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A Voice Signal Filtering Methods for Speaker Biometric Identification

Written By

Eugene Fedorov, Tetyana Utkina and Tetyana Neskorodeva

Submitted: November 22nd, 2021Reviewed: December 12th, 2021Published: February 3rd, 2022

DOI: 10.5772/intechopen.101975

IntechOpen
Recent Advances in BiometricsEdited by Muhammad Sarfraz

From the Edited Volume

Recent Advances in Biometrics [Working Title]

Prof. Muhammad Sarfraz

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Abstract

The preliminary stage of the personality biometric identification on a voice is voice signal filtering. For biometric identification are considered and in number investigated the following methods of noise suppression in a voice signal. The smoothing adaptive linear time filtering (algorithm of the minimum root mean square error, an algorithm of recursive least squares, an algorithm of Kalman filtering, a Lee algorithm), the smoothing adaptive linear frequency filtering (the generalized method, the MLEE (maximum likelihood envelope estimation) method, a wavelet analysis with threshold processing (universal threshold, SURE (Stein’s Unbiased Risk Estimator)-threshold, minimax threshold, FDR (False Discovery Rate)-threshold, Bayesian threshold were used), the smoothing non-adaptive linear time filtering (the arithmetic mean filter, the normalized Gauss’s filter, the normalized binomial filter), the smoothing nonlinear filtering (geometric mean filter, the harmonic mean filter, the contraharmonic filter, the α-trimmed mean filter, the median filter, the rank filter, the midpoint filter, the conservative filter, the morphological filter). Results of a numerical research of denoising methods for voice signals people from the TIMIT (Texas Instruments and Massachusetts Institute of Technology) database which were noise an additive Gaussian noise and multiplicative Gaussian noise were received.

Keywords

  • announcer biometric identification
  • voice signal filtering methods
  • the smoothing adaptive linear filtering
  • a wavelet analysis threshold processing
  • the smoothing non-adaptive linear filtering
  • the smoothing nonlinear filtering

1. Introduction

The preliminary stage of the personality biometric identification on a voice is voice signal filtering. Methods of a signal cleaning from noise arose and gained broad development in the twentieth century. With development a wavelet analysis joined normal time and frequency filters a wavelet filter.

Noise (interference) is the sound of an undesirable additional source added to a desired signal during its record or transfer on communication channel.

Noise can be classified by the following features: periodicity/aperiodicity; additive/multiplicative; continuity/impulsivity; to band width in a signal spectrum; color.

By continuity/impulsivity, noises are divided into: continuous; pulse (point); continuous and pulse.

Noises are divided by band width on:

  • narrowband (noise with a continuous spectrum less than one octave);

  • broadband (noise with a continuous spectrum more than one octave).

From color noise by the most difficult for filtering the white noise which has a uniform energy spectrum in all frequency range. The most widespread kind of a white noise is Gauss’s noise.

Additive and multiplicative continuous and continuous impulse noises are removed from a signal by means of a wavelet analysis with threshold processing, the smoothing linear and many nonlinear filters, spectral subtraction. Impulse noises are removed many smoothing nonlinear filters. Additive aperiodic noise is removed low-frequency filters. Additive periodic noise is removed the bandpass and rejection filters.

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2. The smoothing adaptive linear time filtering

Adaptive linear time filters calllinear filters with adaptive impulse response function [1, 2, 3].

2.1 Algorithm of the minimum root mean square error

Algorithm of the minimum root mean square error which is applied to a signal xnsize N, is as follows [1]:

  1. Impulse response function initialization

    h=h1h2M+1=hMhM=00.E1

  • n=M.

  • Noise vector forming from a noise signal

    v=v1v2M+1=vnMvn+M.E2

  • Signal filtering (receiving noise estimates)

    zn=hTv.E3

  • Error signal current value calculation

    en=xnzn.E4

  • Impulse response function adaptation

    h=h+μven,E5

    where 0<μ<1.

  • If n<NMthen n=n+1, go to a step 2.

  • The signal is algorithm work result en, ensn.

    2.2 Recursive least squares algorithm

    Recursive least squares algorithm which is applied to a signal xnsize N, is as follows [1]:

    1. Initialization of impulse response function and adaptation matrix

    h=h1h2M+1=hMhM=00,P=p11p1,2M+1p2M+1,1p2M+1,2M+1=λI,E6

    where λ-regularization parameter which is small at a big ratio signal/noise and is big at a small ratio signal/noise.

