Computation complexity of DFT and FFT algorithm.
\r\n\tDespite all efforts to find the cause of fever, around 15% FUO cases still remain without a clear diagnose. Such cases will also be looked upon in the book, along with a discussion about the likely causes, approaches and treatment management.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:null,priceUsd:null,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"8ae318ffcea4989e6b0a1827cecd8316",bookSignature:"Dr. Arun Agarwal",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7951.jpg",keywords:"Definition, Pathogenesis, Patient Approach, Tropic Fever, Rash, Cytopenia, Fever In ICU, Infectious Causes, Non-infectious Causes, FUO Type, Patterns, Fever Management",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 13th 2019",dateEndSecondStepPublish:"March 6th 2019",dateEndThirdStepPublish:"May 5th 2019",dateEndFourthStepPublish:"July 24th 2019",dateEndFifthStepPublish:"September 22nd 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"250176",title:"Dr.",name:"Arun",middleName:null,surname:"Agarwal",slug:"arun-agarwal",fullName:"Arun Agarwal",profilePictureURL:"https://mts.intechopen.com/storage/users/250176/images/system/250176.jpg",biography:"Dr. Agrawal graduated in 1989 from SMS Medical College, Jaipur and did his senior\nresidency at Sir Ganga Ram Hospital, New Delhi and Hindu Rao Hospital, Delhi. He is\npresently working as Director of Department of Internal Medicine at Fortis Escorts\nHospital, Jaipur (FEHJ). He is also associated with Narayana Multispecialty Hospital\n(NMHJ) l and Bhagwan Mahaveer Cancer Hospital and Research Centre (BMCHRC),\nJaipur. Major part of his work is focused on critical patients. He has been an executive member of ISCCM Jaipur for the past 6 years and presently he is vice president of the ISCCM Jaipur. He published a lot of articles including original research articles in national and international peer reviewed journals. He is also a peer reviewer in various national and international journals. \nHe was recently awarded Dr. J.C. Patel and Dr. B.C. Mehta Best Paper Award in 2016 by\nAPI for his original article. His areas of interest are tropical fever, Dengue fever, FUO, AOSD, sepsis and hemophagocytic lymphohistiocytosis.",institutionString:"Fortis Escorts Hospital",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"16",title:"Medicine",slug:"medicine"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"177731",firstName:"Dajana",lastName:"Pemac",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/177731/images/4726_n.jpg",email:"dajana@intechopen.com",biography:"As a Commissioning Editor at IntechOpen, I work closely with our collaborators in the selection of book topics for the yearly publishing plan and in preparing new book catalogues for each season. This requires extensive analysis of developing trends in scientific research in order to offer our readers relevant content. Creating the book catalogue is also based on keeping track of the most read, downloaded and highly cited chapters and books and relaunching similar topics. I am also responsible for consulting with our Scientific Advisors on which book topics to add to our catalogue and sending possible book proposal topics to them for evaluation. Once the catalogue is complete, I contact leading researchers in their respective fields and ask them to become possible Academic Editors for each book project. Once an editor is appointed, I prepare all necessary information required for them to begin their work, as well as guide them through the editorship process. I also assist editors in inviting suitable authors to contribute to a specific book project and each year, I identify and invite exceptional editors to join IntechOpen as Scientific Advisors. I am responsible for developing and maintaining strong relationships with all collaborators to ensure an effective and efficient publishing process and support other departments in developing and maintaining such relationships."}},relatedBooks:[{type:"book",id:"6550",title:"Cohort Studies in Health Sciences",subtitle:null,isOpenForSubmission:!1,hash:"01df5aba4fff1a84b37a2fdafa809660",slug:"cohort-studies-in-health-sciences",bookSignature:"R. Mauricio Barría",coverURL:"https://cdn.intechopen.com/books/images_new/6550.jpg",editedByType:"Edited by",editors:[{id:"88861",title:"Dr.",name:"R. Mauricio",surname:"Barría",slug:"r.-mauricio-barria",fullName:"R. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"53909",title:"High Resolution Single-Chip Radix II FFT Processor for High- Tech Application",doi:"10.5772/66745",slug:"high-resolution-single-chip-radix-ii-fft-processor-for-high-tech-application",body:'\nThe prevalent subject of Fourier analysis encompasses a vast spectrum of mathematics where parts may appear quite different at first glance. In Fourier analysis, the term Fourier transform often refers to the process that decomposes a given function into the harmonics domain. This process results in another function that describes what frequencies are in the original function. Meanwhile, the transformation is often given a more specific name depending upon the domain and other properties of the function being transformed.
