A Non-destructive Approach for Noise Reduction in Time Domain

Transcription

1 World Applied Science Journal 6 (1): 53-63, 29 ISSN IDOSI Publication, 29 A Non-detructive Approach for Noie Reduction in ime Domain A. Zehtabian and H. Haanpour School of Information echnology and Computer Engineering, Shahrood Univerity of echnology, Shahrood, Iran Abtract: In thi paper a new time domain noie reduction approach i preented. In exiting noie reduction technique, the tructure of the enhanced ignal might be lightly changed compared to the original ignal. In the propoed non-detructive approach, the noiy ignal i initially repreented in a Hankel Matrix. hen the Singular Value Decompoition (SVD) operator i applied on the matrix to divide the data into ignal ubpace and noie ubpace. Reducing the effect of noie from the ingular vector and uing them in reproducing the matrix, lead to ignificant enhancement of information embedded in the matrix. hi matrix i finally ued to obtain the time-erie ignal. here are everal important parameter, uch a ize of the matrix and the degree of the filter, affecting the performance of the propoed approach. hee parameter are optimally et uing the genetic algorithm. he reult of applying the propoed method on different ynthetic noiy ignal indicate it better efficiency in noie reduction compared to the other time erie method. he obtained reult alo indicate that uing the propoed approach keep the main tructure of the original ignal unchanged. Key word: ime erie Noie reduction SVD Singular value Singular vector Savitzky-golay filter Genetic algorithm INRODUCION Signal enhancement and noie reduction have wide application in ignal proceing. hey are often employed a a pre-proceing tage in variou application uch a audio conferencing, hand-free mobile telephony, cellular mobile communication, computer-baed peech recognition or peaker identification and etc. [1-7]. Since the nature and the characteritic of noie may ignificantly change from application to application, noie reduction i a very challenging problem. In addition, noie characteritic may vary in time. It i therefore very difficult to develop a veratile algorithm that work in diverified environment. Hence the objective of a noie reduction ytem may depend on the pecific context and application. wo point are often required to be conidered in ignal de-noiing application: eliminating the undeired noie from ignal to improve the Signal-tonoie Ratio (SNR) and preerving the hape and characteritic of the original ignal. he exiting noie reduction method reduce the noie by conidering ome prior aumption. Hence they are uitable for pecific application and condition [8, 9]. For example, in uing a typical Low Pa Filter (LPF), it i aumed that the noie i placed at the high frequency region of the noiy ignal. hi mean that the frequency band of noie and the clean ignal are ditinct. hi aumption may not be acceptable in variou condition and may retrict it application. In addition, a can be een in Fig. 1, low pa filter uch a thoe uing the convolution operator, caue hifting the ignal in time domain and changing the hape of the ignal lightly [1]. Depending on the domain of analye, the exiting noie reduction technique can be categorized into three group: time, frequency and time-frequency/time-cale domain. In time-cale baed approache, the ignal i ub-divided into everal frequency band uing wavelet tranform. he noie reduced ub ignal are then ued to recontruct the enhanced ignal. Extenive reearche have been accomplihed on the wavelet baed method with coniderable reult [11-13]. One of thee method i baed on the Bionic Wavelet ranform (BW), an adaptive wavelet tranform baed on a non-linear auditory model of the cochlear [14, 15]. In thi approach, the enhancement i the reult of threholding on the adapted BW coefficient. In [16], the author propoed a time-frequency baed approach for noie reduction. In thi approach, the Singular Value Decompoition (SVD) technique i applied on the Correponding Author: Dr. H. Haanpour, School of Information echnology and Computer Engineering, Shahrood Univerity of echnology, Shahrood, Iran 53

