Empirical Mode Decomposition for Advanced Speech Signal Processing

Transcription

1 Joural of Sigal Processig, Vol.7, No.6, pp.5-9, Noveber 3 INVITED PAPER Epirical Mode Decopositio for Advaced Speech Sigal Processig Md. Khadeul Isla Molla,, Solal Das, Md. Eraul Haid ad Keiichi Hirose Departet of Iforatio ad Couicatio Egieerig, The Uiversity of Toyo, Toyo , Japa Departet of Coputer Sciece ad Egieerig, The Uiversity of Rajshahi, Rajshahi 65, Bagladesh E-ail: {olla, hirose}@gavo.t.u-toyo.ac.jp Abstract Epirical ode decopositio (EMD) is a ewly developed tool to aalyze oliear ad o-statioary sigals. It is used to decopose ay sigal ito a fiite uber of tie varyig subbad sigals tered as itrisic ode fuctios (IMFs). Such data adaptive decopositio is recetly used i speech ehaceet. This study presets the cocept of EMD ad its applicatio to advaced speech sigal processig paradigs icludig speech ehaceet by soft-thresholdig, voiced/uvoiced (V/Uv) speech discriiatio ad pitch estiatio. The speech processig is frequetly perfored i the trasfored doai ad the trasforatio is usually achieved by traditioal sigal aalysis techiques i.e. Fourier ad wavelet trasforatios. These aalysis ethods eploy priori basis fuctio ad it is ot suitable for data adaptive aalysis for o-statioary sigal lie speech. Recetly, EMD is tae uch attetio for speech sigal processig i data adaptive way. Several EMD based potetial soft-thresholdig algoriths for speech ehaceet are discussed here. The V/Uv discriiatio is a iportat cocer i speech processig. It is usually perfored by usig acoustic features. The traiig data is used to deterie the threshold for classificatio. The EMD based data adaptive thresholdig approach is developed for V/Uv discriiatio without ay traiig phase. Noticeable iproveet is achieved with the applicatio of EMD i pitch estiatio of oisy speech sigals. The related experietal results are also preseted to realize the effectiveess of EMD i advaced speech processig algoriths. Keywords: epirical ode decopositio, pitch estiatio, soft-thresholdig, speech ehaceet, voiced/uvoiced speech classificatio. Itroductio Epirical ode decopositio (EMD) is ewly developed tool to aalyze o-liear ad o-statioary sigals. Traditioal data aalysis ethods are all based o liear ad statioary assuptio of the sigals. Oly i recet years have ew ethods bee itroduced to aalyze o-statioary ad o-liear data. Wavelet aalysis ad the Wager-Ville distributio [, ] are desiged for liear but o-statioary data. Additioally, various o-liear tie series aalysis ethods [3-5] are desiged for oliear but statioary ad deteriistic systes. I ost real systes, either atural or eve a-ade oe, the data are ost liely to be both oliear ad ostatioary. Aalyzig the data fro such a syste is a dautig proble. Eve the uiversally accepted atheatical paradig of data expasio i ters of a priori established basis would eed to be eschewed, for the covolutio coputatio of a priori basis creates ore probles tha solutios. A ecessary coditio to represet oliear ad ostatioary data is to have a adaptive basis. A priori defied fuctio caot be relied o as a basis, o atter how sophisticated the basis fuctio ight be. A few adaptive ethods are available for sigal aalysis, as suarized i [6]. However, the ethods give i their boo are well desiged for ostatioary processes. For ostatioary ad oliear data, where adaptatio is absolutely ecessary, o available ethod ca be foud. Beig adaptive eas that the defiitio of the basis has to be data depedet, a a posteriori defied basis, a approach totally differet fro the established atheatical paradig for data aalysis. Therefore, the required defiitio presets a great challege to the atheatical couity. Eve though challegig, ew ethods to exaie data fro the real world are certaily eeded. A recetly developed ethod, epirical ode decopositio (EMD) [7-9] sees to be able to eet the requireet of posterior basis fuctio ecessary for adaptive data aalysis. EMD is a ethod of breaig dow a sigal without leavig the tie doai. It ca be copared to other aalysis ethods lie Fourier Trasfors ad wavelet decopositio. The process is useful for aalyzig atural sigals, which are ost ofte o-liear ad o-statioary. EMD filters out fuctios which for a coplete ad early orthogoal basis for the origial sigal. The fuctios, ow as Itrisic Mode Fuctios (IMFs), are therefore sufficiet to describe the sigal, eve though they are ot ecessarily orthogoal [8]. Locally, ay two copoets are orthogoal i ter of istataeous frequecy. The fact that the fuctios ito which a sigal is decoposed are all i the tie-doai ad of the sae legth as the origial sigal allows for varyig frequecy Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3 5

2 i tie to be preserved. Obtaiig IMFs fro real world sigals is iportat because atural processes ofte have ultiple causes, ad each of these causes ay happe at specific tie itervals. This type of data is evidet i a EMD aalysis, but quite hidde i the Fourier doai or i wavelet coefficiets. EMD also has several liitatios. The ost coprehesive studies o the perforace ad liitatios of EMD with particular applicatios to irregular waves are perfored i []. The authors ae extesive ivestigatio ito the splie iterpolatio ad discuss usig additioal poits, both forward ad bacward, to deterie better evelopes. They also perfored a paraetric study o the proposed iproveet ad showed sigificat iproveet i the overall EMD coputatios. It is liited i distiguishig differet copoets i arrowbad sigals []. If the frequecies of two copoets are very close, it is difficult to separate the by usig EMD. The adaptive ethod ca let the data reveal their uderlyig process without ay udue ifluece fro the basis fuctio. However, o atheatical odel exists for such approach. As etioed above, EMD is ost useful for oliear, o-statioary sigals, ad atural sigals. The EMD based approach is widely used i audio sigal processig [, 3], coputatioal eurosciece [4], cliate sigal aalysis [5], iage processig [6], seisic sigal [7] ad bioedical sigal processig [8]. This study focuses o the applicatio of EMD i advaced speech sigal processig icludig fudaetal frequecy estiatio [9], voiced/uvoiced speech classificatio [] ad speech ehaceet [, ]. The reaiig parts of the paper are orgaized as the basics of EMD ad its liitatios are described i Sectio, the EMD based approaches to speech sigal processig ad ehaceet are explaied i Sectio 3 ad Sectio 4 respectively, soe experietal results ad discussio are illustrated i Sectio 5 ad Sectio 6 icludes the cocludig rears.. EMD Basics Epirical ode decopositio (EMD) represets ay teporal sigal ito a fiite set of AM-FM oscillatig copoets which are bases of the decopositio. The ey beefit of usig EMD is that it is a autoatic decopositio ad fully data adaptive [3]. The priciple of the EMD techique is to decopose a sigal s( ito a su of the bad-liited fuctios d ( called itrisic ode fuctios (IMFs). Each IMF satisfies two basic coditios: (i) i the whole data set, the uber of extrea ad the uber of zero crossigs ust be the sae or differ at ost by oe, (ii) at ay poit, the ea value of the evelope defied by the local axia ad the evelope defied by the local iia is zero. The first coditio is siilar to the arrow-bad requireet for a statioary Gaussia process ad the secod coditio is a local requireet iduced fro the global oe, ad is ecessary to esure that the istataeous frequecy will ot have redudat fluctuatios as iduced by asyetric wavefors.. Uivariate EMD (uemd) The uivariate EMD (uemd) is used to decopose uivariate sigals ito a fiite set of IMFs. There exist ay approaches of coputig EMD [4]. The followig algorith is eployed here to decopose sigal s( ito a set of IMF copoets.. Set g ( = s(. Detect the extrea (both axia ad iia) of g ( 3. Geerate the upper ad lower evelopes h( ad l( respectively by coectig the axia ad iia separately with cubic splie iterpolatio 4. Deterie the local ea as: μ (=[h(+l(]/ 5. IMF should have zero local ea; subtract μ ( fro the origial sigal as: g (=g (-μ ( 6. Decide whether g ( is a IMF or ot by checig the two basic coditios as described above 7. Repeat steps to 6 ad ed whe with a IMF g ( Oce the first IMF is derived, defie (=g (, which is the sallest teporal scale i s(. To fid the rest of the IMF copoets, geerate the residue r ( of the data by subtractig ( fro the sigal s( as: The siftig process will be cotiued util the fial residue is a costat, a ootoic fuctio, or a fuctio with oly oe axia ad oe iia fro which o ore IMF ca be derived Speech sigal IMF IMF IMF 3 IMF 4 IMF 5 IMF 6 IMF Tie (s) Fig. Uivariate EMD (first 7 IMFs out of 3) of speech sigal The subsequet basis fuctios ad the residues are coputed as r,..., r r M M r () M where r M ( is the fial residue. At the ed of the decopositio the sigal s( is represeted as: r R s where r R ( is the fial residue which ca be either the () 6 Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

