogues and other mechanisms, it is essential to appreciate that adaptation to the new climate change regime remains for now, the only realistic and sustainable option that is available [73, 74]. However, household’s private adaptation strategy is becoming an increasingly important component to the urban setting, since the end to the failure of Municipal governments to effectively deal with adaptation to climate change in urban center is indeterminate.
4.1.1 Households’ temperature coping strategies
Occurrence of heat waves as a result of rise in temperature is generally evident in the semi-arid region of South Africa [58] and particularly in Mopani District of Limpopo province [75]. According to [76], households’ and municipal responses to cope with high temperature or heat waves can be undertaken via tree planting and several other strategies. In line with this understanding, household’s individual rising temperature coping strategy in the selected towns in the district were identified. The strategies include tree planting, minimizing bush burning, preservation of water bodies, eco-friendly faming practice, Flower and Grass Planting, the use of Fan and Air conditioner and the creation of Parks and Gardens. Table 1, depicts the responses from households, on the preferred coping strategies for increasing temperature across the selected towns in Mopani, these are subsequently discussed.
Towns
Tree planting
Flower and grass planting
Create parks & garden
Minimize bush burning
preserve water bodies
Eco-friendly farming
Use of fans and air condition
Tzaneen
66.3
45.6
0.0
100.0
0.0
0.0
100.0
Nkowankowa
56.6
18.3
0.0
100.0
0.0
0.6
100.0
Hoedspruit
88.9
100.0
0.0
100.0
83.3
11.1
100.0
Modjadjiskloof
50.0
80.0
0.0
100.0
60.0
0.0
100.0
Phalaborwa
95.2
98.8
0.0
98.0
77.4
0.0
100.0
Giyani
100.0
51.5
0.0
100.0
2.3
0.0
100.0
Table 1.
Temperature coping strategies across Mopani District.
Source: Authors’ Field Data, 2019.
Tree planting is one of the popular coping strategies and was recommended for mitigating the impact of high temperature [77]. This assertion was validated in the selected towns, with the results obtained from our investigation where 63.3% of households in Tzaneen, and 56.6% in Nkowankowa were in agreement with tree planting strategy to cope with heat waves. Hoedspruit accounted for 88.9%, Modjadjiskloof 50% while in Phalaborwa and Giyani 95.2% and 100% of households employed the strategy respectively. The findings suggests wide range of acceptability of tree planting as temperature coping strategy. The general acceptability of the strategy across the towns was adduced to its affordability and effectiveness as a coping strategy for increasing temperature.
An examination of the relevance of reducing bush burning as a strategy for coping with temperature in the selected towns in Mopani District was undertaken and the results of the respondents’ answers to the strategy reveals that in Nkowankowa, Tzaneen, Hoedspruit and Modjadjiskloof, minimizing bush burning was considered by every household, as an appropriate strategy, while in Phalaborwa, 2% of the entire households surveyed declined the choice of the strategy. The employment of bush burning minimization to curtail the impact of heatwaves at municipal level will be an acceptable and effective strategy that will make meaningful impacts across the district.
With respect to the respondents adopting the conservation of water bodies in their communities, Table 1 shows that more than four in every five respondents in Phalaborwa, three in every five in Modjadjiskloof respectively endorsed the strategy to cope with temperature. However, the strategy only enjoyed the acceptability of only 2.3% respondents in Giyani. This strategy was equally unpopular in both Tzaneen and Nkowankowa. The reason for Hoedspruit, Phalaborwa and Modjadjiskloof in favor of this strategy was traced to the awareness of the benefits of the strategy among households, facilitated by NGOs and the respective municipalities. This result reflects that the municipalities of the two towns complied with the water conservation Act No. 36 [78].
In the narratives of current literature reviewed on the adoption of eco-friendly farming practices as temperature coping strategy, it shows that it is a promising strategy as reported by [79]. But the results of the acceptability test of the strategy in the selected towns show otherwise. For example, in Tzaneen, Modjadjiskloof, Phalaborwa and Giyani, no respondent indicated adopting it as a strategy. Only Hoedspruit accounted for 11.1%. The result reflects the economic activities of significant proportion of respondents from non-primary sources particularly agriculture. Thus, prescribing it as coping strategy for temperature in the district might not be very impactful to the majority of households.