    1. n=M.

    2. Noise vector forming

      v=v1v2M+1=vnMvn+M.E7

  • Signal filtering (receiving noise estimates)

    zn=hTv.E8

  • Error signal current value calculation

    en=xnzn.E9

  • Adaptive gain Γvector calculation

    Γ=PvvTPv+r,E10

    where 0<r<1.

  • Estimates covariance matrix Pcalculation

    P=1rPPvvTPvTPv+r.E11

  • Impulse response function calculation

    h=h+Γen.E12

  • If n<NMthen n=n+1, go to a step 2.

  • The signal is algorithm work result en, ensn.

    2.3 Kalman filtering algorithm

    Kalman filtering algorithm which is applied to a signal xnsize N, is as follows [1]:

    1. Estimates and white noise covariance matrixes:

    h=h1h2M+1=hMhM=00,P=p11p1,2M+1p2M+1,1p2M+1,2M+1=λI,E13
    Q=q11q1,2M+1q2M+1,1q2M+1,2M+1=σ12I,

    where λ—regularization parameter which is small at a big ratio signal/noise and is big at a small ratio signal/noise,

    σ12—variance of a white noise of process which has null mean value.

    1. n=M.

    2. Noise vector forming from a noise signal

      v=v1v2M+1=vnMvn+M.E14

  • Signal filtering (receiving noise estimates)

    zn=hTv.E15

  • Error signal current value calculation

    en=xnzn.E16

  • Adaptive gain Γvector calculation

    Γ=PvvTPv+σ22,E17

    where σ22—variance of a white noise of measurement which has null mean value.

  • Estimates covariance matrix Pcalculation

    P=PPvvTPvTPv+σ22+Q.E18

  • Impulse response function calculation

    h=h+Γen.E19

  • If n<NMthen n=n+1, go to a step 2.

  • The signal is algorithm work result en, ensn.

    2.4 Lee algorithm

    Lee algorithm [2] which is applied to a signal xnsize N, is as follows:

    1. Calculate local mean for each signal sample

      μn=12M+1mUnxm,nM,NM+1¯,E20

    where Un—sample nneighborhood size 2M+1.

  • Calculate local variance for each signal sample

    σx2n=12M+1mUnx2mμ2m,nM,NM+1¯.E21

  • Calculate variance for each signal sample

    σν2=1N2Mnσx2n,nM,NM+1¯.E22

  • Execute adaptive filtering of a signal

    sn=m=MMhmxnm,nM,NM+1¯.E23
    hm=12M+1+max0σx2nσν2σx2n112M+1,m=012M+1max0σx2nσν2σx2n12M+1,otherwise.E24

  • Example

    In Figure 1 the source signal, is presented on Figure 2—noisy (additive white is added the noise with a mean 0 and variance 0.001 is Gaussian), on Figure 3—filtered and M=1.

    Figure 1.

    Source signal for smoothing adaptive linear time filtering.

    Figure 2.

    A signal with an additive Gaussian noise for smoothing adaptive linear time filtering.

    Figure 3.

    The signal denoised by the adaptive filter.

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    3. The smoothing adaptive linear frequency filtering

    Adaptive linear frequency filters calllinear filters with adaptive transfer function [4].

    The smoothing adaptive linear frequency filtering is called spectral subtraction.

    Let Xpk—a noisy signal spectrum of on p-th a frame, Vk—mean noise spectrum, Spk—a mean of the restored signal on p-th a frame.

    Adaptive linear frequency filtering represents the inverse discrete Fourier transform of performing adaptive transfer function of the filter Hpkon p-th frame and signal spectrum Xpkon p-th a frame in a next form

    yn=1Nk=0N1XkHkej2πnkN.E25

    The following spectral subtraction methods are selected [1]:

    1. General method (proposed Beruti, Schwartz and Makhoul)

      Spk=HpkXpk,E26
      Hpk=GXpkγαVkγXpkγ1/γ,GXpkγαVkγXpkγ1/γγ>βVkβVk,otherwise,E27

    where G,α,β,γ—parameters.