2 Convolution-Baed Filtering clean ignal noiy ignal low -pa filtering Amplitude Fig. 1: he effect of convolution-baed filtering on a noiy ignal: A Butterworth LPF wa applied on the noiy ignal with SNR=1 (bottom dahed line). Although the noie wa removed (dotted line), the hape of the enhanced ignal i not the ame a the original noie-free ignal (the top olid line) matrix of the time-frequency repreentation of the ignal. hi technique eparate noie ubpace and ignal ubpace uing ingular value of data matrix a criteria for ubpace diviion. hi time-frequency baed technique ha a good performance in reducing noie from both tationary and nontationary ignal. However, there are two deficiencie in the timefrequency baed approach for noie reduction. A high computational time i required for repreenting ignal in the time-frequency domain. In addition, ome time-frequency ditribution, uch a B-ditribution [17], cannot be yntheized to the time erie. here are a number of frequency domain baed approache that ue pectral ubtraction for noie reduction [18-23]. hee approache are only uitable for pecific application. For example, in [19] the noie i conidered to be tationary. In practice, however, the noie i uually nontationary. In another approach [23], the high frequency region of the ignal i ued to etimate the noie. hi approach can be ued to enhance peech ignal, a the high frequency region ha no ignal of human peech. It wa reported that thi approach need a high ampling rate (higher than 3 KHz). he Wiener filter i a well-known noie reduction technique among the time domain baed approache [24]. In thi method, the noiy ignal i paed through a Finite Impule Repone (FIR) filter whoe coefficient are etimated by minimizing the Mean Square Error (MSE) between the clean ignal and it 54 etimation to retore the deired ignal. hi filter i one of the mot fundamental approache for noie reduction, which can be formulated in the time and alo in the frequency domain. he Wiener filter i uually able to reduce noie in a ignal. However, the amount of noie reduction i often accompanied by ignal degradation. In other word, Wiener filter can be ued to reduce noie in a ignal if the SNR i high enough (uually higher than 4 db). When SNR for a ignal i low, uing Wiener filter may not be a uitable olution and may jut tranform the noie from one form to another [1, 24]. hi i a dicouraging factor in chooing Wiener filter for noie reduction. Recently, time domain baed approache for noie reduction have received coniderable attention among cientific reearche [25-27]. hee technique contruct a time data matrix of noiy ignal. he tructure of thee data matrice uually have the Hankel or oeplitz form, which have been introduced in [28-3]. In thi paper, we utilize the Hankel matrix to contruct the data matrix. hi data matrix i ubdivided into ignal ubpace and noie ubpace uing the SVD-baed approach introduced in [27]. In thi article the Savitzky-Golay low pa filter [31] i utilized to reduce noie from the ingular vector. he noie reduced ingular vector with the ingular value of the ignal ubpace are ued to recontruct the matrix. Subequently, thi noie-reduced matrix i ued to extract the time erie, repreenting the

3 (a) (b) (c) Fig. 2: Illutration of (a) an arbitrary white noie, (b) it autocorrelation and (c) it power pectrum noie-attenuated ignal. Some pecific parameter which are determined uing the genetic algorithm, uch a ize of the matrix and the degree of the filter, may affect the performance of our noie reduction approach. he organization of preent paper i a follow: Section 2 decribe the propoed SVD-baed noie reduction technique. he noie ubpace ubtraction i outlined in thi ection after a brief preliminary decription of the SVD operator. We propoe the utilization of the Savitzky-Golay filter to enhance the noiy ingular vector and how how applying the genetic algorithm can be ueful in the optimal etting of the parameter. In Section 3, the propoed noie reduction method i applied on tationary and non-tationary ignal and the reult are compared with thoe obtained uing other time-domain noie reduction method. Finally, the concluion are drawn in ection 4. SVD-BASED NOISE REDUCION ECHNIQUE Fig. 3: Normalized ingular value of the Hankel matrix contructed from a given noiy ignal ( 1) ( 2) ( ) n n n ( 2) ( 3) ( + 1) n n n ( ) ( + 1) ( ) n n n X X X K X X X K H = X L X L X N (2) Preliminarie: In many noiy acoutic environment uch a a moving car or train, or over a noiy telephone channel, the ignal i conidered to be infected by an additive random noie [1]. In thi paper, we uppoe that the clean ignal ha been corrupted by an additive white Gauian noie: X n = X + W n (1) where