However, According to [80] as cited in [81] Green infrastructure is very useful in contributing to mitigate the effects of hard surfacing by modifying ambient temperatures as well as creating recreational opportunities among other advantages. Our investigation revealed that every households in Hoedspruit town adopted the strategy, while 98.8%, 80% and 51.5% households in Phalaborwa, Modjadjisklooof and Giyani towns adopted the green infrastructure strategy respectively too. Flower and grass planting seems to be a widespread and suitable temperature coping strategy in the selected towns, except in Nkowankowa where only 18.3% of the household embraced the strategy.
The use of Fan and Air conditioner appeared to be a very satisfactory strategy that was favored by every households traversing the selected towns in Mopani. This was adduced to by the respondents that the former (fan) is affordable, accessible and environmentally friendly. However, while the latter (air conditioners) was enhanced by the stability of electricity, it does not only escalates the energy bills because of the increased loads resulting from cooling, but it equally exacerbates urban heat island in its own capacity. Thus [82] submit that for effective alleviation of urban warming and enhanced cooling, there is, as a necessity the need to reduce air-conditioning anthropogenic heat.
The responses obtained from the survey conducted on the creation of Neighbourhood Parks and Garden as a temperature coping strategy by the households across the selected towns is presented in Table 1. The result shows a consensus among the households that the siting and development of neighborhood parks and garden was the responsibility of the governments at different levels. This was reflected in households’ responses where no household indicated creating Parks and Garden as a personal temperature coping approach. However, children who desire to recreate use available spaces like access road around them to play soccer, not minding risks involved.
4.1.2 Households’ water scarcity coping strategies
With respect to water scarcity, the households were required to indicate the strategy they use during climate related drought or long heat waves that reduce the water quantity in their area. The variable used to capture the households’ responses include: rain water harvesting, water embankment, use of storage tanks, water treatment to improve quality and use of water vendor service. These results are presented in Figure 2.
Figure 2.
Coping strategies for change in water level across towns and Mopani. Source: Author’s Field Data, 2019.
An examination of household coping strategies regarding change in water level in the selected towns, as summarized in Figure 2, shows that rainwater harvesting as a strategy was not popular among the households. The results shows that 5.1% respondents in Tzaneen and 5% in Nkowankowa adopted water harvesting as a strategy, while in Phalaborwa and Giyani both accounted for 5% and 3.1% respectively. However, both Modjadjiskloof and Hoedsrpruit towns did not use such a strategy because according to them, it is time consuming and that the quality of harvested water was most times compromised.
However, Figure 2 shows the results of the examination of the use of storage tanks to cope with reducing water level. It was discovered that 100% and 81% of households in Hoedspruit and Phalaborwa respectively used the strategy to backup, to forestall the impacts of water shortages. In Tzaneen and Nkowankowa 54.4% and 51% of their respective household used same strategy. Similarly, in Modjadjiskloof and Giyani the households that used storage tanks were respectively 50% and 61.5%. On the average 61.1% of the respondents have used or still using storage tanks to adapt to reducing water level in their communities. The study implied that the storage of water in tanks is an acceptable strategy because water provision is not always at RDP level.
A significant indicator of health is water scarcity, which includes both its availability and quality [83]. Water use is beyond drinking, it is intimately linked to food security, sanitation and hygiene contributing to health burdens. Poor and vulnerable communities suffer the most from the adverse effects of climate change on water and health related issues and that the adaptation strategy which can effectively reduce the strain on water resources include wastewater recycling and reuse [84]. This was tested in the selected towns, and was found that when water became scarce, such as in 2016 and 2017 droughts periods in Limpopo province, most households turned to the re-use of water due to the scarcity of water for domestic and others uses. Our investigation further showed that 100% of the respondents re-use water as was advised by the Department of Water Affairs, when Limpopo Province, was declared a disaster province.
Water treatment was one of the variables we requested the households to give their response if they use such strategy. Although according to the science of water treatment which involved reverse osmosis etc, we were more interested in treatment such as water boiling, using aqua active bleaching agents such as hypochlorite to disinfect the water before use. The results in Figure 2 shows that 100% of the respondents use non-complicated methods to treat their water when it becomes very scarce and necessary.