  • The Ball method

    Hpk=XpkVkXpk,XpkVk>00,otherwise.E28

  • Wiener filtering

    Hpk=Xpk2Vk2Xpk2,Xpk2Vk2>00,otherwise.E29

  • The MLEE method

    Spk=HpkXpk,
    Hpk=12+12Xpk2Vk2Xpk2,Xpk2Vk2>00,otherwise.E30

  • Example

    In Figure 4 the source signal, is presented on Figure 5—noisy (additive white is added the noise with a mean 0 and variance 0.001 is Gaussian), the signals denoised by means of filtering according to general method (G=1,γ=2,α=6,β=0.1) (Figure 6), Ball (Figure 7), Wiener (Figure 8), MLEE (Figure 9). For these methods as frame length, it was selected ΔN= 512 (about 20 ms). In signal quality the word “Sasha” with a sampling rate of 22050 Hz, 8-bits, mono was selected.

    Figure 4.

    Source signal for smoothing adaptive linear frequency filtering.

    Figure 5.

    A signal with additive Gaussian noise for smoothing adaptive linear frequency filtering.

    Figure 6.

    The signal denoised by means of filtering according to general method.

    Figure 7.

    The signal denoised by means of filtering according to Ball.

    Figure 8.

    The signal denoised by means of filtering according to Wiener.

    Figure 9.

    The signal denoised by means of filtering according to MLEE.

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    4. Wavelet analysis threshold processing

    For a wavelet analysis the soft and rigid threshold processing is widely used [5].

    4.1 Signal analysis

    1. Initialization.

      Decompositions level number i=1.

      c0x=sx,x0,N/2i11¯,E31

    where sx—original signal length N.

  • On the current ith the decomposition level signal convolution with impulse response functions of FIR-HP (Finite Impulse Response—High Pass) and FIR-LP (Finite Impulse Response—Low Pass) filter is executed gk, hkrespectively

    dim=2k=0N2/2i11ci1,kgk+2m,m0,N/2i1¯,E32
    cim=2k=0N2/2i11ci1,khk+2m,m0,N/2i1¯.E33

  • If i<Pthen i=i+1, go to a step 1.

  • 4.2 Decomposition coefficients conversion

    1. Decompositions level number i=1.

    2. Create the vector arranged on increase

      ai=di0di,N/2i1,dim<di,m+1.E34

  • Calculate noise standard deviation based on a received vector median

    σi=medianai0.6745,E35

    where medianx—function which returns a median of a vector x.

  • Calculate one of the following thresholds

    1. Calculate a universal threshold

      Ti=σi2lnN/2i.E36

  • Calculate a SURE-threshold

    1. Define a threshold based on minimal risk

      rim=1+2m1+k=0m1aik2+aim2N/2i1mN/2i,m0,N/2i1¯,E37
      m=argminmrim,m0,N/2i1¯,T˜i=aim.E38

  • Calculate a SURE-threshold based on the received threshold

    Ti=σi2lnN/2i,m=0N/2i1dimN/2iσi2εiT˜i,m=0N/2i1dimN/2iσi2>εi,εi=σi2Nf/2ilnN/2i3.E39

  • Calculate a minimax threshold

    Ti=σi0.3936+0.1829lnN/2i,N/2i>320,N/2i32.E40

  • Calculate a FDR-threshold

    μi=m=1N/2i1aimN/2i1,Δim=erfc12aimμiσiqmN/2i1,m0,N/2i1¯,E41
    m=argminmsgnΔimsgnΔi,m+1,m0,N/2i2¯,Ti=aim,E42

    where q—parameter, q00.5, and it is normal q=0.05, erfcx—additional function of errors.

  • Calculate a Bayesian threshold (using Quasi-Cauchy distribution which is the most effective)

    1. Calculate function β(using Quasi-Cauchy distribution)

      βaim=gaimφaim1,m0,N/2i1¯,gx=γφx=12πx21ex2/2,E43
      φx=12πex2/2,γx=12πφxx1Φxφx,E44

    where φx—standard normal distribution density, γx—Quasi-Cauchy’s density of distribution.