X n, X and W n denote noiy ignal, clean ignal and white Gauian noie, repectively. he white noie i defined a an uncorrelated proce with equal power at all frequencie (Fig. 2). he Hankel matrix i a quare matrix, in which all the element are the ame along any northeat to outhwet diagonal. In mathematical term each element of thi matrix can be expreed a a i,j = a i-1,j+1. For X n (i), I = 1,,N repreenting the noiy ignal, the Hankel matrix i contructed a follow: 55 Generally, the ingular value decompoition of matrix H with ize P Q i of the form: H = UΣV (3) where U P r and V r Q are orthogonal matrice and Σ i a r r diagonal matrix of ingular value with component σ ij= if i j and σ ij > and σ ij > Furthermore, it can be hown that σ 11 σ 22. he column of the orthogonal matrice U and V are called the left and right ingular vector repectively. Noie ubpace ubtraction: Subpace filtering i a technique that ha been proven very effective in the area of ignal enhancement [4]. Hence, to enhance information embedded in the Hankel matrix, we propoe dividing the data matrix into ignal ubpace and noie ubpace uing the ingular value. Since ingular vector are the pan bae of the matrix,

4 reducing the effect of noie from the ingular vector and uing them in reproducing the matrix, lead to further enhancement of information embedded in the matrix. Mathematically, the ubpace eparation can be expreed a below: Σ V H = UΣV = ( U ) U n Σ n Vn X = U U H = HV V W = U U H = HV V n n n n n where Σ and Σ n repreent the clean ignal ubpace and noie ubpace, repectively. A can be een from equation (4), we mut determine a threhold point in the Σ matrix where lower ingular value from that point can be categorized a noie ubpace and therefore hould be et to zero. o determine thi point, the ingular value of Σ matrix for a given imple noiy ignal are plotted, repect to their indice (Fig. 3). A break point can clearly be een in thi figure. Conidering thi break point a the threhold and etting the lower ingular value to zero lead to coniderable noie reduction. However, for more complicated ignal, determining thi threhold point i very challenging and need more attention. We have recently developed an approach to obtain thi threhold point, ee [1]. In that tudy, we had utilized the maximum lope of change in the ingular value curve. But in the propoed method we ue the genetic algorithm to find thi value a well a other important parameter. he procedure of thi technique will be explained in the following ubection. A mentioned above, our reearch indicate that the noie ubpace i mainly related to thoe ingular value that are lower than the threhold point. hu, we ugget etting thee ingular value to zero for pace diviion. o clarify the propoing method, the concept of matrix rank i decribed briefly. he rank of a matrix can be directly determined by the number of nonzero ingular value from it SVD. For example, when the clean data matrix i ymmetric (oeplitz) or per ymmetric (Hankel) and the data are inuoidal or complex exponential, with no additive noie, then the rank i equal to twice the number of real inuoid or the number of complex exponential preented in data [32]. But a noiy ignal ha much more nonzero ingular value which belong to the noie ubpace. Hence, they mut be et to zero for noie reduction. (4) (5) (6) 56 Enhancing the ingular vector: We have inferred from our experiment that by merely filtering the ingular value, ome noiy data will till be available in the ignal ubpace. hu beide the noie ubpace ubtraction, we mut filter the ingular vector (SV) for further noie reduction. Figure 4, illutrate the effect of noie on the U matrix (left ingular vector). In thi experiment, an arbitrary tationary ignal i infected by the db white Gauian noie. hen, the firt, third and fifth column of U matrix aociated with the clean and noiy ignal are plotted. A it can clearly be een in thi figure, the noie ha affected the original ignal left ingular vector (Fig. 4). In thi tudy, SV are treated a time-erie. o reduce the effect of noie on SV, we utilize the Savitzky-Golay filter. hi low-pa filter i uitable for moothing data in time erie a well a calculating the firt up to the fifth derivative. In the Savitzky-Golay approach, each value of the erie i replaced with a new value which i obtained from a polynomial fit to 2k+1 neighboring point. he parameter k i equal to, or greater than the order of the