The general practice particularly in the peri-urban areas of the selected towns is that most of them buy water from water vendors who sell water in containers ranging from R5 to R25 depending on the quantity sold. The study showed that not all respondent were disposed to buying water from vendors maybe because some could not be guaranteed the quality of the water. Patronage of water vendors was common among those households who did not have stand pipes in their yards. However, in Modjadjiskloof and Giyani 43% and 48% respectively used water vendor services to cope with water scarcity (Figure 2).
4.1.3 Household strategy for flood control in Mopani
As rightly noted [85] that with increasing havoc of floods in the urban center, and its negative impacts particularly on the poorest and the most susceptible, effective coping strategies require the combination of protective infrastructure, nature-based approaches, and risk financing (insurance) schemes to curtail floods and cushion their adversities. Flash floods has resulted into several degrees of damages in South Africa [65] as well-as some parts of the selected towns in Mopani District Municipality [75]. This occurred at different times, frequencies and intensities. This phenomenon has in the past resulted in households loosing properties ranging from home assets to farm crops and farm produce. The results of the survey showed that with respect to flood control strategies, the most popular include the construction of embankment to prevent over flow of rivers, the use of Furrow around their house, building of walls to protect houses during flash floods, growing of lawns, removal of solid waste from the storm water drainages, re-enforcement of dwellings with stones and concretes.
Our findings suggest that building embankment around houses is a popular strategy particularly among those residing close or whose offices are in close proximity to rivers, along erosion line, or terrain threatening sites. Embankments are usually constructed by the community or the local municipality. One aspect of the embankment as a strategy to cope with floods is that it fends off water and shelters settlements from flooding. About 58% of respondents was recorded in Modjadjiskloof and 32% in Phalaborwa, Hoedspruit was 23%, while Giyani and Nkowankowa both depicted 27% and 36% accordingly. In a further probe to why majority did not adopt the strategy, respondents noted it to be an expensive option, which often failed when the construction was not done to structural specifications.
With respect to the use of Sandbags, as a strategy, in Giyani 24% of the households indicated its adoption as the option to protect their properties against flood. In Nkowankowa 17%, Tzaneen was 11%, while Modjadjiskloof households accounted for 22% that used sandbags. The households’ justification for the use of sandbags as a coping strategy to protect against flooding was hinged on its affordability, ease of building and availability of the material components.
The use of furrow was equally investigated to ascertain whether or not is an acceptable strategy among the households in the district. The result indicates that 5% of Tzaneen residents are using Furrows around their properties, while about one in every four households in Nkowankowa adopted the same strategy. Households in Hoedspruit and Modjadjskloof that used the strategy accounted respectively for 16% and 36% and both Phalaborwa and Giyani accounted for 12% and 18%. The result suggest that the strategy was not embraced by the majority of the households across the selected towns. According to the respondents, the option was considered costly and not an effective strategy compared to others.
The proportion of households’ that adopts the building of protective walls around their houses to cope with flood in the six selected towns indicates that this is a commonly used strategy in the study area. Both Modjadjiskloof and Nkowankowa used it as a strategy mostly. With 76% of its household, Modjadjiskloof recorded the highest proportion of household that used the protective walls as strategy, while 18% of the households in Nkowankowa used the strategy. These results was significantly influenced by the terrain of individual towns under consideration as towns with relatively low lying terrain recorded lower patronage of the strategy, while town with steep slope like Modjadjiskloof adopted it most.
According to [80], Green infrastructure is useful in curtailing surface runoff among other benefits [81]. From the results of analysis, households’ response with respect to growing grasses to reduce the effects of floods in the selected towns revealed that 60% of households in Hoedspruit grew lawn to reduce the flow of surface run off that erodes the top soil. The study showed that 37% of the households in Modjadjiskloof and 36% in Tzaneen grew lawn to reduce erosion while 2.5% and 20% employed the same strategy in Nkowankowa and Giyani towns respectively. This strategy apart from protecting the surface top soil from erosion, it also keep a good ambient of the environment.
The respondents’ answers to the cleaning and removal of waste from drainage channels and systems appeared an acceptable coping strategy across the selected towns in Mopani. 32% of households in Tzaneen do evacuate waste from drainages, while as low as 5% of Nkowankowa households used the strategy to avoid over flow of drainages. However, more than two out of every five Phalaborwa residents engaged in clearing of their drainages to prevent flooding. The study further shows that one tenth of Giyani household embraced the strategy as well. Further to this, drainage and stream channelization was popular, accounting for 25% of Tzaneen households, while one fifth of Hoedspruit households embraced drainage channelization in coping with the incidence of flood.