3 ea tred or a costat, ad fuctios ( are early orthogoal to each other, ad all have zero eas. The EMD (idividual IMF) of speech sigal is illustrated i Fig.. More specifically, the first copoet has the sallest tie scale which correspods to the fastest tie variatio of data. As the decopositio process proceeds, the tie scale icreases, ad hece, the ea frequecy of the ode decreases [4]. Sice the decopositio is based o the local characteristic tie scale of the data to yield adaptive basis, it is applicable to oliear ad ostatioary data i geeral ad i particular.. Istataeous frequecy of IMF Istataeous frequecy (IF) represets sigal s frequecy at ay tie istace ad it is defied as the rate of chage of the phase agle at the istat of the aalytic versio of the sigal. Every IMF is a real valued sigal. The discrete Hilbert trasfor (dht) is used to copute the aalytic sigal for a IMF. The the aalytic versio of the th IMF (is defied as: z j ( t ) jh d[ ] e (3) where ( ad ( are istataeous aplitude ad phase respectively of the th IMF. The discrete Hilbert trasfor H d [.] is defied as [5]: T ( ) Hd[ ( ] (4) t, t The aalytic sigal is advatageous i deteriig the istataeous quatities such as eergy, phase ad frequecy. The IF of th IMF is the give as the derivative of the phase ( calculated at t i.e. ~ f (5) t where ~ ( t ) represets the uwrapped versio of istataeous phase (. The derivative i Eq. (5), is evaluated at discrete istat of t. It should be oted that such derivative itroduces the abrupt fluctuatios of IF ad hece oliear soothig is required. Here, the ovig average soothig filter is used to reove such fluctuatios. The filterig schee iproves the effectiveess of coputig IF usig discrete derivative. The IF of idividual IMF show i Fig. is illustrated i Fig.. The cocept of IF is physically eaigful oly whe applied to oo-copoet sigals. I order to apply the cocept of IF to arbitrary sigals it is ecessary to decopose the sigal ito a series of oo-copoet cotributios. I the recet approaches [8], EMD techique decoposes a tie doai sigal ito a series of oocopoet IMFs. The the IF derived for each copoet provides the eaigful physical iforatio. Although the IMFs ay have frequecy overlaps but at ay tie istat, the istataeous frequecies represeted by each IMF are differet. This pheoeo ca be well uderstood i Fig. which shows the istataeous frequecies of the first 6 IMFs of the oisy speech sigal show i Fig.. Therefore, EMD is a effective decopositio of o-liear ad o-statioary sigals i ters of their local frequecy characteristics. With such property, each frequecy copoet of the sigal is clearly idetified ad localized i both tie ad frequecy scales yieldig the sigal spectra at each saplig poit. IF values IF of IMF IF of IMF IF of IMF 3 IF of IMF 4 IF of IMF 5 IF of IMF 6 IF of IMF Tie (s) Fig. Istataeous frequecies of the first 6 IMFs of oisy speech sigal show i Fig..3 Hilbert spectru Hilbert spectru represets the distributio of the sigal eergy as a fuctio of tie ad frequecy. It is also desigated as Hilbert aplitude spectru H(, or siply Hilbert spectru(hs). This process first oralizes the IF values. The uber of desired frequecy bis is a iput paraeter to costruct HS. The overall HS is expressed as the superpositio of the idividual IMFs HSs defied as: ( b) H(, H (, for b=,,,b []. Hece, each eleet H(, of the overall HS is defied as the weighted su of the istataeous aplitudes of all the IMFs at th frequecy bi. B ( ) H (, a w (6) b b ( ) where the weight factor w b taes if a b ( falls withi th bad, otherwise it is. After coputig the eleets over the frequecy bis, H represets the istataeous sigal spectru i tie-frequecy space as a D atrix. It is oted that the tie resolutio of H is equal to the saplig rate ad the frequecy resolutio ca be chose up to Nyquist liit [6]. Fig. 4 represets the Hilbert spectru (i db) of the voiced speech sigal show i Fig. usig 8 frequecy bis. The ethod of represetig the sigal i tie-frequecy doai usig Hilbert spectru obtaied by EMD together with Hilbert trasfor is also called Hilbert-Huag trasfor (HHT). b Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3 7

4 Noralized Frequecy Tie (s) Fig. 3 Hilbert spectru (HS) of speech sigal illustrated i Fig. The argial spectru represets the cuulated eergy over the etire data spa i a probabilistic sese at a frequecy idex. The argial power spectra correspodig to the Hilbert spectru H(, ca be defied as: T ( ) H (, (7) t where T is the total data legth. The argial HS plays a differet iterpretatio rather tha Fourier spectra []. I the Fourier spectra, the existece of eergy at a frequecy,, eas a copoet of a sie or a cosie wave persisted through the tie spa of the data. The Fourier eergy spectru clearly represets a stac of haroics. Whereas, the existece of eergy i argial Hilbert spectru at the frequecy,, eas oly that, i the whole tie spa of the data, there is a higher lielihood for such a wave to have appeared locally..4 Bivariate EMD (bemd) The traditioal EMD is oly suitable for uivariate (real valued) sigals. The coplex epirical ode decopositio (cemd) is a extesio of the basic EMD suitable for dealig with coplex sigals [7]. The otivatio to exted EMD is that a large uber of sigal processig applicatios have coplex sigals. I additio, this extesio is applied o both the real ad iagiary parts siultaeously because coplex sigals have a utual depedece betwee the real ad iagiary parts. Thus, if the decopositio is doe separately, the utual depedecy will be lost. The bivariate epirical ode decopositio (bemd) is ore geeralized extesio of EMD to coplex sigals. The ai differece betwee bemd ad cemd is that the latter uses the basic EMD to decopose coplex sigals, whereas bemd adapts the ratioale uderlyig the EMD to a bivariate fraewor [8, 9]. I bemd two variables are decoposed siultaeously based o their rotatig properties. The algorith of bemd, as proposed i [8], is as follows: ) For < q < Q, jq a) Project x( o directio q : p Re( e x( ) q q q b) Extract the axia of : ( t i, p ) p q i q q c) Iterpolate the set of poits ( ti, e pi ) to obtai the partial evelope curve i directio q aed e q ( ) Copute the ea of all tagets: e e (8) q q Q 3) Subtract the ea to obtai ˆ x( e( 4) Test if ˆ ( t ) is a IMF: If yes, repeat the procedure fro the step o the residual sigal. If ot, replace x( with ˆ ( t ) ad repeat the procedure fro step. The bivariate EMD ca ow be expressed as: x ( t ) ˆ ( t ) r (9) where ˆ deotes the th extracted coplex epirical ode ad r C ( the residual. bemd is eployed to decopose the speech sigals cotaiated by additive oise. Sig IMF IMF3 IMF5 IMF7 IMF9 IMF IMF3 IMF5 IMF7 Res Noisy speech sigal Tie (sec) C j q Fractial Gaussia oise (fg) Tie (sec) Fig. 4 The illustratio of bemd: A oisy speech sigal ad fg are decoposed together usig bemd. The oisy speech sigal ad fractioal Gaussia oise (fg) together are decoposed usig bemd as sow i Fig. 4. The oralized fg as well as the speech sigal are cosidered as real ad iagiary parts of the coplex sigal. It is well ow that EMD of fg acts as dyadic fitrer-ba [3]. With the use of fg i bemd, the decopositio of speech sigal associated with fg is cosidered as dyadic filter-ba. Sig IMF IMF3 IMF5 IMF7 IMF9 IMF IMF3 IMF5 IMF7 Res 8 Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