polynomial. he main advantage of thi approach in comparion with other adjacent averaging technique i that it tend to preerve the feature of the time erie ditribution. o further tudie, refer to [31]. In thi approach a polynomial of degree d i fit on n w conecutive data point from the time-erie, in which n w i the frame or window ize. Filtered ingular vector can be obtained a follow: i ( U ), i = 1 P i U = F,..., (7) Se S i ( V ), i = 1 Q i VSe = F S,..., (8) In the propoed approach, the amount of noie reduction depend on the degree and frame ize of the Savitzky-Golay filter. A illutrated in Fig. 6 and 7, chooing variou frame ize and polynomial degree for Savitzky-Golay filter lead to achieving different reult. In thi tudy, we have ditinguihed four crucial parameter affecting the performance of propoed noie reduction method. hey are the number of row l (in the data matrix), the optimum threhold point P cut needed for pace ubdiviion, the degree d and the window ize n w of Savitzky-Golay filter. o et thee parameter properly, we define a cot function and ue the genetic algorithm to minimize the cot. Once a filter i applied on a ignal, the level of udden change in ucceive ample i reduced. On the other hand, the enhanced ignal hould till be imilar to the noiy ignal after filtering ince thi i the

5 Noiy ignal with SNR= Firt Column of U matrixe.1 Original Signal Noiy Signal.5 Am Am (a) hird column of U matrixe (b) Fifth column of U matrixe Original Signal Original Signal.1 Noiy Signal.1 Noiy Signal.5.5 Am Am (c) (d) Fig. 4: Effect of noie on the column of U matrix: (a) original arbitrary ignal and it noiy verion with SNR= db; (b), (f) and (d): he effect of noie on the firt, third and fifth column of the U matrix, repectively he effectivene of Savitzky-Golay filtering Different Frame Size for Savitzky-Golay Filter =5 w Am =1 w =2 w =3 w Fig. 5: he reult of applying Savitzky-Golay filter on ingular vector of the noiy ignal. From top to bottom: clean ignal, noiy ignal with SNR=dB, the reult of ubtracting the noie ubpace per e, the reult of filtering the ingular vector a well a noie ubpace ubtraction 57 =4 w Fig. 6: he effect of uing different value a Savitzky-Golay window ize. From top to bottom: clean ignal, noiy ignal and the enhanced ignal after applying n w = 5, n w =15, n w =25, n w =35 and n w = 45, a the window ize of the Savitzky-Golay filter

6 Different Polynomial degree for Savitzky-Golay Filter For more detailed information about the genetic algorithm refer to reference [33]. he enhanced data matrix i then obtained uing: H e = U e Σ V e (1) Fig. 7: he effect of uing different value a Savitzky-Golay polynomial degree. From top to bottom: clean ignal, noiy ignal and the enhanced ignal uing d=5, d=4, d=3 and d=2, a the degree of the Savitzky-Golay filter. he window ize wa et to 15 only thing we know about the hape of the original ignal. Hence, we offer the following cot function for optimally tuning parameter of the filter: J(l,p,d,n ) = (1 α)( x(k) x (k)) cut w e n k +α x (k + 1) x (k) k where x n, x k and k repreent the noiy ignal, enhanced ignal and their ample number repectively. In thi equation, α i a factor determining moothne of the enhanced ignal and mut be choen between and 1. At the right ide of the above equation, the firt term indicate the ditance between the enhanced ignal and the noiy ignal; and the econd term indicate the moothne of the enhanced ignal. We minimize thi cot function uing genetic algorithm. he genetic algorithm i an iterative algorithm which randomly chooe ome value from the earch pace in each repetition. In thi algorithm, the enhanced ignal i initially computed uing ample of thee four parameter and then the cot function in (9) i calculated. In each repetition, the parameter are optimally choen to minimize the cot. After everal iteration, the final optimal parameter are achieved. e e (9) 58 where U e and V e are the enhanced verion of left and right ingular vector and Σ repreent the matrix containing the ignal ubpace ingular value. Finally, the enhanced ignal X e i extracted a follow: X e = [H e (1,1) H e (1,Q), H e (2,Q) H e (P,Q)] (11) PERFORMANCE EVALUAION o evaluate performance of the propoed approach, everal experiment have been carried out on multicomponent periodic ignal a well a linear FM (LFM) ignal corrupted by additive white Gauian noie. he reult of each experiment are decribed in the