  • Calculate the minimum parameter wivalue (using Quasi-Cauchy distribution)

    wimin=12T˜i2eT˜i2/21+ΦT˜iT˜iφT˜i12,T˜i=2lnN/2i.E45

  • Find parameter value wiby the equation numerical solution on an interval wimin1

    Siwi=m=0N/2i1βaim1+wiβaim=0.E46

  • Find a Bayesian threshold Tiby the numerical solution of the equation on an interval 0Tmax(using Quasi-Cauchy distribution)

    ΦTi+TiφTi+12+12Ti2eTi2/21/wi1=0.E47

  • Execute one of the following thresholds processing

    1. Execute soft threshold processing (for universal, minimax, Bayesian, a SURE-threshold)

      d˜im=dimTi,dimTidim+Ti,dimTi0,dimTi,m0,N/2i11¯.E48

  • Execute rigid threshold processing (for universal, minimax, Bayesian, SURE, a FDR threshold)

    d˜im=dim,dim>Ti0,dimTi,m0,N/2i11¯.E49

  • If i<Pthen i=i+1, go to a step 1.

  • 4.3 Signal design

    1. Initialization.

      Level number of recoveries i=P.

    2. On the current i-th the recovery level signal convolution with impulse response functions of FIR-HP and FIR-LP filter is executed gk, hkrespectively

      ci1,n=2m=0N/2i1cimhn+2m+2m=0N/2i1d˜imgn+2m,n0,N/2i11¯.E50

  • If i>1then i=i1, go to a step 1.

  • Example

    In Figure 10 the source signal, is presented on Figure 11—noisy (additive white is added the noise with a mean 0 and variance 0.001 is Gaussian), in Figure 12—filtered. The soft SURE-threshold with Daubechies wavelet with amount of the zero moments L=4was used (i.e., an order of FIR-HP and FIR-LP filter M=8).

    Figure 10.

    Source signal for wavelet analysis threshold processing.

    Figure 11.

    A signal with an additive Gaussian noise for wavelet analysis threshold processing.

    Figure 12.

    The signal cleaned using a wavelet analysis with threshold processing.

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    5. The smoothing non-adaptive linear temporary filtering

    The smoothing non-adaptive linear time filters are low pass filters [6].

    In case of the FIR-LP filter with symmetric impulse response function hM,,h0,,hM, non-adaptive linear time filtering represents convolution of non-adaptive impulse response function hmsignal xnas

    yn=m=MMhmxnm.E51

    Let us give impulse response functions of the most widespread two-dimensional smoothing linear filters:

    1. Impulse response function of the arithmetic mean filter

      hm=12M+1,mM,M¯.E52

  • Impulse response function of the normalized Gauss filter

    hm=12πσ2exp12m2σ2l=MM12πσ2exp12l2σ2,mM,M¯.E53

  • Impulse response function of the normalized binomial filter

    hm=C2MM+ml=02MC2Ml,Cnm=n!m!nm!,mM,M¯.E54

  • Example

    In Figure 13 the source signal, is presented on Figure 14—noisy (additive white is added the noise with a mean 0 and variance 0.001 is Gaussian), on Figure 15—filtered, wherein the arithmetic mean filter with M=1.

    Figure 13.

    Source signal for smoothing non-adaptive linear temporary filtering.

    Figure 14.

    A signal with an additive Gaussian noise for smoothing non-adaptive linear temporary filtering.

    Figure 15.

    The signal denoised by means of the arithmetic mean filter.

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    6. The smoothing nonlinear filtering

    The smoothing nonlinear filters [6] are low-pass filters.

    6.1 Geometric mean, harmonic mean, contraharmonic filters

    1. Geometric mean filter

      yn=m=MMxnm12M+1.E55

  • Harmonic mean filter

    yn=2M+1m=MM1xnm.E56

  • Contraharmonic filter

    yn=m=MMxQ+1nmm=MMxQnm.E57

  • Geometric mean, harmonic mean, contraharmonic filters delete additive and multiplicative continuous and continuous impulse noises.

    The harmonic mean filter in case of an impulse noise suppresses only white points.

    The contraharmonic filter in case of an impulse noise at Q>0suppresses only black points (at Q=1receive the harmonic mean filter), and at Q<0suppresses only white points. At Q=0receive the arithmetic mean filter.

    Therefore, for suppression of an impulse noise it is better to use α-trimmed mean, median or rank, conservative and morphological filters.

