A novel Adaptive Sub-Band Filter design with BD-VSS using Particle Swarm Optimization

Transcription

1 Internatonal Research Journal of Engneerng and echnology (IRJE) e-iss: Volume: 5 Issue: Oct 28 p-iss: A novel Adaptve Sub-Band Flter desgn wth B-VSS usng Partcle Swarm Optmzaton Yuvaraj V Electroncs and Communcaton Engneerng College of Engneerng Gundy Anna Unversty Chenna Inda *** Abstract A delayless Sgn Subband Adaptve Flter algorthm wth Indvdual Weghtng Factors (IWF-SSAF) and Band-ependent Varable Step-Szes (B-VSS) approach s recently proposed to control nose for mpulsve nose reducng the L-norm of the a posteror error vector of Subband flter to mtgate the mpulsve nterferences [7]. Also Varable Regularzaton Parameter wth SSAF s presented for lower the steady-state error of the SSAF [8]. envronments. However such approaches have slow convergence rate and hgh computaton complexty for realtme applcatons. o address these ssues Partcle Swarm Optmzaton (PSO) algorthm delayless closed loop IWF-SSAF wth B-VSS s proposed. he proposed algorthm s appled for Actve Impulsve ose Control (AIC) technque to suppress the mpulsve nose. he proposed algorthm attans hen some varable step sze SSAF approaches were presented from dverse prncples of the step sze update to allevate the trade-off problem of the SSAF [9]. But these convergence rates of several varable step sze SSAF approaches are not reasonable [8]. o address ths concern a novel SAF approach s developed from Huber s cost better convergence performance by employng the functon usng the gradent descent technque []. hs approach offers an automatc scheme to adjustment between mnmzaton approach to sub-bands and decorrelatng the SAF and SSAF approaches by teratvely updatng the propertes of SSAF. Furthermore the proposed algorthm has cut-off metrcs and provdes good robustness to the acheved more computatonal effcency wth the ad of PSO mpulsve noses. Hence ths approach s called as the robust algorthm. he expermental result shows that the proposed varable step sze SAF (RVSS-SAF) []. algorthm obtaned better performance than the conventonal SSAF algorthms n terms of computatonal complexty. Key words Sgn Subband Adaptve Flter Partcle Swarm Optmzaton Actve Impulsve ose Control Varable Step- Szes.. IROUCIO ormalzed Least Mean Square (LMS) s one of the fundamental approaches n adaptve flterng technques whch has been broadly used n several real-tme applcatons ncludng channel estmaton system dentfcaton and Actve nose cancellaton (AC) []. However LMS approach has the dsadvantage of slow converges for the colored nput sgnals. An nnovatve approach whch s used n the Sub-band Adaptve Flter (SAF) for revng the dsadvantage of LMS approach [2]. It splts the coloured nput sgnal nto the equally dvded multple sub-band sgnals where each sub-band sgnal s almost whte. hen the ormalzed Sub-band Adaptve Flter (SAF) approach s ntroduced whch converges the LMS for the coloured nput sgnals owng to the nherent decorrelatng features of SAF n a faster manner [3] [4]. In addton SAF approach has the same computatonal complexty of the LMS approach for the applcatons of echo cancellaton [5]. Also the tradtonal LMS approach and SAF approach has a trade-off between the rate of convergence and steady-state error for the selecton step sze. hen more varable step sze SAF approaches were establshed to attan both low steady-state error and fast convergence rate [6]. However these approaches may devate for the presence of mpulsve noses. A Sgn Subband Adaptve Flter (SSAF) approach s developed for Moreover SSAF approach wth Indvdual Weghtng Factors (IWF-SSAF) approach s presented to mprove the convergence rate of SSAF approach [2] [3]. An mproved proportonate IWF-SSAF s proposed for sparse system to further mprove the convergence rate of the IWF-SSAF algorthm. wo delayless structures for SAF were proposed to allevate the concern of undesrable sgnal path delay snce ths s essental for the dfferent real-tme applcatons such as AEC and AC [4]. SSAF approaches have an nherent sgnal path delay ssue for real-tme systems. Hence a delayless IWF-SSAF wth band-dependent varable step-szes (B-VSS) algorthm s developed whch offers more robustness under mpulsve nose condtons [4]. 