following ubection. Multi-component periodic ignal: Let x(t) =.2in(2π ft) + in(2 π(3f)t) +.5co(2 π(5f)t) + 1.5co(2 π (7f)t) +η(t) (12) repreent a multi-component ignal infected by noie η (t). In thi experiment, we ue thi ignal with f=25 Hz and the ampling frequency f i et to 2kHz. Performance of the propoed method i compared with that of Butterworth LPF and Wiener filter, which are conidered a time erie approache. he ignal in equation (12) wa filtered uing the three different approache and the time domain repreentation of the clean, noiy and enhanced ignal are hown in Fig. 8 for 5dB and db ignal-tonoie ratio (SNR). A the figure how, the convolution-baed filter (the low pa filter) can reduce the noie, but with the cot of hifting and lightly changing the hape of the ignal. hi deformation i proportional to the filter window length. Although there are no uch deficiencie in uing the Wiener filter, the noie attenuation level i le than the propoed method. In addition, Wiener filter i not able to reduce noie in a ignal with a low SNR. On the other hand, not only i the propoed method able to reduce the noie from ignal without any coniderable ditortion or deformation, but i able to reduce noie even where the SNR value i very low. In thi experiment, utilizing the

7 Multi-Component ine wave with SNR=5 Multi-Component ine wave with SNR= Pro Propoed Meth. Wiener Meth. LPF Meth. Noiy Sig. Clean Sig (a) (b) Fig. 8: Comparing the performance of the three different noie reduction technique on multi-component ignal corrupted by white Gauian noie with SNR=5 db (a) and SNR= db (b). In each ub-plot, from top to bottom: clean ignal, noiy ignal, output of LPF, Wiener filter and the propoed approach -1-2 PSD Welch of multi-component ignal with SNR=5 x xn propoed method LPF Wiener Filter -1-2 PSD Welch of multi-component ignal with SNR= x xn propoed method LPF Wiener Filter Po Power/frequency (db/hz) Frequency (khz) Frequency (khz) (a) (b) Fig. 9: Conidering PSD of the ignal on 1 realization to compare the performance of the three different noie reduction technique on multi-component ignal with SNR=5 db (a) and SNR= db (b) genetic algorithm lead to achieving the following optimum parameter. In the cae of 5dB noiy ignal, the number of row (l), the optimum threhold point (P cut ), the degree (d) and window ize (n w ) of the Savitzky-Golay filter are equal to 352,.1523, 3 and 5, repectively. On the other hand, in the cae of db noiy ignal, the above parameter obtain 37,.2392, 3 and 13, repectively. 59

8 Linear FM wave with SNR=5 Linear FM wave with SNR= Fig. 1: Pr Propoed Meth. Wiener Meth. LPF Meth. Noiy Sig. Clean ig (a) (b) Comparing the performance of the three different noie reduction technique on LFM ignal with SNR=5 db (a) and SNR= db (b) In each ub-plot, from top to bottom: clean ignal, noiy ignal, output of LPF, Wiener filter and the propoed approach o further evaluate performance of the three different de-noiing approache, it i deired to compare Power Spectrum Denity (PSD) of the clean and the enhanced ignal. Hence, we have computed the PSD of thee ignal uing the Welch type etimation method on 1 realization and the reult are hown in Fig. 9. A the figure how, the propoed method i able to retrieve the frequency information of the ignal better than either Wiener or LPF method, epecially where the SNR i very low. LFM ignal: he three approache in the previou experiment have been applied on linear FM ignal conidered a nontationary ignal. In thi experiment, the LFM ignal frequency begin from 1 Hz and terminate at 15 Hz. he ampling frequency i f = 4kHz and the number of ample i N = 6. he time domain repreentation of the clean, noiy and enhanced ignal are hown in Fig. 1. Similar to the previou Experiment, the LPF hift and deform the ignal. But deformation amount i more coniderable compared to the previou Experiment. hi event eem reaonable, becaue the noie and the clean ignal may have more overlap in frequency region for a LFM ignal. Hence by filtering the high frequency band of noiy ignal, ome noie may till be preent in the filtered ignal. On the other hand, Wiener filter ha a good performance when SNR i not le than about 4 db. Indeed, where the energy of noie i ignificant and SNR i low, the performance of Wiener filter drop dratically. A can be een in the figure, the propoed method i able to reduce the noie from the noiy nontationary ignal, even