Fourier transform was introduced with the main concepts of discrete Fourier transform (DFT) [1] in the heart of most DSP processor. The DFT is a Fourier representation of a finite‐length sequence which is the most important fundamental operation in digital signal processing and communication system [2, 3]. However, the computation complexity of the direct evaluation of an N‐point DFT involves a long phase computational time and large power consumption [4]. As a result of these problems, it is important to develop a fast algorithm. There are numerous viewpoints that can be taken toward the derivation and interpretation of the DFT representation of a finite‐duration sequence. The sequence of
The DFT X(ω) is a function of continuous‐frequency variable ω, and the summation in Eq. (1) extends toward positive and negative infinitively. Therefore, the DFT is a theoretical Fourier transform of a digital signal. However, it cannot be implemented for real applications. It is the sample of the signal in time domain at a particular time and can be expressed as:
\nThe frequency analysis of a finite‐length sequence is equal to the sample of continuous frequency variable ω at N equally spaced frequencies ωk = 2πk/N for k = 0, 1, 2, …, N - 1 on the unit circle. These frequency samples are expressed as:
\nwhere the twiddle factors are defined as:
\nThe DFT is based on the assumption that the signal x(n) is periodic. Therefore, X(k) for k = 0, 1, …, N - 1 can uniquely represent a periodic sequence x(n) of period N. The inverse DFT is the reversed process of the DFT. It converts the frequency spectrum X(k) back to the time domain signal x(n) [5]:
\nDirect computation of an N-point DFT according to Equation Eq. (5) requires N(N- 1) complex additions and N(N- 1) complex multiplications. The complexity for computing an N-point DFT is therefore O(N2). High computation complexity in DFT algorithm and need for having efficient Fourier processor leads for introduction of a fast Fourier transform (FFT) processor.
\nIn 1965 Cooley and Tukey [6] developed the use of FFT in order to save time and avoid unnecessary complex calculations. FFT algorithm computes an N‐point forward DFT or inverse DFT (IDFT) where N is 2 power of M. FFT algorithm divides N‐point data into two N/2‐point series and performs the DFT on series individually results in the order of
DFT | Radix II FFT | |||
---|---|---|---|---|
Number of points | Complex addition | Complex multiplication | Complex addition | Complex multiplication |
N | N(N - 1) | N2 | Nlog2N | (N/2)log2N |
4 | 12 | 16 | 8 | 4 |
8 | 56 | 64 | 24 | 12 |
16 | 240 | 256 | 64 | 32 |
32 | 992 | 1024 | 160 | 80 |
64 | 4032 | 4096 | 384 | 192 |
127 | 16,256 | 16,384 | 896 | 448 |
Computation complexity of DFT and FFT algorithm.
To calculate FFT algorithm, there are two well‐known methods identified as DIT‐FFT and DIF‐FFT calculations [7–9]. In general, FFT processor has many types in terms of Fourier calculation. Taking into account different types of FFT algorithms are:\n
Different Radixes, such as Radix II, Radix IV, etc., and mixed‐radix algorithms.
DIT and DIF.
Real and complex algorithm.
Here, further detail is provided for DIT and DIF processor.
\nThe FFT structure divides input series into odd and even sequences. The number of stream in FFT is N = 2mwhen m is a positive integer:
\nBased on the DFT definition and combination of the FFT concept, X(k) can be written as:
\nSince
where
8‐point FFT twiddle factor.
By assuming
Butterfly calculation is the fundamental concept of the FFT algorithm and 8‐point butterfly structure is shown in Figure 2.
Decomposition of 8‐point DIT FFT structure.
Radix II butterfly FFT is decomposed into
Decomposition of 8‐point DIT‐FFT.
DIF‐FFT calculation is similar to the DIT‐FFT algorithm. As far as FFT calculation is involved, the time domain sequence is divided into two subsequences with N/2 samples: The DFT concept of x(n) expressed as:
\nGiven that
Later, Eq. (11) is expanded into two parts including even
Similarly, 8‐point DIF FFT structure is shown in Figure 4 with detail complex calculation in three stages. The output sequence
Internal calculation of 8‐point DIF‐FFT processor.
Unlike the DIF structure, input data in DIT‐FFT is in bit‐reverse format while the output is sorted. On the other hand, both the DIT and DIF can go from normal to shuffled data or vice versa. In order to apply Radix II FFT structures, DIT and DIF algorithms require the same number of operations and bit‐reversal to compute the FFT calculation. The overall performance of the FFT processor is dependent on the application, hardware implementation, and convenience. If the design is focused on high speed structure, the processor has to take the most efficient approach and algorithm to perform the FFT calculation accordingly. In this chapter DIT‐FFT architecture is considered for floating‐point implementation.
Measured frequency by FFT will be subjected to quantization noise error with respect to the real frequency. This is caused by the fact that the FFT only computes the spectrum at discrete frequencies. This error is said to affect the accuracy. In addition, spectral leakage effect becomes very significant when small amplitude harmonics are close to large amplitude ones since they become hidden by the energy distribution of the larger harmonics. Furthermore, the fixed internal arithmetic calculation generates white noise in frequency domain. To reduce the generated noise effect and enhance signal strength, floating‐point technique is designed and implemented. The floating‐point technique allows numbers to be represented with a large dynamic range. Therefore, floating‐point arithmetic enables the reduction of overflow problems that occur in fixed‐point arithmetic. Although it is at the expense of throughput and chip area size, the new architecture is designed and investigated to avoid undesired effects in floating‐point FFT algorithm. Floating‐point arithmetic provides higher precision and a much larger dynamic range under IEEE 754 standard [10]. Therefore, floating‐point operations support more accurate DSP operations. Table 2 compares the efficiency between fixed‐point and the floating‐point FFT processor.
Fixed‐point FFT | Floating‐point FFT |
---|---|
16‐bit or 24‐bit | 32‐bit |
Limited dynamic range | Large dynamic range |
Overflow and quantization errors | Less error |
Higher frequency | Low frequency |
Less silicon area | More silicon area |
Cheaper | More expensive |
Low power consumption | High power consumption |
Fixed‐point and floating‐point FFT processor properties.