2. RELAE WORKS M-Estmator based approach s developed to control the context of actve mpulse nose where M-Estmator ams to mnmze the effect of outlers [5] [2]. hs result proved the better effcency of the M-Estmator than the exstng algorthms based on nose control performance. However ts complexty s lower than the other conventonal approaches. A B-VSS based SSAF s presented usng the concept of mean-square devaton (MS) mnmzaton []. In ths the flter performance s mproved based on the assgn of dfferent step sze to each band. From the results ths approach performs better than the conventonal technques based on the steady-state estmaton error and convergence rate. An actve control of mpulsve nose wth symmetrc α-stable (SαS) dstrbuton s developed AC system [6]. A common step-sze normalzed fltered-x Least Mean Square (FxLMS) approach s derved based on the Gaussan dstrbuton 28 IRJE Impact Factor value: 7.2 ISO 9:28 Certfed Journal Page 925

2 Internatonal Research Journal of Engneerng and echnology (IRJE) e-iss: Volume: 5 Issue: Oct 28 p-iss: functon s used to regularze the step sze. he results demonstrate that the developed approach has good performance for SαS mpulsve nose attenuaton. hen the fltered-x state-space recursve least square (FxSSRLS) s presented for actve nose control (AC) [7]. From the results FxSSRLS approach s more effectve n extermnatng hgh-peaked mpulses than other approaches for AC applcatons. SAF approach s developed for reducng mpulsve noses usng Huber s cost functon [2]. In general ths approach operates n the normalzed SAF mode and t performs lke SSAF approach. he sub-band cut-off metrcs are derved n a recursve manner for enhancng the robustness of the approach aganst mpulsve noses. For mpulsve AC an altered b-normalzed data-reusng (BR) based adaptve approach s developed [8]. he approach s resultng from a adapted cost functon and t s based on reusng the past and present data samples. he results demonstrates the effectveness of the BR-based adaptve approach wth a ratonal ncrease n the complexty. elayless SSAF approaches were derved wth IWF-SSAF and B-VSS n mpulsve nose condtons for real-tme applcatons [4]. In ths two delayless flter structures mplemented for the l2- norm based SAF are appled together wth IWF-SSAF. Fnally the performance of the approach s proved effcency n dfferent mpulsve nterference stuatons. 3. PRELIMIARIES 3. Sgn Subband Adaptve Flter Algorthms wth Indvdual Weghtng Factors (IWF-SSAF) Subband adaptve flter (SAF) s an attractve opton to mnmze the computatonal complexty problem of the Least Mean Squares (LMS). Fg. shows the structure of SAF algorthm. he desred sgnal dn ( ) s expressed as () d( n) w u( n) v( n) () opt un () s the nput sgnal that s represented by u( n) [ u( n) u( n ) u( n 2)... u( n L )] wopt s the weght vector of the unknown system wth L-length and vn () ncludes an mpulsve nose n ( ) and the background nose bn (). he sub-band sgnals are represented by d ( n) and u ( n ) whch are attaned by flterng the dn ( ) and un () usng flter examnaton H number sub-bands. In addton decmatng z for =23... s the d k s obtaned by d n by a factor of the decmated sequence s represented as k. he error vector of decmated sub-band e ks calculated as (2) e d U w (2) wk s the calculate of wopt teratons U [ u u... u ] 2 d [ d d... d ] 2 u [ u... u ( k L )] at k -number of he coeffcent vector s attaned by reducng the cost functon usng a stochastc gradent decent [2]: J e (3) d k s the th element of e k n (2) and represents the weghtng feature. Besdes the