where the SNR i low and the frequency range of the ignal i wide enough. In thi experiment, utilizing the genetic algorithm reult in following optimum parameter: In the cae of 5dB noiy ignal, the number of row (l), the optimum threhold point (P cut ), the degree (d) and window ize (n w ) of the Savitzky-Golay filter are equal to 452,.1332,3 and 17, repectively; and for the cae of db noiy ignal, the above parameter obtain the value of 473,.3489, 3 and 19, repectively. he PSD of the linear FM ignal on 1 realization have been plotted in Fig. 11. It can be noticed that in the cae of LFM ignal, the PSD of the filtered ignal uing LPF may converge to the PSD of the clean ignal at very low power/frequency magnitude (in db) a properly a the one obtained uing the propoed method. But at higher power/frequency magnitude, the propoed method clearly demontrate it prominence in retrieving the frequency component of the clean ignal in comparion with the other approache. 6

9 able 1: he Monte-carlo imulation on 1 realization of different SNR value for the multi-component and LFM ignal Final SNR (db) Initial euclidean ditance Final euclidean ditance Initial SNR (db) Method Multi-component LFM Multi-component LFM Multi-component LFM 5 Wiener LPF Propoed approach Wiener LPF Propoed approach Wiener LPF Propoed approach Wiener LPF Propoed approach PSD Welch of FM wave with SNR=5 x xn propoed method LPF Wiener Filter -1-2 PSD Welch of FM wave with SNR= x xn propoed method LPF Wiener Filter Po -5 Po Fig. 11: Frequency (khz) Frequency (khz) (a) (b) Conidering PSD of the ignal on 1 realization to compare the performance of the three different noie reduction technique on LFM ignal with SNR=5 db (a) and SNR= db (b) Monte-carlo imulation: In thi ection, we have a performance comparion between the propoed method and the other approache uing the two mot common criteria, SNR and Euclidean ditance. In the firt criterion, the SNR i computed in the enhanced ignal and then compared with that of the noiy ignal. In uing the econd criterion, the Euclidean ditance between the clean and the noiy ignal i computed and then compared with the ditance between the clean and the enhanced ignal. Wherea the convolution-baed filtering of the ignal caue hifting in time domain and thi occurrence dratically affect the value of the 61 Euclidean ditance, the hifting effect of the filter i initially removed from the filtered ignal before meauring the criterion. he reult of Monte-Carlo imulation on 1 realization of different SNR value for the multicomponent and the LFM ignal are hown in able 1. hee reult attet that the propoed approach ha a better performance compared to the other exiting approache in noie reduction. he reult in thi table indicate that while SNR of the noiy ignal highly affect performance of Wiener filter, the propoed method can enhance the ignal even at the preence of

10 very energetic noie (SNR<2 db). Since, noie (epecially Gauian noie) ha a wide frequency activity; LPF cannot reduce noie at their pa-band frequency area. CONCLUSIONS he technique propoed in thi paper i a new approach for ignal enhancement in time domain. In thi paper the noie ubpace i initially eliminated from the ignal ubpace uing the SVD-baed technique. hen the ingular vector are filtered utilizing the Savitzky-Golay moothing filter. he optimal number of Hankel matrix row, the threhold point where the lower ingular value mut be et to zero, the polynomial degree and window ize of the Savitzky-Golay filter are determined uing the genetic algorithm. Reult in thi paper indicate the coniderable advantage of the propoed approach over the exiting approache for noie reduction in time domain. REFERENCES 1. Vaeghi, S.V., 26. Advanced Digital Signal Proceing and Noie Reduction. hird Edition. John Wiley and Son Ltd. 2. Winder, S., 22. Analog and Digital Filter Deign. NEWNESS Pub. Co. 3. Btocker, J., U. Parlitz and M. Ogorzalek, 22. Nonlinear Noie Reduction. Proceeding of the IEEE on Communication, Vol: 9 (5). 4. Hermu, K. and P. Wambacq, 24. Aement of Signal Subpace Baed Speech Enhancement for Noie Robut Speech Recognition. IEEE International Conference on Acoutic, Speech and Signal Proceing, pp: Doclo, S., I. Dologlou and M. Moonen, A novel iterative ignal enhancement algorithm for noie reduction in peech. 