In floating‐point format, the data are translated based on power and mantissa in the decimal system. This notation can be expanded into the binary system. Representing the data in power and mantissa system gives the data the capability of storing a much greater range of numbers than if the binary points were fixed. Floating point refers to the “truth” of the Radix point, which refers to the decimal point or in computers it is known as the binary point that has the capability to float. This entails the event to occur anywhere that is relative to the significant digit of the number. Thus, a floating‐point representation, with its position indicated separately in the internal representation, is a computer\'s recognition of a scientific concept. Although the benefit of floating‐point representation over fixed‐point (and integer) representation is much wider in range of values, but the floating‐point format needs more storage. Hence, the implementation of high performance system requires applying efficient and fast floating‐point processor, which is competitive with the fixed‐point processor. Various types of floating‐point representation have been used in computers in the past. However, in the last decade, the IEEE 754 standard [10] has defined the representation. According to the IEEE 754 standard [10], the single precision is chosen to represent the floating‐point data. The IEEE standard specifies a way in which the three values described can be represented in a 32‐bit or a 64‐bit binary number, referred to single and double precision, respectively [11, 12]. In this project, single precision is selected to function. For the 32‐bit numbers, the first bit (MSB) specifies the sign, followed by 8 bits for the exponent, and the remaining 23 bits are used for the mantissa. This arrangement is illustrated in Figure 5. The sign bit is set to zero if the number is positive, and the bit is set to 1 if the number is negative. The mantissa bits are set to the fractional part of the mantissa in the original number in bits 22 to 0.
Floating‐point structure in IEEE 754 standard [10].
Floating‐point algorithm finds huge demand in industry. To conclude this section, Table 3 summarizes the FFT algorithm application in fixed‐point and floating‐point architectures.
Fixed‐point FFT | Floating‐point FFT |
---|---|
Low resolution disk drive | Radar, Image processing |
Consumer audio application | High‐end audio application, ambient acoustics simulators |
Channel coding | Professional audio encoding/decoding and audio mixing |
Communication device | Sound synthesis in professional audio and video coding/decoding |
Prototyping | |
4G OFDM Transceiver | |
High resolution motor monitoring |
Fixed and floating‐point FFT application.
In 2009, Xilinx Logic core [13] introduced the FFT processor using the Radix structure on a chip. The introduced FFT processors were designed to offer a trade‐off between core sizes and transform time. These architectures are classified below:\n
FFT Processor with Radix II pipelined serial I/O architecture
FFT Processor with Radix IV, parallel I/O (burst) architecture
FFT Processor with Radix II, parallel I/O (burst) architecture
FFT Processor Radix II lite, parallel I/O (burst) architecture
The pipeline serial I/O allows to continue data processing, whereas the burst parallel I/O loads and processes data separately by using the iterative approach. It is smaller in size than the parallel but has a longer transform time. In the case of Radix II algorithm, it uses the same iterative approach as Radix IV with the difference of smaller butterfly size that differentiates it. Yet, the transformation time is longer. Finally, for the last category, based on Radix II architecture, this variant uses a time multiplexed approach to the butterfly for an even smaller core, at the expense of longer transformation time. Figure 6 shows the throughput versus resource among the four architectures.
FFT architecture resources vs. throughput.
In this design, n‐stage of Radix II butterfly is connected as a serial structure. Each unit of Radix II butterfly has its own RAM memory to upload and download data. The input data are stored in the RAM while the processor simultaneously performs transform calculations on the current frame of data and loads input data for the next frame of data and unloads the result of the previous frame of data. Input data are presented in sorted order. The unloaded output data can either be in bit‐reversed order or in sorted order. When sorted output data are selected, an additional memory resource is utilized. Figure 7 illustrates the architecture of the pipeline serial I/O with individual memory bank, which connects in a serial structure.
FFT processor with Radix II pipelined, serial I/O [13].
Radix IV structure accepts 4 input data simultaneously whereas Radix II takes only 2 input data at the time to perform FFT calculation. Radix IV input data uploaded into the FFT processor, cannot be uploaded while the calculation is underway. When the FFT is started, the data are loaded. After a full frame has been loaded, the core computes the transformation. The result can be downloaded after the full process is over. The data loading and unloading processes can be overlapped if the data are unloaded in digit‐reversed order. Figure 8 shows the Radix IV structure when 4 input data are loaded for FFT calculation.
FFT processor with Radix IV architecture [13].
FFT processor with burst I/O architecture utilizes Radix II butterfly calculation to execute the arithmetic structure. In spite of Radix IV with burst I/O processor, which the input data cannot be loaded and unloaded simultaneously, the Radix II processor accepts the input data during the FFT processor and data can be used concurrently when the output samples are in bit‐reversed order. The twiddle factors are stored in the ROM blocks while the output and input data are stored in a separate or mixed RAM blocks. Figure 9 shows the Radix II structure when 2 input data are loaded for FFT calculation.
FFT processor with Radix II burst I/O architecture [13].