5 .5 Multivariate EMD (EMD) The ultivariate EMD (EMD) is ore geeralized extesio of EMD suitable for dealig with direct processig of ultivariate data for real world applicatios [3]. Stadard EMD revealed that IMFs ted to iic a filter ba-lie decopositio, siilar to wavelet decopositios. Multivariate EMD ot oly exposes filter ba structure, but also esures the overlappig of the frequecy resposes of the filters associated with IMFs of the sae idex fro ultiple chaels. To exted geeral idea of ultivariate sigals for EMD, iput data are straightforwardly processed i -diesioal spaces to geerate ultiple -diesioal evelopes by taig sigal projectios alog differet directios i -diesio spaces. The calculatio of the local ea ca be cosidered a approxiatio of the itegral of all the evelopes alog ultiple directios i a -diesios space. This step is coplex to perfor due to the lac of foral defiitio of axia ad iia i -diesioal doais i geeral EMD. The saplig based o low discrepacy Haersley sequece is used to geerate projectios of iput sigal i [3]. Oce the projectios alog differet directios i ultidiesioal spaces are obtaied, their extrea are iterpolated via cubic splie iterpolatio to obtai ultiple sigal evelopes. Thus obtaied evelopes are the averaged to obtai the local ea of the ultivariate sigal. The followig algorith proposed i [3] is eployed here to decopose sigal s( ito a set of IMF copoets.. Geerate the poitset based o the Haersley sequece for saplig o a (-)-sphere [3]; T. Calculate a projectio, deoted by p ( t )} t,of T the iput sigal { ( t )} alog the directio X s t vector, for all (the whole set of directio K vectors), givig t )} as the set of projectios; p ( K t i } 3. Fid the tie istats correspodig to the K axia of the set of projected sigals p ( t )} ; 4. Iterpolate [ t i, s ( t i ) ], for all values of, to K obtai ultivariate evelope curves t )} ; e ( 5. For a set of K directio vectors, calculate the ea μ( of the evelope curves as: K e () 6. Extract the detail d( usig d( = X( - μ(. If the detail d( fulfills the stoppage criterio for a ultivariate IMF, apply the above procedure to X(- d(, otherwise apply it to d(. Cosider a sequece of N-diesioal T vectors { s ( t )} ={s t (,s (,..s N (} represetig a ultivariate sigal with N copoets, ad X ={ x, x,..., xn } deotig a set of directio vectors alog the directios give by agles = {,,..., ( N ) } o a (-)-sphere. Oce the first IMF is extracted, it is subtracted fro the iput sigal ad the sae process is applied to the resultig sigal yieldig the secod IMF ad so o. I the ultivariate case, the residue correspods to a sigal whose projectios do ot cotai eough extrea to for a eaigful ultivariate evelope. The stoppig criterio for EMD of IMFs is siilar to stadard EMD [3], the differece beig that the coditio for equality of the uber of extrea ad zero crossigs is ot iposed, as extrea caot be properly defied for ultivariate sigals..6 Liitatios of EMD The EMD ethod has gaied soe recogitio over the past few years. The theoretical base has ot bee fully established. Up to this tie, ost of the progress with EMD has bee i its applicatios, while the uderlyig atheatical probles have bee ostly left utreated [33]. All the results have coe fro case-by-case coparisos coducted epirically. It is producig great results but waitig for atheatical foudatio o which to rest its case. We ca cosider square wave with costat aplitude over tie as show i Fig. 5. Aplitude sigal upper evelope lower evelope Tie (sec) Fig. 5 Square wave with costat aplitude over tie Theoretically, it cotais ifiite uber of haroics ad if it is decoposed usig Fourier trasfor, all the copoets will be extracted. No decopositio is possible usig EMD. The upper ad lower evelopes will be the straight lies ad their local ea value will zero. The aalyzig square wave will be treated as a IMF ad hece o ore IMF will be produced which does ot eet the theoretical hypothesis. Aother liitatio is that EMD requires high coputatioal power ad it is early ipossible to ipleet ay applicatio with EMD i real tie. It is required to uderstad the uderlyig decopositio process of EMD before applyig it to ay data. Ay sigal ca be aalyzed by atheatical odel based approach i.e. Fourier trasforatio while it is ecessary to ivestigate the data before applyig EMD for ultibad decopositio..7 Coparative study Hilbert-Huag Trasfor (HHT) is obtaied by cobiig EMD ad Hilbert spectral aalysis. Epirically, all tests idicate that HHT is superior tool for tiefrequecy aalysis of o-liear ad o-statioary sigals. It is based o the adaptive basis, ad the frequecy is Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3 9

6 defied through Hilbert trasfor. There is o eed for the spurious haroics to represet oliear wavefor deforatios as ay of the a priori basis ethods. There is o ucertaity priciple liitatio o tie or frequecy resolutio. A copariso of Fourier, wavelet ad HHT aalysis is suarized i Table. Table A coparative suary of Fourier, Wavelet ad Hilbert-Huag trasforatios Fourier Wavelet Hilbert Basis A priori A priori Adaptive Frequecy Global, ucertaity Regioal, ucertaity Local, certaity Presetatio Eergyfrequecy Eergy-tiefrequecy Eergy-tiefrequecy Noliear No No Yes No-statioary No Yes Yes Theoretical base Theory coplete Theory coplete Epirical 3. Speech Ehaceet The ters speech ehaceet ad speech cleaig properly refer respectively to the iproveet i the quality or itelligibility of a speech sigal ad the reversal of degradatios that have corrupted it. Although there are uerous ethods [] of speech ehaceet, this study focuses o soft-thresholdig based approach. The softthresholdig is the way to suppress the oise effects fro the oisy speech sigal by coparig the aalyzig sigal with a predefied threshold value. 3. Soft-thresholdig with DCT (sdct) I the trasfor doai, speech ehaceet ethods cooly use aplitude subtractio based soft thresholdig defied by [34, 35] Xˆ sig( X )( X v) if X v () otherwise where v deotes the oise level, X is the th coefficiet of the oisy sigal obtaied by the aalyzig trasforatio ad Xˆ represets the correspodig thresholded coefficiet. Sice all the coefficiets are thresholded by v, the speech copoets are also degraded durig this process. This degradatio results i a loss i speech quality. Ulie the covetioal costat oise-level subtractio rule i equatio Eq. (), a frae based soft thresholdig strategy is proposed i [36]. The strategy depeds o segetig the sigal ito short tie itervals ad applyig discrete cosie trasfor (DCT) o each frae. The DCT coefficiets of each frae are divided ito frequecy bis which are categorized as either sigal or oise doiat depedig o its speech ad oise eergy distributio. The classificatio pertais to the average oise power associated with that particular bi. If the ith bi satisfies the followig iequality, K K i X () where σ deotes the variace of the oise, X i is the th DCT coefficiet of the ith frequecy bi ad K (=64) is the uber DCT coefficiets of the bi, the the bi is characterized as sigal doiat, otherwise as oise doiat. The sigal doiat bis are ot thresholded, sice it is highly possible to degrade the speech sigal, especially for high SNRs. I the case of a oise doiat frequecy bi, the absolute values of the DCT coefficiets are sorted i ascedig order ad a liear thresholdig is applied: Xˆ sig( X )[ax{, ( X )}] (3) where j is the liear threshold fuctio obtaied as, K j j (4) K where j is the idex of sorted X. It is evidet fro Eq. () that for the oise-doiat frequecy bis, the average oise power added would be less tha the average oise power estiated over the etire speech sigal. Here, the added average oise power over ay of these frequecy bis is deoted as λσ. The reasoable value of λ (.35 to.8 [36]) is deteried experietally. Usig the categorizatio i Eq. () at each frequecy bi, the oise doiats are idetified ad value of λ is calculated by siply dividig the variace of that frequecy bi with the overall oise variace. 3. EMD based soft-thresholdig (semd) The data adaptive uemd ethod is ore suitable to decopose speech, o-statioary sigal yieldig better perforace i soft-thresholdig. The odified ethod is based o applyig the soft thresholdig algorith i Eq. (3) to the IMFs of the oisy speech. First, uemd is applied to the oisy speech. The obtaied IMFs are divided ito sub-fraes (8s). Siilar to the DCT case, these subfraes are characterized as either a sigal doiat or a oise doiat sub-frae. However, for categorizig the sub-fraes, ulie the liit defied i Eq. (), a differet strategy is itroduced [37]. This ew soft-thresholdig strategy provides a effective liit for the sub-frae categorizatio. Moreover, the oise variace used i thresholdig is estiated separately for each IMF. This ew strategy is applied to IMFs of the oisy speech sigal. The sub-fraes classificatio ito sigal ad oise doiats is oe of the ey poits of the soft thresholdig algorith. It aes possible to eliiate the oise sigals without degradig the origial speech copoets. It is ot feasible to use the soft-thresholdig directly to IMFs. Each IMF cotais differet oise ad speech eergy distributio, which suggests that each IMF will have a differet oise ad speech variace. Therefore, the oise variace of each IMF should be defied separately ad the liit for sub-frae categorizatio should have a larger value the the liit defied i Eq. (), i order to guaratee that all the oisy sub-fraes are thresholded. A j Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