The use of concrete and stones by households to reinforce their housing foundation serves dual purposes as a way to stabilize the building as well-as safeguard it against any unexpected floods that can erode the building foundation. About 88% of Hoedspruit household endorsed it, while 87% of the households in Modjadjiskloof as well-as 78% of them in Phalaborwa used it as a strategy to cope with floods. However, Tzaneen account for 40% of houses in this category, while Giyani town accounted for 34%.
Obviously without waiting endlessly for government, households across the district have taken creative initiatives to respond within the available resources at their disposal to climate change related hazards. However, households’ capacities are limited by several factors, ranging from economic, social, and attitudinal. Unless pioneered, championed and facilitated by government, household adaptation may not achieve the desired goal. Although several factors collaborate to hamper the success of urban adaptation in the semi-arid region of Mopani, South Africa. These limiting factors are identified in the next section.
4.2 The factors hindering the success of urban adaptation strategies in the Mopani region
This section identifies the factors that inhibit the successes of urban adaptation to climate change hazards. Through our interactions with the households in the selected towns, the key informant (particularly the municipal staff and professionals) and other stakeholders, buttressed by the findings from the planning instruments (IDPs) of the five local municipalities in Mopani District, several inhibiting factors clogging the successes of urban climate change adaptation in these municipalities were uncovered. These out of others can be stratified into both internal and external factors. These are discussed as follow:
Internal factors are those factors that the local municipalities recognized as being within their mandates and powers, on one hand. These include but are not limited to paucity of fund, principally from budgetary allocation. Limited human capacity to embark on the required types of planning for integrated adaptation mainstreaming, compounded by the paucity of knowledge of adequate climate issues at the local municipal level. Higher competition that exist between the mandates of government, resulting in less priority being accorded to long-term planning issues (like climate change) in favor of short-term actions and gains. The Situation is further compounded by the South African need to tackle the backlogs of service amidst coping with both current and future needs of the people. Thus, rendering long-term interventions unattractive to politicians who run a short political tenure to execute. With long-term horizon nature of climate change projections, it contradicts with the short-term political and development programs of these municipalities.
In addition, system’s failure manifest across the selected towns, for instance drainages and water ways blockages, absence of drainages in many instances, sewer leakages (like the case of Nkowankowa and Phalaborwa), and backlogs of service across the municipalities are clear indicators. Others factors include policy inadequacies resulting from municipal reliance on national policies (such as urban and other climate adaptation-related policies). The dichotomized land management and operational deficiencies where traditional institutions are in charge of unproclaim land with no responsibility to provide services. Absence of interface programs between the municipalities and the Universities and other research institutions for information and knowledge sharing as well-as research activities regarding climate change and urban development. There was equally no evidence to show collaborations with private sector (banks, insurance and individual philanthropists) on adaptation issues.
Furthermore, external factors include high poverty rate, low literacy level and unemployment. Lack of reliable and verifiable hazard incident reporting systems that can guarantee disaster hotspot identification and monitoring for early warning. Nevertheless, some of these identified factors (policy shortcomings, institutional weakness etc.), lack of political will plays a significant role.
5. Conclusion
There is no doubt that the new climate is here so also are the attendant hazard that we have to live with in decades to come. With the long-term nature of ongoing global mitigation efforts, adaptation remains the available strategy that must be collaboratively embraced to cope with climate change prone hazards in the urban centers of semi-arid region of South Africa.
Thus, we emphasize the need for a participatory urban management strategy for sustainable adaptation to climate-related hazards, while calling on Scholars to develop models of urban adaptation to climate change that may not necessarily be highly mathematical, but recognize the technological level, social and economic peculiarities of urban Africa, particularly in the semi-arid region of Mopani, South Africa.
The need to urgently review the procedure for reporting climate change hazards and emergencies to promote early warning system, should be revisited. Hazards reporting should be facilitated by the incorporation of instant reporting components in to the existing or a new reporting protocols. This chapter referred to this as “hotspot reporting and monitoring system”, through the implementation and development of a mobile phone facilitated protocol that makes citizens the reporters of climate hazards.