FFT processor with Radix II lite architecture uses one shared RAM, hence reducing resources at the expense of an additional delay per butterfly calculation. The multiplier in this structure multiplies the real part of complex number in one clock cycle and the imaginary in the next. In this architecture, the data can be simultaneously loaded and unloaded if the output samples are in bit‐reversed order. In this architecture, sine and cosine twiddle factor coefficient will be saved in the ROM and the output data will be saved in a single RAM. Although this proposed architecture saves the resources, the throughput is significantly limited by the FFT structure due to the sequence calculations. Figure 10 shows the Radix II lite structure when 2 input data are loaded for FFT calculations.
FFT processor with Radix II lite burst I/O architecture [13].
In Section 2, FFT fundamental was discussed and elaborated. Furthermore, different FFT architectures were provided with the detail on IO configuration. Here, advance FFT processor with the focus on 1024 floating‐point parallel architecture for high performance application is provided.
\nHigh‐tech FFT principle is based on Radix II algorithm in floating‐point format to conduct 1024 point FFT structure. Figure 11 illustrates the main block diagram of the 1024‐point Radix II floating‐point parallel pipeline (FPP) FFT processor in detail.
1024 point Radix II FPP‐FFT block diagram.
As shown in Figure 11, there are six major subprocessor units in the high‐tech 1024 point Radix II FPP‐FFT algorithm. These units are shared memory, bit reverse, butterfly arithmetic, smart controller, ROM, and finally address generator unit. The floating‐point input data act as a variable streaming configuration into the processor. The variable streaming configuration allows continuous streaming of input data and produces continuous stream of output data. Figure 12 shows the internal schematic of the pipeline butterfly algorithm with the parallel architecture at a glance.
Designed FPP Radix II butterfly structure.
To enhance the speed of calculation in Radix II butterfly algorithm, the pipeline registers are located after each addition, subtraction, and multiplication subprocessors. Hence, the pipeline butterfly algorithm keeps the final result in the register to be transferred into the RAM by the next clock cycle. Additionally, the parallel architecture splits the data in real and imaginary format and increases the speed of FFT calculation by 50%. As a result of the design algorithm, Radix II FPP‐FFT processor calculates 1024 point floating‐point FFT exactly after
Radix II butterfly unit is responsible for calculating the complex butterfly equations as
Butterfly processor efficiency greatly depends on its arithmetic units, and high‐speed floating‐point adder is the bottle neck of butterfly calculation. Based on IEEE‐754 standard [10] for floating‐point arithmetic, 32‐bit data register is considered to allocate mantissa, exponent, and sign bit in a portion of 23, 8, and 1 bits, respectively. The advantages of floating‐point adder are that the bias power is applied to complete the calculation and avoid using unsigned value. Additionally, the floating‐point adder unit performs the addition and subtraction using substantially the same hardware as used for the floating‐point operations. This functionality minimizes the core area by minimizing the number of elements. Furthermore, each block of floating‐point adder/subtraction operates the arithmetic calculation within only one clock cycle that results high‐throughput and low latency for the entire FFT processor. Figure 13 shows the novel structure of the floating‐point adder when it is divided into four separate blocks while detail algorithm is presented in Figure 14.
Schematic diagram of advance floating‐point adder.
Flowchart of advance floating‐point adder.
The purpose of having separate blocks is to share the total critical path delay into three equal blocks. These blocks calculate the arithmetic function within one clock cycle. However, the propagation delay can be associated with continuous assignment to increase the overall critical path delay and for the slowing down of the throughput. Based on combinational design, the output of each stage depends on its input value at the time. The unique structure of floating‐point adder enables feeding of the output result in the pipeline registers after every clock cycles. Hence, the sequential structure is applied for the overall pipelined add/subtraction algorithm to combine the stages. The processing flow of the floating‐point addition/subtraction operation consists of comparison, alignment, addition/subtraction, and normalization stages.
\nThe comparison stage compares two input exponents. This unit compares two exponents and provides the result for the next stage. The comparison is made by two subtraction units and the result is revealed by compare_sign bit.
\nAccording to the results of the comparison stage, the alignment stage shifts the mantissa and transfers it to the adder/subtraction stage. The number of shifting will be selected by the comparison stage output. Consequently, each stage of the floating‐point adder algorithm is executed within one clock cycle. Floating‐point adder/subtraction unit satisfies high speed and efficiency of arithmetic unit in cost of die area size. The floating‐point arithmetic unit is designed to calculate entire numbers regardless of the number sign. As shown in Figure 15, there is a logic gate involved with the stages, which cause higher delay propagation through the circuit.
Addition/subtraction structure.
Floating‐point numbers are generally stored in registers as normalized numbers. This means that the most significant bit of the mantissa has a nonzero value. Employing this method allows the most accurate value of a number to be stored in a register. For this purpose, the normalized stage is required. This unit is located after the add/sub stage. The output signal representing the add/sub block leads to zero digits of an unnormalized result of the calculation operation. The normalized block ignores the digital value of zero from the MSB of the mantissa and shifts the mantissa to imply value of one in digital as MSB in mantissa.
In a floating‐point multiplier, numbers are represented in single‐precision normalized mantissa and 8‐bit exponent format defined by the IEEE 754 standard. This structure has developed the architecture for partial‐product reduction for the IEEE standard floating‐point multiplication, leading to a structured high‐speed floating‐point multiplier. The shortening of the data path is desirable because they require shorter wires and therefore support faster operation. The former approach uses a reduction scheme based on combination unit and connects it as parallel architecture. Implementing floating‐point multiplier is simpler than floating‐point adder since it does not require alignment stage. The processing flow of the floating‐point multiplication operation consists of multiple stage and normalized stage. Figure 16 shows the overall block diagram of the floating‐point multiplier while the flowchart of the functionality of the multiplier is shown in Figure 17.