updated equaton for the coeffcent vector derved as follows n the IWF-SSAF Jk ( ) W ( k ) w wk ( ) = w u sgn( e ) (4) sgn s denotes the sgn functon and s a step-sze to make sure that the coeffcent vector does not change rapdly and sgn( ) represents the sgn functon. When s derved as a small postve constant to keep away from dvdng by zero s u u employed as the weghtng feature n the orgnal SSAF [5]. Also the ndvdual weghtng feature for IWF-SSAF s consdered n all sub-bands: 2... u u (5) Form the outcome IWF-SSAF completely uses the decorrelatng possessons of SSAF and provdes speedy convergence. At last the coeffcent vector update n IWF- SSAF s w( k ) w u sgn( e (6) u u 28 IRJE Impact Factor value: 7.2 ISO 9:28 Certfed Journal Page 926

3 Internatonal Research Journal of Engneerng and echnology (IRJE) e-iss: Volume: 5 Issue: Oct 28 p-iss: he delayless closed loop IWF-SSAF algorthm as follows Algorthm: elayless Closed-Loop IWF-SSAF algorthm [4] Fg. Sub-band adaptve flter structure [2]. 3.2 elayless IWF-SSAF IWF-SSAF approach [2] enhances the convergence rate of the conventonal SSAF approach [5]. In [7] developed two delayless IWF-SSAF namely-loop and closed-loop desgns by applyng the new delayless confguratons n the SAF. In the delayless open-loop based IWF-SSAF the obtaned convergence performance s same as the IWF-SSAF. Besdes the error sgnal en () n the proposed approach s developed wthout delay and estmated n a supplementary loop although the sgnal path delay can be produced n IWF- SSAF because t s recreated by the combnaton flter bank. In addton a delayless closed-loop based IWF-SSAF s acheved based on confguraton of closed-loop shown n Fg.2. In ths sub-band error sgnal derved by d en () usng the examnaton of flter H ( z ). hen by decmatng t based on a factor of and update the adaptve flter wk. herefore t s adjusted based on pror data of the error sgnal due to the nterrupton of the analyss flters H ( z ). In delayless closed-loop IWF-SSAF the results show that the upper bound of the step sze s reduced for fxed convergence [9]. o address ths drawback the delayless closed-loop structure s used n some benefcal applcaton called as actve mpulsve nose control (AIC) whle only the error sgnal s obtanable and t s consdered as mpulsve nterference. Fg.2 elayless closed-loop SAF structure [4] Input : u( n) nput sgnal vector e( n) error sgnal Output : update equaton for the coeffcent vector w( k). For n e( n) d( n) w u 3. u ( n) h a( n) For k when n k 5. e h e u u u sgn( e ) 7. w( k ) w end end 3.3 B-VSS based delayless IWF-SSAF Besdes a B-VSS approach s ntroduced to enhance the open-loop convergence rate and closed-loop delayless IWF- SSAF approach. In ths the l normalzaton s ntegrated nto each subband of the delayless IWF-SSAF [9]. hs provdes the robustness aganst mpulsve nterferences. Hence to acheve the expected convergence rate varable step szes are arranged to be consdered to correspondng subbands. Some VSS subband approaches have been proposed [8]. Although most of these algorthm needs the past nformaton whch may be bascally unavalable and a pror knowledge s not requred n l-norm based VSS approach. 4. PROPOSE MEHOOLOGY he proposed IWF-SSAF wth B-VSS and Partcle Swarm optmzaton (PSO) [2] s assgned and ts closedloop desgn s developed. Fg.3 shows the structure of proposed approach wth PSO for the AIC. We proposed methodology ncorporates AIC technque nto the Flterng technque to suppress the noses. th he posteror error of sub-band s derved as s e d u w ( k ) (7) p u sgn( e ) w( k ) w u u he step sze of the th subband and e s rewrtten as follows p p e e u g (8) 28 IRJE Impact Factor value: 7.2 ISO 9:28 Certfed Journal Page 927