    6.2 α-trimmed mean filter

    Algorithm α-trimmed mean filtering applied to a signal xnsize N, is as follows:

    1. Create for each sample of a signal a vector from elements of its neighborhood Unsize 2M+1as

      an=xnMxn+M,nM,NM+1¯.E58

  • Sort for each sample of a signal element of its vector by increase

    a˜n=sortan,nM,NM+1¯.E59

  • Execute α-trimmed mean filtering of a signal in a form

  • yn=m=1+α/22M+1+α/2a˜nm2M+1α,nM,NM+1¯,E60

    where α—parameter, which multiple 2, 0α2M.

    At α= 0 we receive the arithmetic mean filter, and at α=2Mreceive the median filter. α-trimmed mean filter deletes additive and multiplicative continuous both continuous impulse noises and impulse noises.

    6.3 Median and rank filters

    Median filtering is defined in a form.

    yn=medianmUnxm,nM,NM+1¯.E61

    where Un—neighborhood of sample nsize 2M+1.

    Median filtering is a special case of rank filtering at a rank r=M+1. In case of rank filtering not the central sample, but sample which number corresponds to a rank undertakes r, and 1r2M+1.

    Median and rank filters delete additive and multiplicative continuous both continuous impulse noises and impulse noises.

    6.4 Midpoint filter

    Algorithm of the midpoint filtering applied to a signal xnsize N, is as follows:

    1. Calculate for each sample of a signal the minimum and maximum value in its neighborhood in a form

      αn=minmUnxm,βn=maxmUnxm,nM,NM+1¯,E62

    where Un—neighborhood of sample nsize 2M+1.

  • Signal midpoint filtering execute in a form

  • yn=12αn+βn,nM,NM+1¯.E63

    The Midpoint filter deletes additive and multiplicative continuous and continuous impulse noises.

    6.5 Conservative filter algorithm

    Conservative filtering algorithm applied to a signal xnsize N, is as follows:

    1. Calculate for each sample of a signal the minimum and maximum value in its neighborhood in a form

      αn=minmUn\nxm,βn=maxmUn\nxm,nM,NM+1¯.E64

    where Un—sample neighborhood nsize 2M+1.

  • Signal conservative filtering execute in a form

  • yn=xn,αn<xn<βnαn,xnαnβn,xnβn,nM,NM+1¯.E65

    The conservative filter deletes additive and multiplicative continuous both continuous impulse noises and impulse noises.

    6.6 Morphological filter

    Morphological filtering is carried out by consecutive performing operations of open and close or close and open. At open, operations dilatation and an erosion are consistently executed, and at close—an erosion and dilatation.

    Dilatation can be defined in a form.

    zn=maxmUnxmnM,NM+1¯.E66

    Erosion can be defined in a form.

    zn=minmUnxm,nM,NM+1¯,E67

    where Un—sample neighborhood n.

    The morphological filter deletes impulse noises.

    Example

    In Figure 16 the source signal, is presented on Figure 17—noisy (additive white is added the noise with an mean 0 and variance 0.001 is Gaussian), the signals denoised by means of the geometric mean filter (M=1) (Figure 18), α-trimmed mean filter (M=2, α=M=2) (Figure 19), median filter (M=2) (Figure 20), midpoint filter (M=1) (Figure 21), conservative filter (M=1) (Figure 22). In signal quality the syllable “sa” with a sampling rate of 22050 Hz, 8-bits, mono was selected.

    Figure 16.

    Source signal for smoothing nonlinear filtering of additive Gaussian noise.

    Figure 17.

    A signal with an additive Gaussian noise for smoothing nonlinear filtering.

    Figure 18.

    The signal denoised by means of the geometric mean filter.

    Figure 19.

    The signal denoised by means of the α-trimmed mean filter.

    Figure 20.

    The signal denoised by means of the median filter.

    Figure 21.

    The signal denoised by means of the midpoint filter.

    Figure 22.

    The signal denoised by means of the conservative filter.

    Example

    In Figure 23 the source signal, on Figure 24—noisy (the impulse noise “salt and pepper” with a noisiness of 1% of sample of a signal is added), the signals denoised by means of the α-trimmed mean filter (M=2, α=M=2) (Figure 25), the median filter (M=2) (Figure 26), the conservative filter (M=1) (Figure 27), the morphological filter (consistently executed by open and close with M=3) (Figure 28). In signal quality the syllable “sа” a sampling rate of 22050 Hz, 8-bits, mono was selected.