\nFloating‐point multiplier block diagram.
Floating‐point multiplier flow chart.
In a floating‐point multiplier, the bias power format is applied to avoid having negative exponent in the data format. Additionally, the multiplier is designed as pipelined structure to enhance speed calculation, with the intention of the initial result appearing after the latency period where the result can then be obtained after every clock cycle. The multiplier offers low latency and high throughput and is IEEE 754 compliant. This design allows a trade‐off between the clock frequency and the overall latency by adding the pipeline stage.
Smart controller unit significantly affects the efficiency of the 1024 Radix II FPP‐FFT processor. As such, small die area can be achieved by designing high performance controller for the FFT processor. In this architecture, FFT controller is designed with the pipeline capability. The global controller unit provides the signal control to the different parts of the FFT processor. Additionally, several paths are switched between the data input and data output in architecture design and the data path is controlled. To calculate the 1024 point Radix II FFT processor, it is necessary to have
Smart controller state machine.
There are several control signals in smart controller to clarify the presence of correct output after finishing the current cycle of FFT calculation. The control signals transfer information through the RAM, ROM, butterfly preprocessor, and address generator. The designed controller operates according to the provided state machine (Figure 18) and makes the high performance FFT calculation feasible for implementation. The controller unit is structured into the subblocks such as in sequential and combination units. Sequential unit is responsible for updating the state of the processor, while the combinational unit performs the states individually. The state machine waits for processor core to complete the entire FFT calculations and then records data points into the memory. Reset state is received every time the reset input is asserted then holds the entire calculation. The processor gets activated after the reset input signal is removed.
Address generator has a significant task in Radix II FFT processor, since it delivers the address of the input/output data for each computational stage in an appropriate way. Address generator architecture consists of ROM address generator, Read address generator, and Write address generator. ROM address generator produces the reading address for the ROM module. The reading address represents the address of the twiddle factor, which must be taken to feed the butterfly structure. This address generator is designed to select the specific twiddle factor for the butterfly calculations. Meanwhile, the Write address generator is designed to save the result of the butterfly calculation in the proper location in the complex RAM. The proposed smart address generator is designed to provide the correct result for the next stage of the butterfly in 1024‐point Radix II FFT calculations. The architecture of the Read address generator is similar to the Write address generator. The butterfly will save the data result after reading from the certain address and input it to the butterfly, in the previous address line. The reading RAM select control signal ensures the correct location of data in the complex RAM. On the other hand, memory modules are used for the storing input and output results with 1024 complex long words of 32‐bit registers. The implemented architecture for the memory is shown in Figure 19. The capacity of the memory is 1024‐point data for real and imaginary data. In high‐tech implementation, shared RAM architecture is designed and implemented in a single‐chip FFT processor. The high‐tech design makes the Radix II FFT architecture entirely independent of the type of FPGA board since it has on board memory system. Furthermore, each complex RAM has the capability of saving real and imaginary input data separately. The module is programed with a dual‐in‐line header to provide the appropriate location for storing input and output result in each stage consequently. It is composed of two delay memories and multiplexer, which allows straight through or crossed input‐output connection as required in the pipeline algorithm. Memory unit similarly contains the controller trig. The controller, which is connected directly to the memory modules, takes the responsibility of transferring data through the memory and arithmetic blocks ensuring that no data conflict occurs within the complete process of the FFT calculations. This is another advantage of high‐tech smart memory modules, by which data can be read and written in the memory simultaneously without sending bubble data in the FFT processor.
RAM internal architecture.
Design algorithm of the 1024 point Radix II FPP‐FFT processor was based on the smart subblocks where the result was optimized accordingly. The designed processor takes the advantages of (i) shared memory to store the input and output data and makes the system as single chip. Hence, it reduces hardware complexity. Furthermore, (ii) the entire individual arithmetic unit is designed to operate within one clock cycle to increase the maximum clock frequency. Additionally, (iii) the butterfly structure is in parallel and pipelined architecture to minimize delay caused by the FFT calculations, and finally, (iv) the strong controller with collaboration of address generator unit ignores the need of using N numbers of butterfly unit, since Radix II calculation is carried out within one butterfly unit that results reduction of power consumption, area, and avoid system complexity. The high performance processor is implemented with optimizing the architecture to enable the system in maintaining a reasonable clock rate and with low latency of
Section 4 details the implementation of introduced 1024‐point floating‐point parallel pipeline Radix II FFT algorithm. Hardware implementation of the algorithm as system on chip (SOC) is presented here.
\nIn order to verify the functionality of the 1024‐point FPP‐FFT processor, the VHDL code for the overall processor is developed. Register transfer level (RTL) behavior description of the processor is generated for downloading into FPGA prototyping. The procedure is continued by attaching the library cell and constraint file for ASIC implementation. High performance FFT is transferred into the gate level synthesis to complete postsimulation stage. The design moves forward to the back‐end implementation by 0.18 µm Silterra technology and 0.35 Mimos technology library. Generated netlist with constraint file is transferred to complete floor planning and place and route stage. The implementation process is summarized in Figure 20.