4 Internatonal Research Journal of Engneerng and echnology (IRJE) e-iss: Volume: 5 Issue: Oct 28 p-iss: u u sgn( e ) g. u u Also the B-VSS for 2... optmum n the l -norm regularzaton control [8] s derved by mnmzng l -norm of e as p arg mn e u g ( k ) subject to L U (9) In (9) the postve constrants the lower and upper bounds for u ( k ) are represented as L and U respectvely. he s chosen to be adjacent to zero U and s consdered as less than one for constancy of the U adjusted l -norm approach. Moreover dverse numbers for L and U are consdered for every sub-band. evertheless the dentcal L and U are employed n every sub-bands. From (9) we examne that the l -norm regularzaton that s a one-dmensonal lnear curved constrant. herefore the result of s expressed from the l -norm regularzaton approach. hs should be derved as e k ( ) 2... g () s used to evade dvdng by zero and developng the convexty of l -norm the optmum result (9) s derved. U f U L f L () otherwse Further the convergence performance of the B- VSS approach s assumng the consequence of the mpulsve nterference n step sze control. However from equaton () when the mpulsve nose works on few sub-band whch controls the mpulsve nose and the convergence behavour s weakened. o prevent ths n the B-VSS s acheved by applyng the tme average method as follows ( k ) ( )mn ( k ) (2) opt s the smoothng parameter that s expressed and L the nput sgnal and coeffcent vector ( ) s a varable whch s based wk correlaton. Fg.3 he proposed structure of delayless closed-loop IWF- SSAF approach wth BVSS and PSO for the AIC he equaton (2) expresses the B-VSS approach s derved from the aforementoned step sze ( k ) where th the mpulsve nterferences nfluence the subband that provdes heftness n contradcton of mpulsve nose. Else the algorthm s performed wth the tme normalzed optmal step sze as follows ( k ) ( ) (3) opt Moreover the computatonal complexty s dmnshed usng proposed approach wth PSO. 28 IRJE Impact Factor value: 7.2 ISO 9:28 Certfed Journal Page 928

5 ose Control[dB] Averaged nose reducton(db) Internatonal Research Journal of Engneerng and echnology (IRJE) e-iss: Volume: 5 Issue: Oct 28 p-iss: RESULS A ISCUSSIO In ths we present the results of computatonal complexty and convergence operaton of the proposed algorthm. Intally we have consdered the nput sgnal n tme doman whch ncludes the nose sgnal Fg.4 shows the nput sgnal n tme doman representaton. o analyze the performance enhancement by the proposed closed-loop algorthm ths s better than wthout optmzaton algorthm. Fg.6 shows the nose suppresson of proposed method. Smultaneously the nput sgnal s dvded nto multples subband usng Mexcan Hat Wavelet transformaton. Fg.7 shows the Mexcan Hat wavelet Mexcan Hat Wavelet Row n the me oman Row 2 n the me oman Row 3 n the me oman Fg.4 Input sgnal n tme doman hen the sgnal s swtched nto frequency doman from tme doman usng FF transformaton. Fg.5 llustrates the nput sgnal n frequency doman representaton..5 Row n the Frequency oman Row 2 n the Frequency oman Row 3 n the Frequency oman Fg.7 Mexcan Hat Wavelet ow there are two sgnals are acheved one from output of FF and another from Mexcan Wavelet result. hese sgnals are undergone wth analyss of ROC and the results are obtaned. hen the Machne learnng algorthms are ncorporated to analyse on the best values of ROC n the Mexcan wavelet transformaton and FF and the best values are collected n a structured array. Moreover the evaluaton factors are analysed to have an concept on the sgnal accuracy and strength. hs evaluaton parameter gves an dea on the extenson of the sgnals. In Fg.8 show that the Averaged ose Reducton (AR) performances acheved by the proposed approach wth Partcle Swarm Optmzaton (PSO) algorthm. hs demonstrates the approach produced the effectve AR operaton Fg.5 Input sgnal n frequency doman 25 he analyss of IWF-SSAF wth B-VSS wth PSO approach was proved n AIC whch s assgned as an mpulsve nose stuaton of the closed-loop structure AIC echnque umber of teratons k Fg.6 ose suppresson usng AIC technque Iteratons Fg.8 AR performance of proposed algorthm he closed-loop l -norm acheved a effectve performance under the same envronments and hgh mpulsve nose control compared to other exsted algorthms. In addton the mpulsve noses by all assgned algorthms whch prove that the algorthm accomplshed a effcent nose control than other approches. 28 IRJE Impact Factor value: 7.2 ISO 9:28 Certfed Journal Page 929