It is therefore important to identify and simplify trends and carry out assessment of the effectiveness of prevailing and future policies that may be directed towards urban households’ adaptation to climate change hazard in semi-arid region of Mopani South Africa for impactful delivery. In addition, such adaptation policies should be locally-driven and must address climate change as a multifaceted phenomenon and not limited as solely to being tackled as an environmental issue, while integrating local knowledge approaches.
Although, it may be uneasy to convince politicians to prioritize climate change (a long-term development agenda) over and above short tenure political agenda, conversations and strategies to encourage the implantation of long-term sustainable projects should be persuaded. But, because climate change phenomenon as well-as its related consequences are real and already manifesting [58], thus, research institutions, private sector (corporate organization) and NGOs are urged to assist in facilitating training of municipal staff and reorientation program for politicians, particularly by promoting the inclusion of climate change hazard management agenda in the political parties manifestoes while facilitating private adaptation strategies at community level.
Strategies like tree planting, urban greening, drainage channelization, and harmonization of the dichotomized land management in the district are some of the strategic window to curtail climate change hazards in the semi-arid region of Mopani South Africa.
Acknowledgments
University of Venda, Thohoyandou, South Africa is acknowledge for funding the research. The University of Ilorin is equally acknowledge for granting me the permission and sponsorship of the Ph.D program.
\n',keywords:"households, adaptation, climate change, semi-arid, South Africa",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/75303.pdf",chapterXML:"https://mts.intechopen.com/source/xml/75303.xml",downloadPdfUrl:"/chapter/pdf-download/75303",previewPdfUrl:"/chapter/pdf-preview/75303",totalDownloads:32,totalViews:0,totalCrossrefCites:0,dateSubmitted:"June 26th 2020",dateReviewed:"October 27th 2020",datePrePublished:"February 18th 2021",datePublished:null,dateFinished:"February 18th 2021",readingETA:"0",abstract:"New climate change realities are no longer a doubtful phenomenon, but realities to adapt and live with. Its cogent impacts and implications’ dispositions pervade all sectors and geographic scales, making no sector or geographic area immune, nor any human endeavor spared from the associated adversities. The consequences of this emerging climate order are already manifesting, with narratives written beyond the alterations in temperature and precipitation, particularly in urban areas of semi-arid region of South Africa. The need to better understand and respond to the new climate change realities is particularly acute in this region. Thus, this chapter highlights the concept of adaptation as a fundamental component of managing climate change vulnerability, through identifying and providing insight in respect of some available climate change adaptation models and how these models fit within the premises and programmes of sustainable adaptation in semi-arid region with gaps identification. The efforts of governments within the global context are examined with households’ individual adaptation strategies to climate change hazards in Mopani District. The factors hindering the success of sustainable urban climate change adaptation strategic framework and urban households’ adaptive systems are also subjects of debate and constitute the concluding remarks to the chapter.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/75303",risUrl:"/chapter/ris/75303",signatures:"Musa Yusuf Jimoh, Peter Bikam, Hector Chikoore, James Chakwizira and Emaculate Ingwani",book:{id:"7712",title:"Natural Hazards - Impacts, Adjustments & Resilience",subtitle:null,fullTitle:"Natural Hazards - Impacts, Adjustments & Resilience",slug:null,publishedDate:null,bookSignature:"Dr. Ehsan Noroozinejad Farsangi",coverURL:"https://cdn.intechopen.com/books/images_new/7712.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"70678",title:"Dr.",name:"Ehsan",middleName:null,surname:"Noroozinejad Farsangi",slug:"ehsan-noroozinejad-farsangi",fullName:"Ehsan Noroozinejad Farsangi"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Literature review",level:"1"},{id:"sec_2_2",title:"2.1 Adaptation, a fundamental component of climate change vulnerability",level:"2"},{id:"sec_3_2",title:"2.2 Climate change adaptation models",level:"2"},{id:"sec_3_3",title:"2.2.1 Gaps regarding climate change adaptation models",level:"3"},{id:"sec_3_4",title:"2.2.1.1 Gaps in relations to the current climate change adaptation models",level:"4"},{id:"sec_4_4",title:"2.2.1.2 Gaps related to policies",level:"4"},{id:"sec_5_4",title:"2.2.1.3 Gaps related to reporting climate change events",level:"4"},{id:"sec_8_2",title:"2.3 Efforts of South African governments within the global