Flowchart of hardware implementation.
The high‐tech 1024‐point FPP‐FFT specification generated by Xilinx ISE synthesis report is provided in Table 4.
HDL synthesis report | Timing summary | ||
---|---|---|---|
Registers flip‐flops | 1175 | Minimum period (ns) | 4.391 |
Shift registers | 43 (6%) | Maximum frequency (MHz) | 227.747 |
LUTs slice | 4419 (23%) | Min. input arrival time (ns) | 3.788 |
Logic slice | 2584 (13%) | Max. output required time (ns) | 6.774 |
RAM cells | 1835 (35%) | Total equivalent gate count | 998678 |
IOs | 88 (40%) | Total number of path | 220310 |
Memory usage (MB) | 254 (40%) | Total number of destinations | 5926 |
Multiplexers | 77 | ||
Tri‐states | 98 |
1024‐point FPP‐FFT specification.
As stated in Table 4, high‐tech FFT processor operates with the maximum clock frequency of 227.7 MHz and the total latency of 5131 clock cycles (Figure 21) to prove the computation complexity derived from (N/2log2N) + 11 when N = 1024.
1024‐point FPP‐FFT processor output signal.
Place and route (PAR) process was completed and the processor routed successfully on silicon chip (Figure 22).
Chip layout of high‐tech FFT processor.
Later, the 1024‐point FPP‐FFT processor was optimized in Silterra 0.18 µm and Mimos 0.35 µm technology for power consumption and die size measurement in maximum clock frequency. Table 5 shows the optimization result of FFT processor implementation in Silterra 0.18 µm and Mimos 0.35 µm technology library.
FPP‐FFT specification | Silterra 0.18 µm technology | Mimos 0.35 µm technology |
---|---|---|
Active core area (mm2) | 2.32 × 2.32 | 4.256 × 4.256 |
Power consumption (mW) | 640 | 1198 |
Optimized power consumption and die area size in different technology library.
To conclude, after FPGA implementation and ASIC optimization and with considering available software and hardware resources, the high‐tech 1024‐point Radix II FPP‐FFT processor was implemented and tested in FPGA prototyping under Xilinx ISE software and CAD tools in synopsis. Figure 23 shows relevant FPGA board, and Table 6 summarizes the design property.
Parameters | Unit | specification |
Processor machine | Radix II | |
Calculation type | Floating‐point | |
Latency (µs) | 22 | |
Maximum precision | 32‐bit | |
No. of input data | 1024 | |
Data rate (ms/s) | 25 | |
Max. clock frequency | 227 MHz | |
Signal to noise ratio | SNR | 192 dB |
Power consumption (Silrerra 0.18 μm library) | 640 mW | |
Active core area (Silrerra 0.18 μm library) | mm | 2.32 × 2.32 |
Accuracy | ≤0.01 |
High‐tech 1024 point FFT specification.
FPGA implementation of high‐tech FFT processor.
In this chapter, high‐tech 1024‐point Radix II FFT processor was implemented. The design was launched with introducing 32‐bit data single precision floating‐point parallel pipeline architecture. Then, it was followed by implementing the subcomponents such as Radix II butterfly and smart controller. The implementation result of high‐tech 1024‐point Radix II FPP FFT processor was provided accordingly. Designing high speed floating‐point arithmetic unit such as adder/subtraction (278 MHz), multiplier (322 MHz), implementing smart controller to save area and increase system efficiency, design processor as single chip by implementing complex dual memory, and providing pipeline and parallel architecture lead to present a high‐tech 1024‐point Radix II FPP FFT processor. In addition, the processor was synthesized using the Xilinx ISE platform. From synthesis report, it was found that the FPP FFT processor shows the maximum clock frequency of 227 MHz. The latency for calculating 1024‐point FFT is 22 µs. After FPGA implementation, the proposed processor was optimized in ASIC under Silterra 0.18 µm and Mimos 0.35 µm technology libraries. The estimation power consumption was reported 640 mW in Silterra and 1.198 W in Mimos technology library with sample rate of 25 ms/s. The procedure was followed by defining the constraints and the netlist (gate level) to produce the ASIC layout. The design compiler result shows the die size of
The ketogenic diet is a mixed diet containing low carbohydrates, consisting primarily of proteins and fat [1, 2]. Some healthy foods are eaten on a ketogenic diet, for example, seafood, low-carb vegetables, cheese, eggs, meat, poultry, coffee, and tea. The importance of high fat in aging-related sarcopenic obesity reducing regimens on different metabolic models are shown by comparing the effects of four different types of ketogenic dietary regimens [3, 4]. Standard ketogenic diet (SKD): This typically contains a very low, only 5% carbohydrate, 15% moderate proteins, 80% high fat diet. This classic SKD contains a 3:1 ratio to combined protein and carbohydrate. High protein ketogenic diet (HPKD): This contains 5% carbohydrate, 35% protein, and 60% fat. This type is similar to a standard ketogenic diet, but includes more protein [5]. Cyclical ketogenic diet (CKD): This ketogenic diet involves 5 periods of ketogenic days followed by 2 high carbohydrate days [6]. Targeted ketogenic diet (TKD): This ketogenic diet allows you to add carbohydrate around workouts. Although this ketogenic diet is usually safe for weight loss, diabetes, epilepsy, and aging-related sarcopenic obesity, there maybe have some initial side effects while your body adapts [7–9]. Ketogenic diets forces to burn fats rather than carbohydrates. A ketogenic diet, a high fat, in food is converted triglyceride (TG). The liver convers triacylglycerol (TAG) into fatty acid and ketone bodies [10]. Elevated ketone bodies in the blood eventually lowers the aging-related sarcopenic obesity. We hoped to obtain the benefits of ketone dietary therapy that could be maintained indefinitely. Ketone bodies were produced β-hydroxybutyrate, acetoacetate, and acetone by the liver in they consumed a very low-carbohydrate, and excess high-fat diet (Figure 1) [11, 12].