6 Internatonal Research Journal of Engneerng and echnology (IRJE) e-iss: Volume: 5 Issue: Oct 28 p-iss: COCLUSIO In ths paper B-VSS based delayless closed-loop IWF- SSAF approach s proposed. he mpulsve nose s successfully suppressed usng AIC technque. he proposed approach has better convergence performance based on the l -norm mnmzaton technque and decorrelatng propertes of SSAF algorthm. PSO technque s appled together wth IWF-SSAF algorthm for reducng the computatonal complcaton. he performance evaluaton verfes the proposed algorthm has mproved convergence rate wth condensed complexty compared to the other SSAF algorthms. REFERECES ) Benesty J. & Huang Y. (Eds.). (23). Adaptve sgnal processng: applcatons to real-world problems. Sprnger Scence & Busness Meda. 2) Lee K. A. Gan W. S. & Kuo S. M. (29). Subband adaptve flterng: theory and mplementaton. John Wley & Sons. 3) Lee K. A. & Gan W. S. (24). Improvng convergence of the LMS algorthm usng constraned subband updates. IEEE sgnal processng letters (9) ) Lee K. A. & Gan W. S. (26). Inherent decorrelatng and least perturbaton propertes of the normalzed subband adaptve flter. IEEE ransactons on Sgnal Processng 54() ) J. & L F. (2). A varable step-sze matrx normalzed subband adaptve flter. IEEE ransactons on Audo Speech and Language Processng 8(6) ) Seo J. H. & Park P. (24). Varable ndvdual step-sze subband adaptve flterng algorthm. Electroncs Letters 5(3) ) J. & L F. (2). Varable regularsaton parameter sgn subband adaptve flter. Electroncs letters 46(24) ) Shn J. Yoo J. & Park P. (23). Varable step-sze sgn subband adaptve flter. IEEE Sgnal Processng Letters 2(2) ) Vega L. R. Rey H. Benesty J. & ressens S. (28). A new robust varable step-sze LMS algorthm. IEEE ransactons on Sgnal Processng 56(5) ) Yu Y. & Zhao H. (26). ovel sgn subband adaptve flter algorthms wth ndvdual weghtng factors. Sgnal Processng ) Shao. Zheng Y. R. & Benesty J. (2). An affne projecton sgn algorthm robust aganst mpulsve nterferences. IEEE Sgnal Processng Letters 7(4) ) Km J. H. Km J. Jeon J. & am S. W. (27). elayless ndvdual-weghtng-factors sgn subband adaptve flter wth band-dependent varable stepszes. IEEE/ACM ransactons on Audo Speech and Language Processng. 5) Wu L. & Qu X. (23). An M-estmator based algorthm for actve mpulse-lke nose control. Appled Acoustcs 74(3) ) Zhou Y. Zhang Q. & Yn Y. (25). Actve control of mpulsve nose wth symmetrc α-stable dstrbuton based on an mproved step-sze normalzed adaptve algorthm. Mechancal Systems and Sgnal Processng ) Mrza A. Zeb A. & Shekh S. A. (26). Robust adaptve algorthm for actve control of mpulsve nose. EURASIP Journal on Advances n Sgnal Processng 26() 44. 8) Akhtar M.. (26). Bnormalzed data-reusng adaptve flterng algorthm for actve control of mpulsve sources. gtal Sgnal Processng ) Lee K. A. & Gan W. S. (27 July). On delayless archtecture for the normalzed subband adaptve flter. In Multmeda and Expo 27 IEEE Internatonal Conference on (pp ). IEEE. 2) Wu L. & Qu X. (23). Actve mpulsve nose control algorthm wth post adaptve flter coeffcent flterng. IE Sgnal Processng 7(6) ) u K. L. & Swamy M.. S. (26). Partcle swarm optmzaton. In Search and optmzaton by metaheurstcs (pp ). Brkhäuser Cham. 9) Km J. H. Chang J. H. & am S. W. (23). Sgn subband adaptve flter wth l-norm mnmsaton-based varable step-sze. Electroncs Letters 49(2) ) Yoo J. Shn J. & Park P. (24). A band-dependent varable step-sze sgn subband adaptve flter. Sgnal Processng IRJE Impact Factor value: 7.2 ISO 9:28 Certfed Journal Page 93