context of adaptation framework",level:"2"},{id:"sec_8_3",title:"2.3.1 Apartheid era",level:"3"},{id:"sec_9_3",title:"2.3.2 Post-apartheid era",level:"3"},{id:"sec_12",title:"3. Study area and methods",level:"1"},{id:"sec_12_2",title:"3.1 Description of the study area",level:"2"},{id:"sec_13_2",title:"3.2 Climate of Mopani District",level:"2"},{id:"sec_14_2",title:"3.3 Methods",level:"2"},{id:"sec_16",title:"4. Result and discussion",level:"1"},{id:"sec_16_2",title:"4.1 Households’ efforts towards adapting to climate change in the semi-arid region of Mopani District",level:"2"},{id:"sec_16_3",title:"Table 1.",level:"3"},{id:"sec_17_3",title:"4.1.2 Households’ water scarcity coping strategies",level:"3"},{id:"sec_18_3",title:"4.1.3 Household strategy for flood control in Mopani",level:"3"},{id:"sec_20_2",title:"4.2 The factors hindering the success of urban adaptation strategies in the Mopani region",level:"2"},{id:"sec_22",title:"5. Conclusion",level:"1"},{id:"sec_23",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Mertz O, Halsnæs K, Olesen JE, Rasmussen K. Adaptation to climate change in developing countries. 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Department of Urban and Regional Planning, University of Venda, South Africa
Department of Urban and Regional Planning, University of Ilorin, Nigeria
Department of Urban and Regional Planning, University of Venda, South Africa
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IntechOpen’s Academic Editors and Authors have received funding for their work through many well-known funders, including: the European Commission, Bill and Melinda Gates Foundation, Wellcome Trust, Chinese Academy of Sciences, Natural Science Foundation of China (NSFC), CGIAR Consortium of International Agricultural Research Centers, National Institute of Health (NIH), National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), National Institute of Standards and Technology (NIST), German Research Foundation (DFG), Research Councils United Kingdom (RCUK), Oswaldo Cruz Foundation, Austrian Science Fund (FWF), Foundation for Science and Technology (FCT), Australian Research Council (ARC).
Open Access publication costs can often be designated directly in the grants or in specific budgets allocated for that purpose. Many of the most important funding organisations encourage, and even request, that the projects they fund are made available at no cost to the wider public. IntechOpen strives to maintain excellent relationships with these funders and ensures compliance with mandates.
\\n\\n
In order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
\\n\\n
\\n\\t
Does your institution already have a budget for covering Open Access publication costs?
\\n\\t
Does your grant list Open Access publication fees as legitimate direct/indirect costs?
\\n
\\n\\n
If you are associated with any of the institutions in our list below, you can apply to receive OA publication funds by following the instructions provided in the links. Please consult the Open Access policies or grant Terms and Conditions of any institution with which you are linked to explore ways to cover your publication costs (also accessible by clicking on the link in their title).
\\n\\n
Please note that this list is not a definitive one and is updated regularly. To suggest possible modifications or the inclusion of your institution/funder, please contact us at oapf@intechopen.com
\\n\\n
Please be aware that you must be a member, or grantee, of the institutions/funders listed in order to apply for their Open Access publication funds.
Open Access publication costs can often be designated directly in the grants or in specific budgets allocated for that purpose. Many of the most important funding organisations encourage, and even request, that the projects they fund are made available at no cost to the wider public. IntechOpen strives to maintain excellent relationships with these funders and ensures compliance with mandates.
\n\n
In order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
\n\n
\n\t
Does your institution already have a budget for covering Open Access publication costs?
\n\t
Does your grant list Open Access publication fees as legitimate direct/indirect costs?
\n
\n\n
If you are associated with any of the institutions in our list below, you can apply to receive OA publication funds by following the instructions provided in the links. Please consult the Open Access policies or grant Terms and Conditions of any institution with which you are linked to explore ways to cover your publication costs (also accessible by clicking on the link in their title).
\n\n
Please note that this list is not a definitive one and is updated regularly. To suggest possible modifications or the inclusion of your institution/funder, please contact us at oapf@intechopen.com
\n\n
Please be aware that you must be a member, or grantee, of the institutions/funders listed in order to apply for their Open Access publication funds.
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