\nKetone bodies. Interrelationships of these three substances. Under certain a high rate of fatty acid oxidation, the liver products collectively of β-hydroxybutyrate, acetoacetate and acetone.
Sarcopenic obesity is caused reduced skeletal muscle mass and strength in order adults. Sarcopenic obesity is most commonly caused by a combination of age and excessive food energy intake, not exercising enough, smoking or heavy alcohol use, although a few caused by genes [13]. Inflammation with aging is known to be a major contributor to sarcopenia [14]. Therefore, sarcopenic obesity has been defined as the loss of skeletal muscle mass and overweight in the older age. As sarcopenic obesity grow older, up to half of the muscle is lost and skeletal muscle is often replaced with fat tissue, particularly in sarcopenic obesity [15]. This is an importance of sarcopenic obesity in the health care for older people. Sarcopenia obesity starts at approximately 40 years of age and there is an estimated muscle mass loss of about 3 ~ 8% per decade, stretching process speeds up until the age of 70 years; after that age, a 15% loss ensues per decade [16]. This group proposed that sarcopenic obesity is diagnosed based on over whole-body weight combination with poor physical functioning [17].
\nThe production of ketone bodies is from the liver. The reverse situation occurs in extrahepatic tissue. Responsible for ketone body formation are associated mainly with the mitochondria. Acetoacetate was formed from the terminal four carbons of a fatty acid upon oxidation. The liver is equipped with the production of acetoacetate from acetoacetyl-CoA (Figure 2). This accounts for the net production of ketone bodies by the liver. Sarcopenic obesity is a newly recognized geriatric syndrome by age-related decline of low skeletal muscle plus a combined approach of overweight body mass that occurs with advancing age [18]. There are several factors contributing to the disorder. Chronic low-grade inflammation has been identified as the initiator in the early stages of many disorders such as physical disability, poor nutrition, and smoking [19, 20]. However, a widely accepted definition of sarcopenic obesity or obese sarcopenia suitable for use in research and clinical practice is still lacking. Sarcopenic obesity is increases the risk of aging-related type 2 diabetes susceptibility to obesity, and it can be the cause of functional dependence and disability in the elderly population [21]. Sarcopenic obesity was significantly associated with greater odds of sarcopenia, overfat, and sarcopenic obesity in women, but not in men [22]. Among older adult sarcopenic obesity characteristics, reduced lean mass at its extreme termed sarcopenia and excess body fatness are predictors of poor health outcomes in the general population. Sarcopenic obesity is at its extreme referred to as ketogenic diet of theorized compound these individual risks [23]. On average, by 20–40% for both men and women in sarcopenic obesity-induced muscles loss and overweight. Overall prevalence of sarcopenia was 26.7% in women and 73.3% in men, which increased with age. Prevalence of obesity was 74.6% in women and 67.1% in men [24]. Thus, defining sarcopenic obesity only in terms of muscle mass is too narrow maybe of limited clinical value that becomes more common in people over the age of 65. Sarcopenic obesity factor seropositivity, and a lack of current treatment with disease-modifying anti-sarcopenic obesity drugs were significantly associated with abnormal body composition such as increasing joint deformity, disability scores and C-reactive protein levels [25]. After middle age, adults lose 3% of their muscle strength every year, on average, to perform many routine activities [26]. These factors contribute to sarcopenic obesity to the characteristic skeletal muscle atrophy and weakness. Sarcopenic obesity also shortens life expectancy in those it affects, compared to individuals with normal muscle strength. Aging-related-sarcopenic obesity is caused by an imbalance between signals for muscle cell growth and signals for teardown [27]. Skeletal muscle cell growth processes are called “muscle anabolism,” and fat cell teardown processes are called “fat catabolism” (Figure 3). Ketogenic diet acts with protein-destroying enzymes to keep muscle steady through a cycle of growth, stress or injury, destruction, and then healing. However, during aging your body becomes resistant to the growth signals, tipping the balance toward catabolism and muscle loss [28].
\nKetogenesis.
The ketone bodies use. Extrahepatic tissues utilize them as respiratory substrates. The ketone bodies from the liver to the extrahepatic tissues coupled with very low activity of enzymes responsible for their utilization. Ketone bodies serve as a fuel for extrahepatic tissues.