7 ovel liit relies o the idea that a sub-frae ca be defied as a oise doiat sub-frae, if the oise power is higher tha the speech power. Therefore, the liit should be set to the case where the oise ad speech variace ( ad s ) are sae. The variace σ of the oise cotaiated speech sub-frae is represeted as, ( s, ) (5) s where (s,) is the covariace ter of sigal ad oise. If the sigal ad oise are idepedet, the covariace fuctio gives zero, thus we have (6) s For frae categorizatio (ito sigal ad oise doiat fraes), the threshold is cosidered with equal oise ad speech power, ad hece. Therefore, i case of equal oise ad speech power, the variace of the subfrae is equal to. That is why the liit for the categorizatio of the sub-frae i Eq. () should be set to this value. With the proposed strategy, if K K i X (7) where σ i deotes the variace of the oise ad X is the th saple of the ith sub-frae. The sub-frae is categorized as sigal doiat, otherwise as oise doiat. Noise doiat sub-fraes are thresholded as i Eq. (3) ad the oise variace i Eq. (4) is calculated separately for each IMF. variace ad the legth of the speechless parts of IMFs ca be observed i Fig. 6. The oise sigals are cocetrated i the lower order IMFs. The higher order IMFs are aily cotai the speech sigals. With this ethod we have a very good estiatio of oise variace of each IMF ad the oise copoets i all the IMFs ca effectively be reoved. 3.3 DCT-EMD hybrid soft-thresholdig (dctemd) The DCT-EMD hybrid algorith is based o applyig the soft thresholdig algorith i two stages. I the first stage, we use the soft thresholdig for DCT ehaceet algorith as a pre-process. As discussed above, this algorith is effective i reovig the oise copoets for a wide rage of SNR values. However, due to the thresholdig criteria, the oise sigals i the sigal doiat sub-fraes are ot reoved. Moreover, a sigificat aout of the oise sigals i the oise doiat sub-fraes reais withi the sigal due to the subtractio rule. Therefore a sigificat aout of oise still exists i the ehaced sigal. This loos lie a white oise ad results i a irritatig soud. It is ot a easy tas to detect these oise copoets ad to reove the without degradig the speech sigal. It is possible to extract a cosiderable aout of this residual oise i the secod stage fro the IMFs of the ehaced speech. Due to the frequecy characteristics of uemd, the oise ad speech sigals ostly doiate i differet IMFs. Maily, the high frequecy oise copoets cetre i the first few oes. Therefore a oticeable aout of high frequecy oise copoets that were i sigal doiat bis i the first stage ca be idetified fro the first IMFs of the ehaced speech. Fig. 6 Sorted oise variace of 8s sub-fraes for the first 6 IMFs of a oisy speech sigal at db The estiatio of the variace of each IMF plays a iportat role i the perforace of the EMD soft thresholdig algorith. The calculatio is achieved by a data adaptive, efficiet algorith. IMFs are divided ito sub-fraes (8s) ad the variace of each frae is stored i ascedig order i a variace array. Sice the speechless parts will ostly have the lowest variace, the oise variace of the sub-fraes ca be estiated fro these speechless parts of the array. Fig. 6 shows a plot of the variace of the sub-fraes for the first 6 IMFs of a oisy speech sigal at db. The differece betwee the oise Fig. 7 Spectrogras of (a) Clea speech, (b) Noisy speech corrupted with white oise at db SNR, (c) Recovered speech after soft thresholdig with sub-bad DCT, ad (d) Overall recovered speech of the DCT-EMD based hybrid ethod Siilarly, the lower frequecy oise sigals ca be idetified fro the later IMFs. The uemd based softthresholdig techique as described i Sectio 3. is applied i the secod stage to reduce the oise reaiig after the first stage of the hybrid ethod. The ehaceet perforace of DCT ad DCT-EMD based hybrid Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

8 ethods are illustrated i Fig. 7. It is observed that a oticeable aout oise reais after the first stage (DCT soft-thresholdig) as show i Fig. 7(c). I the secod stage, EMD based soft-thresholdig is applied to suppress the residual oise. The spectrogra of the overall recovered sigal i Fig. 7(d) illustrates the effectiveess of our proposed ethod. We ca observe that the spectrogra of the recovered sigal is very close to that of the clea speech sigal. 3.4 Adaptive soft-thresholdig (ASTh) Soft-thresholdig strategy proposed by Salahuddi i [36] is a powerful techique of speech ehaceet for a wide rage of iput SNRs. It thresholded oly the oise-doiat fraes ad ept reai the sae i case of the sigal-doiat fraes. The isclassificatio of fraes is a ajor drawbac that causes usical oise [38]. All the fraes are processed with a uique oise variace estiated globally fro the iput speech. May oise-doiat fraes ca be idetified as sigal-doiat due to the fluctuatios i the oise variace of the fraes whe oise eergy distributio is ot uifor over the speech. The drawbacs of traditioal soft-thresholdig algoriths are sigificatly reduced by adaptive thresholdig techique. The frae classificatio criteria described i [36] is odified. The soft thresholdig is applied o each IMF. It is ow that the thresholdig fuctio is depedet o the sigal (speech) ad oise variaces of each IMF. The sigal ad oise variaces are coputed for idividual IMF. Each IMF is divided ito sub-fraes ad soft thresholdig techique is applied o each sub-frae of o the basis of coputed variaces. The threshold fuctio is coputed for idividual IMF ad hece such thresholdig techique is tered as adaptive thresholdig. We calculate the oise variace of speech fro its silet part of the observed speech sigals. The sub-fraes are classified as either a speech doiat or a oise doiat based o the oise variace [39]. The adaptive thresholdig techique provides a effective boudary for the sub-frae classificatio. The soft thresholdig is carried out o each sub-frae of each IMF adaptively. After properly suppressig oises usig soft-thresholdig, all IMFs are sued up to obtai the ehaced speech sigal. The value of λ is a iportat factor softthrehsoldig ad its value is coputed adaptively as: /, where f ad represet the variace f of globally estiated oise ad that of oise added to the sub-frae respectively. I the experiet we use 5 differet speech sigals (fro TIMIT database) of db SNR degraded by white oise ad the variatios of λ are illustrated i Fig. 8. It ca be observed fro Fig. 8 that the value of λ varies i betwee.35 to.8 for all speech sigals. Therefore, the value of λ is selected i this rage experietally. The oise variace of idividual IMF is deteried fro the sorted variace array described i Sectio 3.) as show i Fig. 6. Fig. 8 Estiated values of λ i oise doiat subfraes The results of average output SNR usig EMD based thresholdig algorith is used to estiate the optiu adaptatio factor λ. I this experiet, the speech sigals of Eglish seteces uttered by 7 ale ad 7 feale are radoly selected fro TIMIT database. It is observed that the higher value of λ is ore effective at lower iput SNR ad lower value for higher iput SNR. For this reaso, we itroduce a expressio for the optiu value λ opt of adaptatio factor based o the iput SNR of the give oisy speech. The derived optiu value of λ iproves the perforace of uemd based ethod. The Iput SNR of oisy speech sigal is calculated i the siilar way of estiatig the oise variace of IMFs. The observed speech sigal is segeted ito fraes of legth s ad the variace of each frae is stored i a variace array i ascedig order. The oise variace of the oisy speech is estiated fro lower (sile parts of the array. The iput SNR ca be estiated as: s s SNR log log (8) iput where, ad are represet the observed, clea s s ad oise variace, respectively. It is foud that a specific value of adaptatio factor correspodig to a iput SNR produces the axiu output SNR. We itroduce a forulatio to copute the optiu value of λ for ay give iput SNR to achieve axiu speech ehaceet. The expressio to calculate the optiu adaptatio factor (λ opt ) is defied as 3 opt f ( v) p pv pv p3v (9) to fit the data poits (v i, w i ), i=,,.., d(=9); where v i ad w i are the iput SNR ad optiu value of λ (to obtai the axiu output SNR) respectively as listed i Table. We experietally foud that there is a oliear relatio betwee the iput SNR ad adaptatio factor, for that we choose a third degree polyoial to fit the o-liear data poits with iiu stable coefficiets [4]. To obtai the coefficiets, Eq. (9) ca writte as W=VP where W=[w, w,, w d ] T, P=[p, p, p, p 3 ] T ad V is a atrix with d rows. The i th row of V 3 ca be defied as Vi [ vi vi vi ]. The atrix represetatio W=VP ca also be writte as V T W=V T VP Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