    Figure 23.

    Source signal for smoothing nonlinear filtering of impulse noise.

    Figure 24.

    A signal with an impulse noise “salt and pepper” for smoothing nonlinear filtering.

    Figure 25.

    The signal denoised by means of the α-trimmed mean filter.

    Figure 26.

    The signal denoised by means of the median filter.

    Figure 27.

    The signal denoised by means of the conservative filter.

    Figure 28.

    The signal denoised by means of the morphological filter.

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    7. Numerical research of denoising methods noise

    For the voice signals containing vocal sounds the sampling rate of 8 kHz and quantity of quantizing levels 256 was set.

    Numerical research results of denoising methods on a basis a wavelet analysis with threshold processing in case of Daubechies wavelet about 8 with soft threshold processing with a SURE-threshold, the adaptive filter about 1, it is Gaussian the filter about 1 with parameter σ=0.7, the arithmetic mean filter about 1, geometric mean filters about 1, harmonic mean filters about 1, contraharmonic filters about 1 with parameter Q=1, median filter about 2, α-trimmed mean filter of about 2 with parameter α=2, the midpoint filter about 1, conservative filters about 1 for voice signals people from the TIMIT database which were noise an additive Gaussian noise with mean 0 and variance 0.001 (a signal-to-noise ratio about 11 dB) and multiplicative Gaussian noise with mean 1 and variance 0.07 (a signal-to-noise ratio about 23 dB), are presented to Table 1, where MSE—Mean Square Error.

    Denoising method on a basisMSE
    Additive Gaussian noiseMultiplicative Gaussian noise
    Wavelet analysis with threshold processing11.280914.7860
    Adaptive filter9.907213.3914
    Gaussian filter14.339514.7662
    Arithmetic mean filter13.473814.0495
    Geometric mean filter15.584615.3252
    Harmonic mean filter20.429819.8623
    Contraharmonic filter13.355213.4845
    Median filter6.86976.5193
    α-Trimmed mean filter5.08434.9043
    Midpoint filter6.76676.4873
    Conservative filter9.02949.6437

    Table 1.

    Results of a numerical research of denoising methods from additive Gaussian noise and multiplicative Gaussian noise.

    The result is provided in Table 1 shows that the smallest MSE is provided α-trimmed mean filter.

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    8. Conclusion

    For biometric identification are considered and in number investigated the following methods of noise suppression in a voice signal. The smoothing adaptive linear time filtering (the minimum root mean square error algorithm, the recursive least squares algorithm, the Kalman filtering algorithm, the Lee algorithm), the smoothing adaptive linear frequency filtering (the generalized method, the MLEE method, a wavelet analysis with threshold processing (universal threshold, SURE-threshold, minimax threshold, FDR-threshold, Bayesian threshold were used), the smoothing non-adaptive linear time filtering (the arithmetic mean filter, the normalized Gauss’s filter, the normalized binomial filter), the smoothing nonlinear filtering (geometric mean filter, the harmonic mean filter, the contraharmonic filter, the α-trimmed mean filter, the median filter, the rank filter, the midpoint filter, the conservative filter, the morphological filter). Numerical research results of denoising methods for voice signals people from the TIMIT database which were noise an additive Gaussian noise and multiplicative Gaussian noise were received. The α-trimmed mean filter proved to be the most effective for both noise types.

    References

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    2. 2.Lim JS. Two-Dimensional Signal and Image Processing. Englewood Cliffs, NJ: Prentice Hall; 1990. p. 694
    3. 3.Rabiner LR, Schafer RW. Theory and Applications of Digital Speech Processing. Upper Saddle River, NJ: Pearson Higher Education, Inc.; 2011. p. 1042
    4. 4.Yektaeian M, Amirfattahi R. Comparison of spectral subtraction methods used in noise suppression algorithms. In: Proceedings of 6th International Conference on Information, Communications and Signal Processing (ICICS 2007). 2007. pp. 1-4
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    Written By

    Eugene Fedorov, Tetyana Utkina and Tetyana Neskorodeva

    Submitted: November 22nd, 2021Reviewed: December 12th, 2021Published: February 3rd, 2022