5th International Conference on Spoken Language Proceing (ICSLP98), Sydney, Autralia, pp: Lilly, B.. and K.K. Paliwal, Robut Speech Recognition Uing Singular Value Decompoition Baed Speech Enhancement. IEEE ENCON- Speech and Image echnologie for Computing and elecommunication, pp: Athanaeli,., S.E. Fotinea, S. Bakamidi, I. Dologlou and G. Giannopoulo, 23. Signal Enhancement for Continuou Speech Recognition. 13th International Conference on Artificial Neural Network and 1th International Conference on Neural Information Proceing (ICANN/ICONIP), LNCS 2714, pp: Hananpour, H., M. Mebah and B. Boahah, 24. ime-frequency Feature Extraction of Newborn EEG Seizure Uing SVD-Baed echnique. EURASIP Journal of Applied Signal Proceing, 16: You, C.-H., S.-N. Koh and S. Rahardja, 25. Subpace peech enhancement for audible noie reduction. In Proc. IEEE International Conference on Acoutic, Speech and Signal Proceing, pp: Haanpour, H., S.J. Sadati and A. Zehtabian, 28. An SVD-Baed Approach for Signal Enhancement in ime Domain. IEEE International Workhop on Signal Proceing and It Application. 11. Bahoura, M. and J. Rouat, 26. Wavelet peech enhancement baed on time-cale adaptation. Speech Communication Journal of ELSEVIER, 48: Chen, S.H., S.Y. Chau and J.F. Want, 24. Speech enhancement uing perceptual wavelet packet decompoition and teager energy operator. J. VLSI Signal Proceing Sytem, 36 (2-3): Hu, Y. and P.C. Loizou 24. Speech enhancement baed on wavelet threholding the multitaper pectrum. IEEE ranaction on Speech and Audio Proceing, 12 (1): Yao, J. and Y.. Zhang, 21. Bionic wavelet tranform: A new time-frequency method baed on an auditory model. IEEE ranaction on Biomedical Engineering, 48 (8): Johnon, M.., X. Yuan and Y. Ren, 27. Speech ignal enhancement through adaptive wavelet threholding. Speech Communication Journal of ELSEVIER, 49: Haanpour, H., 28. A ime-frequency Approach for Noie Reduction. Digital Signal Proceing, 18: Barkat, B. and B. Boahah, 21. A Highreolution Quadratic ime-frequency Ditribution for Multi-component Signal Analyi. IEEE ranaction on Signal Proceing, 49 (1): Yamahita, K. and. Shimamura, 25. Nontationary Noie Etimation Uing Low- Frequency Region for Spectral Subtraction. IEEE Signal proceing letter, Vol: 12 (6). 19. Boll, S.F., Suppreion of acoutic noie in peech uing pectral ubtraction. IEEE ranaction of Acoutic Speech Signal Proceing, 27 (2):

11 2. Paliwal, K.K., Etimation of noie variance from the noiy AR ignal and it application in peech enhancement. IEEE ranaction of Acoutic Speech Signal Proceing, 36 (2): Martin, R., Spectral ubtraction baed on minimum tatitic. In Proc. EUSIPCO, pp: Martin, R., 21. Noie power pectral denity etimation baed on optimal moothing and minimum tatitic. IEEE ran. Speech Audio Proceing, 9 (5): Yamauchi, J. and. Shimamura, 22. Noie etimation uing high frequency region for pectral ubtraction. IEICE tranaction on fundamental of electronic, communication and computer cience, E85-A (3): Chen, J., J. Benety, Y. Huang and S. Doclo, 26. New Inight Into the Noie Reduction Wiener Filter. IEEE ranaction on Audio, Speech and Language Proceing, 14 (4): Shin, K., J.K. Hammond and P.R. White, Iterative SVD Method for Noie Reduction of Low-Dimenional Chaotic ime Serie. Mechanical Sytem and Signal Proceing, Article No. mp Hermu, K., I. Dologlou, P. Wambacq and D. Van Compernolle, Fully Adaptive SVD-Baed Noie Removal for Robut Speech Recognition, ESA-PSI. 27. Haanpour, H., 27. Improved SVD-Baed echnique for Enhancing ime-frequency Repreentation of Signal. he IEEE International Sympoium on Circuit and Sytem (ISCAS), New Orlean, USA, pp: Lim, R.K., M.Q. Phan and R.W. Longman, State-Space Sytem Identification with Identified Hankel Matrix. Department of Mechanical and Aeropace Engineering echnical Report No. 345, Princeton Univerity, Princeton, NJ. 29. Gray, R.M., 26. oeplitz and Circulant Matrice: A review. Deptartment of Electrical Engineering, Stanford Univerity, Stanford 9435, USA. 3. Bottcher, A. and S.M. Grudky, 2. oeplitz Matrice, Aymptotic Linear Algebra and Functional Analyi. Birkh Auer. 31. Luo, J., K. Ying and J. Bai, 25. Savitzky-Golay moothing and differentiation filter for even number data. Signal Proceing, 85 (7): Andrew, M.S., Structured Subpace and Rank Reduction echnique for Signal Enhancement in Speech Proceing Application. PhD thei in Electrical Engineering, he Univerity of exa at Dalla, USA. 33. Sivanandam, S.N. and S.N. Deepa, 28. Introduction to Genetic Algorithm. Springer. 63