9 ad hece the fial expressio to fid the coefficiet vector P is defied as: T T P ( V V ) V W () Equatio () is solved by usig least square ethod to obtai the values of the coefficiets P=[p, p, p, p 3 ] T. The the value of optiu adaptatio factor opt ca easily be calculated usig Eq. (4). It is ot ecessary to use the oly iput SNRs listed i Table. opt ca be coputed for ay give iput SNR satisfyig the least square fit ethod. Table Values of λ to obtai axiu output SNR for differet iput SNRs SNR iput λ Noise assisted Soft-thresholdig (NaSTh) The perfect estiatio of oise level is a priori to ipleet the soft-thresholdig based speech ehaceet algoriths. I the existig algoriths the oise is usually estiated fro the speechless part of the oisy speech sigal. Such ethod degrades the perforace of speech ehaceet whe the speechless is ot detected perfectly. Bivariate EMD (bemd) based approach is ipleeted for effective oise estiatio to derive the paraeters required for soft-thresholdig [4]. I bemd, two variables are decoposed siultaeously without losig utual depedecy. The fractioal Gaussia oise (fg) ad oisy speech sigal are decoposed together usig bemd producig two separate sets of IMFs correspodig to idividual sigals. It is foud that that the lower order (higher frequecy) IMFs cotributes higher eergies i fg. It is agreed with the assuptio that speech sigal cotais ore oise at higher frequecy ad hece it is justified to use the fg as the referece sigal to deterie the oise variace. Moreover, ore IMFs are geerated whe fg is cobied with speech to apply bemd. The aplitude of fg is adjusted accordig to the oise variace of the observed speech sigal. The effective estiatio of oise variace of the oisy speech plays a vital role to the perforace of the proposed bemd based speech ehaceet algorith. The speech sigal is cosidered as a soothly varyig sigal with additive Gaussia oise of zero ea ad both are ucorrelated fro each other. It ca be trasfored through a low order polyoial for as: f L l ( s ) a s l l () where L is the degree of polyoial. The purpose of the trasforatio is to fid out the variace of a rado variable y f (s) resultig fro the propagatio of the oisy speech sigal s through the oliear polyoial fuctio. The Taylor series expasio is used to obtai exact expressio of variace of the rado variable distributio [4]. The low order polyoial ters are suppressed usig filter based o a fiite differece expressio. So the iitial distributio ca be writte as:, where s is the expectatio value of s ad z is a s s z zero ea rado variable. The the Taylor expasio for y as l l L z d f y f ( s) () l l l! ds ss ad we ca deterie the first order oet l L l d f y E( y) f ( s) (3) l l l! ds ss where l deotes the th order oet of the rado variable z. The variace of a rado variable is its secod cetral oet, the expected value of the squared deviatio fro the ea [43]. Cosiderig agai the Taylor series expasio, the oise variace ca be coputed as follows E ( y y) y l l l L z d f L l d f E( ) l l (4) l l l! ds l! ds ss ss The overall oise variace thus obtaied is used to adjust the eergy of fg prior to the decopositio. The the derived fg is cobied with the oisy speech to for the coplex sigal to be decoposed by bemd. The observed speech sigal s( is cobied with fg, (, yieldig the coplex sigal x s( j(. After copletio of bemd, x( ca be expressed as su of coplex IMFs ( ad fial residue r C (. The real part a Re ˆ( represets IMFs of the speech sigal s( ad the iagiary part b I ˆ( correspods to IMFs of (. Hece, the idividual sigals ca be represeted as: M s( a Re r (5) M b I rc (6) IMFs are divided ito fraes ad the a frae by frae basis the oise variace of a( is copared with the variace of b( to classify the fraes ito sigal ad oise doiats. The variace of fg is used here as the referece oise variace. The thresholdig is perfored oly to the oise doiat fraes. This process copletely overcoes the liitatio of coputig oise variace fro silece part as required i the case of traditioal EMD based approach. The bemd based speech ehaceet algorith ca be suarized as: i) The overall oise variace is estiated fro observed speech sigal by Eq. (4) ad such variace is used to adjust the aplitude of fg. ii) Noisy speech sigal ad fg are cobied producig coplex sigal x(. iii) bemd is used to decopose x( ito coplex valued IMFs i which real ad iagiary parts correspod IMFs of speech ad fg, respectively. iv) Each IMF is divided ito sub-fraes (8s) to perfor very local soft-thresholdig. The frae variace of fg s IMF ad eergy of the correspodig frae of speech is coputed. v) The frae variace of fg is used as data adaptive referece eergy for biary classificatio of the C Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3 3