The Older women with sarcopenic obesity have an increased all-cause mortality risk independent of obesity [29]. Sarcopenic obesity with obesity and aging, loss of muscle mass as a primary event, and this loss is a major contributor to fat gain, which in turn reinforces the muscle loss. Markedly elevated acetoacetic acid and β-hydroxybutyric acid production in the liver sarcopenic obesity. The various etiologic factors of sarcopenia in aging all lead to loss of muscle [30]. With the increase ketone body in skeletal muscle, acetoacetic acid and β-hydroxybutyric acid secretion are increased, and both lead to sarcopenic obesity resistance, which reduces the fat mass in sarcopenic obesity skeletal muscle and normal anabolic effect of insulin on amino acid transport in muscle [30, 31]. In addition, there is some evidence that acetoacetic acid and β-hydroxybutyric acid reduces fat mass secretion, suppressing another major anabolic stimulus. In addition, higher acetoacetic acid and β-hydroxybutyric acid levels may exert direct catabolic effects on muscle [32] (Figure 4).
\nA ketogenic diet can rebuild skeletal muscle. A ketogenic diet can help you lose fat in the skeletal muscle from sarcopenic obesity. β-hydroxybutyric acid provides the main fuel for moderate and high-intensity exercise.
Sarcopenic obesity in older adults is associated with skeletal poorer performance and strength parameters. Despite β-hydroxybutyric acid in clinical use as a therapy for sarcopenic obesity for several years, the ketogenic diet remains a therapy in search of an explanation [33]. The action of the ketogenic diet is the optimal indications for its clinical use are incompletely defined. We defined the abnormalities in body composition and abdominal fat that occur in sarcopenic obesity is associated with the aging-related presence of skeletal muscle dysfunction. Some features of clinical experience have been replicated in animal models, including the role of ketosis, elevation of triglyceride, total cholesterol, HMG CoA reductase, testosterone. Sarcopenic obesity by both classic ketogenic and β-hydroxybutyric acid diets are better effective at younger ages, and rapid reversal of the sarcopenic obesity effect when the diet is discontinued [34]. Sarcopenic obesity have been implicated in muscle atrophy and dysfunction due to denervation, muscular dystrophy, and disuse. A ketogenic diet plays key roles in sarcopenic obesity in muscle atrophy and the potential of the ketogenic diet for the treatment of sarcopenic obesity in regulating metabolism in skeletal muscle. Several β-hydroxybutyric acid isoforms are potential targets for intervention in sarcopenic obesity. Supplementary of acetoacetic acid and β-hydroxybutyric acid prevents muscle atrophy due to nutrient deprivation [35]. A ketogenic diet regulates metabolism in skeletal muscle and may inhibit oxidative metabolism during aging. Both of acetoacetic acid and β-hydroxybutyric acid have been implicated in muscle atrophy due to skeletal muscle denervation, a process implicated in sarcopenic obesity. Acetoacetic acid or β-hydroxybutyric acid is already in use in the clinic, and there is promise in targeting skeletal muscle for the treatment of sarcopenic obesity [36]. As in the clinical arena, there has been a recent resurgence of interest in pursuing basic questions related to the ketogenic diet. There have been very few animal studies of the ketogenic diet, and those that have been performed are difficult to compare because of wide discrepancies in experimental methods [37]. Earlier models concentrated on the effect of the ketogenic diet on sarcopenic obesity. The effects on the ketogenic diet and satiety, weight loss, and nitrogen balance are discussed as well as influences on electrolytes and the sympathetic system [38]. Hormonal changes of the ketogenic diet regimens and the impact on mood and subjective acceptance are compared. Experimental approaches such as brain metabolic pathways and histological techniques hold much promise in the effort to understand this intriguing alternative to standard ketogenic diet [39]. Though no recommendation for a particular dietary regimen is given, the different implications on the parameters described are pointed out. The global population is aging, the disease is younger and the influence of modern lifestyle, the clinic promotes personalized anti-aging programs, natural nutritional prescriptions, and preventive medical health management to awaken the body’s original anti-aging self-healing power, allowing everyone to reverse the sub-healthy and healthy life, but it does also face the impact of modern diseases. It may be necessary to face the torture of the disease in advance, so the concept of health and advocating naturalness has gradually increased [40].
\nThe ketogenic diet is good for your health. This results in the production of ketones, acetoacetic acid, and β-hydroxybutyric acid. The body uses for acetoacetic acid or β-hydroxybutyric acid to burns body fats, they can lead to weight loss. The possible mechanisms are a decrease in lipogenesis, an increase in lipolysis, and an increase in the metabolic cost of gluconeogenesis. Sarcopenia, obesity and their coexistence, obese sarcopenia, as well as sarcopenic obesity, are among the greatest health concerns in the aging population. A clear age-dependent increased prevalence of sarcopenia and sarcopenic obesity has been registered in the ketogenic diet therapy patients, suggesting mechanistic relationships.
\nInflammation aging is a common ground for age-related sarcopenic obesity. Ketogenic diet therapy is observed greater weight loss compared with other balanced diets. The short-term ketogenic diet is by an almost carbohydrate-free oral diet might have weight loss effectively. Therefore, we suggest the benefits of the ketogenic diet and its risks including supports weight loss, reduce risk of cancers, improve heart health, protect brain function, aging-related sarcopenic obesity, and potentially reduces seizures. In this Chapter, we discuss the aging-related sarcopenic obesity. Nutrition, β-hydroxybutyric acid, in the early development of sarcopenic obesity, cardiomyopathy, dysbiosis and age-associated diseases is our future project. We want to know about sarcopenic obesity during COVID-19 lockdown restrictions. Like many difficult global health problems, the COVID-19 solutions maybe apparent but the logistics of implementing them may be lacking.
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