10 correspodig speech frae ito oise or sigal doiat. vi) Oly the oise doiat fraes are processed usig data adaptive soft-thresholdig. The optiu adaptatio factor is coputed usig Eq. (9). The sigal doiat fraes are left utouched. vii) All the processed IMFs of speech sigals are sued up to obtai the ehaced speech. Figure 9 shows the spectrogra of the speech cleaed by ASTh ad NaSTh as well as the clea ad oisy (db) speech sigals. It is observed that soe speech degradatio is occurred with ASTh while NaSTh does ot ae such loss of speech iforatio. Frequecy (Hz.) Frequecy (Hz.) Tie (sec.) (a) Tie (sec.) (b) 4. Voiced/uvoiced speech classificatio The efficiet classificatio of short tie speech sigal ito voiced ad uvoiced is a crucial preprocessig step i ay speech processig applicatios ad is essetial i ost aalysis ad sythesis syste. The essece of classificatio is to deterie whether the speech productio syste ivolves the vibratio of the vocal cords. The speech sigal origiated fro the speaer s vocal cords cotais a sequece of periodic correlatio. Such sigal is also called voiced speech sigal ad uvoiced with absece of periodically correlated sequeces. The voiced-uvoiced (V/Uv) discriiatio proble is a iportat oe ad has bee wored o extesively durig the last three decades [44]. The HHT based voiced/uvoiced speech classificatio is perfored i []. EMD is used to filter the additive oise with the speech sigal. The oralized autocorrelatio of the filtered speech sigal is coputed to ehace the periodicity if ay. Two features: the eergy ratio of the higher frequecy bad to that of the lower bads ad the zero-crossig rate (ZCR) coputed i autocorrelatio doai are used i classificatio. The etioed eergy ratio ad the ZCR both are lower for the voiced speech sigal ad that is relatively higher for the uvoiced speech sigals. Fig. shows the voiced ad uvoiced speech sigals ad its two (eergy based ad ZCR) features for each seget. There is a clear correlatio betwee the behaviors of the two features, providig strog basis for arig voiced ad uvoiced regios withi the sigal. Voiced ad uvoiced speech aplitude Frequecy (Hz.) (c) Tie (sec.) (d) Fig. 9 Spectrogra of (a) Clea speech, (b) Noisy speech corrupted with white oise at db SNR, (c) Recovered speech after adaptive soft-thresholdig with ASTh, (d) Ehaced speech usig bemd based NaSTh 4. Speech Aalysis The speech sigal processig with EMD is recetly tae ito attetio due to its data adaptive ature. The speech sigal is beig o-statioary, there are liited applicatios of traditioal priori basis based aalysis ethods i.e. Fourier ad wavelet trasforatio. The voiced/uvoiced speech classificatio ad fudaetal frequecy estiatio are two iportat issues. These issues ipleeted usig EMD are discussed here. value tie (s) Two features 3 ZCR Eergy ratio Frae idex Fig. Voiced-uvoiced speech sigals ad its correspodig features pair The argial Hilbert spectru (MHS) derived fro Hilbert-Huag trasforatio (HHT) represetig precise spectra of the sigal is eployed to derive the eergy based feature. It perfors better tha that of the Fourier based spectru. Although this ethod produces oticeable ehaceet of V/Uv discriiatio perforace, it requires traiig to deterie the threshold classificatio. A robust voiced/uvoiced classificatio ethod by usig liear odel of epirical ode decopositio (EMD) cotrolled by Hurst expoet is ipleeted i [45]. uemd decoposes ay sigals ito IMFs. It is assued that voiced speech sigal is coposed of tred due to vocal cord vibratio ad soe oises. No tred is preset i uvoiced speech sigal but i voiced oe. It is 4 Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

11 cosidered that the first IMF cotais oly the oise. A liear odel is developed that IMF. The a specified cofidece iterval of the liear odel is set as the data adaptive eergy threshold [46]. There exists higher eergy tred i the voiced speech sigal ad o tred is detected i uvoiced speech. If there exists at least oe IMF exceedig the threshold ad its fudaetal period is withi the pitch rage, the speech is classified as voiced ad uvoiced otherwise. The EMD based algorith is suarized here: a. The oisy speech sigal is decoposed usig uemd. The first IMF is cosidered as oise sigal b. Liear oise odel [46] is derived o the basis of eergy of the first IMF. Its upper liit of 99% cofidece iterval is defied as threshold. c. Costruct a set of IMFs whose eergies exceed the threshold. Deterie the fudaetal periods of those IMFs. d. If the fudaetal period of least oe IMF i is withi the pitch rage, the speech seget is classified as voiced ad uvoiced otherwise [45]. The eergy distributio of voiced ad uvoiced speech sigals alog with the correspodig oise odels are illustrated i Fig. ad Fig., respectively. The superiority of the algorith is that it does ot require ay traiig data. The threshold is deteried i a adaptive way o the basis of the curret speech frae. (a) (b) aplitude.5.5 log (eergy) oisy voiced speech sigal tie (s) 5 99% CI boudary Noise odel Speech sigal IMF Fig. (a) Noisy speech sigal (db SNR), (b) Eergies of IMFs 3-5 exceed the threshold of 99% cofidece iterval ad hece they collectively represet the tred of the sigal (a) (b) aplitude.5 oisy uvoiced speech.5 tie (s) 3 Log (eergy) 5 Noise odel 5 99% CI boudary Speech sigal IMF Fig. (a) Uvoiced speech sigal of db SNR, (b) Tred detectio sceario with uvoiced sigal: There is o IMF whose eergy exceeds the upper liit of 99% cofidece iterval ad hece the speech is uvoiced. 4. Pitch estiatio Pitch, the auditory attribute of speech sigal, is a iportat paraeter that is ofte deteried to easure the superiority of perforace of ay speech processig algoriths [47]. The estiatio of pitch period plays a iportat role i differet speech processig applicatios icludig speech ehaceet usig haroic odel, autoatic speech recogitio ad uderstadig, aalysis ad odelig of speech prosody, low-bit-rate speech codig etc. There are ay pitch estiatio algoriths available ow-a-days. Differet algoriths have bee ipleeted i the tie doai [48, 49] but oe of the eets the desired perforace of pitch estiatio. The pitch estiatio is also perfored i the trasfored doai. The trasforatio is usually achieved by traditioal Fourier [5] ad wavelet trasfors [5]. The speech sigal is beig o-statioary these trasforatios are ot suitable eough. As a data adaptive sigal aalysis tool EMD is recetly used for pitch estiatio [9, 5, 53]. A efficiet algorith for pitch deteriatio is ipleeted i [54] usig cobiatio of doiat haroic odificatio ad EMD. Its basic idea is to reshape the speech sigal usig a cobiatio of the doiat haroic odificatio (DHM) ad data adaptive tie doai filterig techiques. The oisy speech sigal is filtered withi the rages of fudaetal frequecies (5-5Hz) to obtai the pre-filtered sigal (PFS). The doiat haroic (DH) of the PFS is deteried ad ehaced its aplitude. The doiat haroic is the frequecy with axiu eergy i Fourier doai. Noralized autocorrelatio fuctio (NACF) is applied to that odified sigal. The epirical ode decopositio (EMD) based data adaptive tie doai filterig is applied to the NACF sigal. Partial recostructio is perfored i EMD doai. The pitch period is deteried fro the partially recostructed sigal. The perforace of the EMD based algorith is better tha the other recetly developed ethods for oisy ad clea speech sigals. The proposed algorith for pitch estiatio is as follows: aplitude.5 (a) (b) Origial Speech Noisy Speech Pre Filtered Speech (c) tie (s) Fig. 3 (a) Clea speech, (b) Noisy speech (db SNR) ad (c) Pre-filtered speech (PFS) Apply pre-filterig to the oisy speech sigal to reove a sigificat portio beyod the pitch rage Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3 5

12 5-5Hz. It is tered as pre-filtered speech (PFS) as show i Fig. 3. Perfor sigal odificatio usig doiat haroic ehaceet [55] to the PFS sigal. Copute NACF of the odified sigal Apply EMD to NACF of the odified sigal show i Fig. 4. Pitch period ref pitch EMD DHM IMF IMF IMF3 IMF lag (saples) Fig. 4 EMD of NACF with DHM of sigal show i Fig. 3 Aplitude Aplitude Su up IMFs whose fudaetal period lies withi the specified pitch rage for partial recostructio of NACF of the odified PFS. The origial ad partially recostructed sigals are show i Fig NACF with DHM Sigal Recostructed fro NACF (with DHM) usig EMD Lag (saple) Fig. 5 NACF of the sigal after perforig the DH ehaceet (top), the partially recostructed sigal fro NACF with DHM usig EMD (botto): The d ad 3 rd IMFs are added for partial recostructio. Tae the right half of the recostructed sigal. The aplitude at zero-lag is selected as the startig idex of the pitch period. Fid the ext highest pea fro the right half of the recostructed sigal. Calculate the pitch period fro the differece betwee the startig idex ad the ext highest pea idex. The perforaces of differet pitch estiatio algoriths are illustrated i Fig Frae idex Fig. 6 Copariso of preliiary pitch period estiated by EMD (proposed) ad DMH [55] ethods with the referece pitch for ale speech: The proposed EMD based ethod perfors better tha DHM. 5. Coclusios A detail study o advaced speech sigal processig usig EMD is preseted here. It cosists of EMD based soft-thresholdig, voiced/uvoiced speech discriiatio ad effective pitch estiatio of oisy speech sigals. The soft-thresholdig based speech ehaceet is a potetial approach to speech ehaceet which is usually perfored i the trasfored doai rather tha the origial tie doai of the oisy speech sigals. The discrete cosie trasfor ad wavelet trasfor are widely used i soft-thresholdig. These trasforatios use priori basis fuctios which are ot suitable for o-statioary speech sigal. EMD is suitable to decopose ay ostatioary ad o-liear sigal ito a fiite set of subbad sigals. It is fully data adaptive ad does ot require ay priori basis fuctio. Differet soft-thresholdig algoriths based o EMD are developed recetly with higher perforace i speech ehaceet. The perfect detectio of threshold value is a crucial factor to obtai better perforace i soft-thresholdig based algorith. The adaptatio factor is a iportat ter which is used to weight the threshold. Several algoriths (semd, dctemd) use costat value of ad soe algoriths (ASTh, NaSTh) eploy the value of adapted with iput SNR. The latter category perfors better. EMD is recetly used i advaced speech sigal aalysis. The voiced/uvoiced speech discriiatio is a iportat issue i speech aalysis. It is usually perfored usig differet acoustic features. A extesive traiig is required to deterie the threshold for classificatio. The data adaptive EMD based approach is itroduced for V/Uv classificatio without ay traiig. The threshold value is adaptively deteried i each speech seget. It is ore effective i real world applicatio. Aother iportat speech aalysis techique is the perfect estiatio of fudaetal frequecy (pitch). The error i pitch estiatio is usually occurred due to the half-pitch ad double-pitch errors. A EMD based pre-filterig approach is recetly itroduced [55] to reduce such errors ad hece better perforace is achieved. EMD requires very high coputatioal power which does ot support to ipleet olie processig syste. It is suitable whe oly for the case of offlie processig. It is fully reversible ethod. Whe the syste requires the recostructio of decoposed sigal, EMD perfors better. 6 Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3

13 It has very poor capability of frequecy doai represetatio of the aalyzig sigal. Oe should thi about the etioed iportat characteristics of EMD before cosiderig it for ay applicatio. The research couity of sigle chael speech ehaceet will be greatly beefited fro this study. Refereces [] P. Fladri: Tie-Frequecy/Tie-Scalfe Aalysis, Acadeic Press, 999. [] K. Grocheig: Foudatio of Tie-Frequecy Aalysis, Birhauser,. [3] H. Tog: Noliear Tie Series Aalysis, Oxford Uiversity Press, 99. [4] H. Katz ad T. Schreiber: Noliear Tie Series Aalysis, Cabridge Uiversity Press, 999. [5] C. Dis: Noliear Tie Series Aalysis: Methods ad Applicatios, World Scietific Press, 999. [6] B. Widrow ad S. D. Stears: Adaptive Sigal Processig, Pretice Hall, 985. [7] N. E. Huag, S. R. Log ad Z. She: The echais fir frequecy dow-shift i oliear wave evolutio, Adv. Appl. Mech., Vol. 3, pp. 59-, 996. [8] N. E. Huag et al.: The epirical ode decopositio ad Hilbert spectru for oliear ad o-statioary tie series aalysis, Proc. R. Soc. Lodo, Ser. A, Vol. 454, pp , 998. [9] N. E. Huag, Z. She ad S. R. Log: A ew view of water waves The Hilbert spectru, Au. Rev. Fluid Mech., Vol. 3, pp , 999. [] M. Datig ad T. Schlura: Perforace ad liitatios of the Hilbert-Huag trasforatio (HHT) with a applicatio to irregular water waves, Ocea Eg., Vol. 3, No. 4, pp , 4. [] Y. Che ad M. Q. Feg: A techique to iprove the epirical ode decopositio i the Hilbert-Huag trasfor, Earthquae Egieerig ad Egieerig Vibratio, Vol., No., pp , 3. [] M. K. I. Molla ad K. Hirose: Multibad liear predictio of speech sigals with adaptive order usig epirical ode decopositio, Joural of Sigal Processig, Vol., No. 6, pp , 7. [3] K.-H. Wu, C.-P. Che ad B.-F. Yeh: Noise-robust speech feature processig with epirical ode decopositio, EURASIP Joural o Audio, Speech, ad Music Processig, Vol., pp. -9,. [4] A. Pigorii et. al.: Tie-frequecy spectral aalysis of TMS-evoed EEG oscillatios by eas of Hilbert-Huag trasfor, J Neurosci Methods, Vol. 98, No., pp ,. [5] J. I. Salisbury ad M.Wibush: Usig oder tie series aalysis techiques to predict ENSO evets fro the SOI tie series, Noliear Processes i Geophysics, Vol. 9, pp ,. [6] J. C. Chag, M. Y. Huag, J. C. Lee, C. P. Chag ad T. M. Tu: Iris recogitio with a iproved epirical ode decopositio ethod, Optical Egieerig Vol. 48, No. 4, pp , 9. [7] J. Ha ad M. va der Baa: Epirical ode decopositio for seisic tie-frequecy aalysis, Geophysics, Vol. 78, No., pp. 9-9, 3. [8] A. Karagiais ad P. Costatiou: Noise copoets idetificatio i bioedical sigals based o epirical ode decopositio, It. Cof. o Iforatio Techology ad Applicatios i Bioedicie, pp. -4, 9. [9] H. Huag ad J. Pa: Speech pitch deteriatio based o Hilbert-Huag trasfor, Sigal Processig, Vol. 86, No. 4, pp , 6. [] M. K. I. Molla ad K. Hirose: Robust voiced/uvoiced classificatio of speech sigals usig Hilbert-Huag trasforatio, Joural of Sigal Processig, Vol., No. 6, pp , 8. [] M. K I Molla, K. Hirose ad N. Mieatsu: Separatio of ixed audio sigals by decoposig Hilbert spectru with odified EMD, IEICE Tras. Fudaetals of Electroics, Co. ad Coputer Sciece, Vol. E89-A, No. 3, pp. 7-34, 6. [] M. K. I. Molla ad K. Hirose: Sigle ixture audio source separatio by subspace decopositio of Hilbert spectru, IEEE Tras. Audio, Speech, ad Laguage Processig, Vol. 5, No. 3, pp: 893-9, 7. [3] P. Fladri, G. Rillig ad P. Goqalves: Epirical ode decopositio as a filter ba, IEEE Sigal Processig Letters, Vol., No., pp. -4, 4. [4] B. Z. Wu ad N. E. Huag: A study of the characteristics of white oise usig the epirical ode decopositio ethod, Proc. Roy. Soc. Lodo A, Vol. 46, pp , 4. [5] D. G. Log: Coets o Hilbert trasfor based sigal aalysis, MERS Techical Report, Id: MERS 4-, Brigha Youg Uiversity, USA, 4. [6] N. E. Huag, et al.: Applicatio of Hilbert-Huag trasfor to o-statioary fiacial tie series aalysis, Applied Stochastic Model i Busiess ad Idustry, Vol. 9, pp , 3. [7] T. Taaa ad D. P. Madic: Coplex epirical ode decopositio, IEEE Sigal Processig Letters, Vol. 4, No., pp. -4, 7. [8] G. Rillig, P. Fladri, P. Goc alves ad J. Lilly: Bivariate epirical ode decopositio, IEEE Sig. Proc. Lett., Vol. 4, No., pp , 7. [9] M. U. Altaf, T. Gautaa, T. Taaa ad D. P. Madic: Rotatio ivariat coplex epirical ode decopositio, Proc. of IEEE It. Cof o Acoust. Speech ad Sigal Proc. (ICASSP), Vol. III, pp. 9-, 7. [3] N. Reha ad D. P. Madic: Multivariate epirical ode decopositio, Proc. of the Royal Society A, Vol. 466, pp. 9-3,. [3] N. Reha ad D. P. Madic: Filter ba property of ultivariate epirical ode decopositio, IEEE Tras. Sigal Processig, Vol. 59, pp. 4-46,. [3] N. E. Huag et. at.: A cofidece liit for the epirical ode decopositio ad Hilbert spectral aalysis, Proc. R. Soc. Lod. A, Vol. 459, pp , 3. [33] N. E. Huag ad S. R. Log: Noralized Hilbert trasfor ad istataeous frequecy, NASA Patet Pedig, GSC 4, 673-, 3. [34] D. L. Dooho: De-oisig by soft thresholdig, IEEE Tras. If. Theory, Vol. 4, pp , 995. [35] M. Bahoura, ad J. Rouat: Wavelet speech ehaceet based o the teager eergy operator, IEEE Sigal Proc. Lett., Vol. 8, pp. -,. [36] S. Salahuddi, S. Z. Al Isla, M. K. Hasa ad M. R. Kha: Soft thresholdig for DCT speech ehaceet, Electroics Letters, Vol. 38, pp ,. [37] E. Deger, M. K. I. Molla, K. Hirose, N. Mieatsu ad M. K. Hasa: EMD-based soft-thresholdig for speech ehaceet, Proc. of INTERSPEECH, pp.8-83, 7. Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3 7

14 [38] E. Deger, M. K. I. Molla, K. Hirose, N. Mieatsu ad M. K. Hasa: Speech ehaceet usig soft thresholdig with DCT-EMD based hybrid algorith, Proc. of EUSIPCO, pp , 7. [39] S. Das, M. E. Haid, K. Hirose ad M. K. I. Molla: Siglechael speech ehaceet by NWNS ad EMD, Sigal Processig: A Iteratioal Joural (SPIJ), Vol. 3, No. 5, pp. 79-9,. [4] M. E. Haid, S. Das, K. Hirose ad M. K. I. Molla: Speech ehaceet usig EMD based adaptive soft-thresholdig (EMD-ADT), It. Joural of Sigal Processig, Iage Processig ad Patter Recogitio Vol. 5, No., pp. -6,. [4] M. E. Haid, M. K. I. Molla, X. Dag ad T. Naai: Sigle chael speech ehaceet usig adaptive softthresholdig with bivariate EMD, ISRN Sigal Processig, Vol. 3, pp. -9, 3. [4] M. B. Luca, S. Azou, G. Burel ad A. Serbaescu: O exact Kala filterig of polyoial systes, IEEE Tras. Circuits ad Systes I, Vol. 53, No. 6, pp , 6. [43] A. Kaga ad L. A. Shepp: Why the variace?, Statistics ad Probability Letters, Vol. 38, No. 4, pp , 998. [44] S. Ahadi ad A. S. Spaias: Cepstru-based pitch detectio usig a ew statistical V/UV classificatio algorith, IEEE Tras. Speech Audio Pro., Vol. 7 No. 3, pp , 999. [45] M. K. I. Molla, K. Hirose, S. K. Roy ad S. Ahad: Adaptive thresholdig approach for robust voiced/uvoiced classificatio, Proc. of IEEE It. Sypo. o Circuits ad Systes (ISCAS), pp. 49-4,. [46] G. Rillig, P. Fladri ad P. Gocalves: Detredig ad deoisig with epirical ode decopositio, Proc. of EUSIPCO, pp , 4. [47] W. Hess: Pitch Deteriatio of Speech Sigals: Algoriths ad Devices, Spriger, Berli, 983. [48] K. Kasi ad S. A. Zahoria: Yet aother algorith for pitch tracig, Proc. of IEEE It. Cof o Acoust. Speech ad Sigal Proc. (ICASSP), pp ,. [49] T. Shiaura ad H. Kobayashi: Weighted autocorrelatio for pitch extractio of oisy speech, IEEE Tras. Speech ad Audio Proc., Vol. 9, No. 7, pp ,. [5] J. C. Brow ad M. S. Pucette: A high resolutio fudaetal frequecy deteriatio based o phase chages of the Fourier trasfor, J. Acoust. Soc. A. Vol. 94, No., pp , 993. [5] N. A. Kader: Pitch detectio algorith usig a wavelet correlatio odel, Proc. of Radio Sciece Coferece, pp. C33/ - C33/8,. [5] M. K. I. Molla, K. Hirose, N. Mieatsu ad M. K. Hasa: Pitch estiatio of oisy speech sigals usig epirical ode decopositio, Proc. of EUROSPEECH, pp , 7. [53] Z. Yag, D. Huag ad L. Yag: A ovel pitch period detectio algorith based o Hilbert-Huag trasfor, LNCS 3338, Siobioetrics, pp , 4. [54] S. K. Roy, M. K. I. Molla, K. Hirose ad M. K. Hasa: Haroic odificatio ad data adaptive filterig based approach to robust pitch estiatio, Iteratioal Joural of Speech Techology (Spriger), Vol. 4, pp ,. [55] M. K. Hasa et. al.: Sigal reshapig usig doiat haroic for pitch estiatio of oisy speech, Sigal Processig, Vol. 86, No. 5, pp. -8, 5. Md. Khadeul Isla Molla received his B.Sc. ad M.Sc. degrees i electroics ad coputer sciece fro Shahjalal Uiversity of Sciece ad Techology, Bagladesh, i 995 ad 997, respectively. He obtaied his Ph.D. degree fro the Departet of Frotier Iforatics uder the Graduate School of Frotier Scieces, The Uiversity of Toyo, Toyo, Japa i 6. He joied as a Associate Professor i the Departet of Coputer Sciece ad Egieerig of the Uiversity of Rajshahi, Bagladesh, i August 6, ad he has bee a Professor sice May. Fro Septeber 6 to Septeber 8, he was worig as JSPS Postdoctoral Research Fellow i the Departet of Iforatio ad Couicatio Egieerig, The Uiversity of Toyo, Toyo, Japa. He was a research fellow at the Uiversity of Alberta, Caada, fro Nov. to Oct.. He visited several uiversities i Japa as guest researcher. His research iterests iclude audio sigal processig, blid source separatio, braicoputer iterface (BCI), bioedical sigal ad iage processig. He is a eber of the Istitute of Electrical ad Electroics Egieers (IEEE). I 7, he received the Best Paper Award fro the Research Istitute of Sigal Processig, Japa (RISP). Solal Das received his B.Sc. ad M.Sc. degrees fro the Departet of Applied Physics ad Electroics, Rajshahi Uiversity, Bagladesh i 993 ad 995, respectively. Durig 998-, he was a Lecturer i the Departet of Coputer Sciece ad Egieerig, Rajshahi Uiversity. He obtaied his Ph.D. degree fro the Departet of Coputer Sciece ad Egieerig, Rajshahi Uiversity, Rajshahi, Bagladesh i. He is worig as a Associate Professor i the sae Departet fro. His research iterests iclude digital sigal processig ad speech ehaceet. Md. Eraul Haid received his B.Sc. ad M.Sc. degrees fro the Departet of Applied Physics ad Electroics, Rajshahi Uiversity, Bagladesh i 99 ad 994, respectively. After that he obtaied his M.Sc. degree i coputer sciece fro Pue Uiversity, Idia i. He received his Ph.D. degree fro Shizuoa Uiversity, Japa i 7. Durig 997-, he was a Lecturer i the Departet of Coputer Sciece ad Egieerig, Rajshahi Uiversity. Dr. Haid wored as a Assistat Professor at the Kig Khalid Uiversity, Abha, KSA fro 9 to. He is worig as a Associate Professor i the Departet of Coputer Sciece ad Egieerig, Rajshahi Uiversity fro Jue, 7. His research iterests iclude digital sigal processig, aalysis ad sythesis of speech sigal, speech ehaceet ad iage processig. 8 Joural of Sigal Processig, Vol. 7, No. 6, Noveber 3