I Signal Processing Signal Processing Edited by Sebastian Miron In-Tech intechweb.org Published by In-Teh In-Teh Olajnica 19/2, 32000 Vukovar, Croatia Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the In-Teh, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2010 In-teh www.intechweb.org Additional copies can be obtained from: [email protected] First published March 2010 Printed in India Technical Editor: Maja Jakobovic Cover designed by Dino Smrekar Signal Processing, Edited by Sebastian Miron p. cm. ISBN 978-953-7619-91-6 V Preface The exponential development of sensor technology and computer power over the last few decades, transformed signal processing in an essential tool for a wide range of domains such as telecommunications, medicine or chemistry. Signal processing plays nowadays a key role in the progress of knowledge, from the discoveries on the universe underlying structure, to the recent breakthroughs in the understanding of the sub-atom structure of the matter. Internet, GSM, GPS, HDTV technologies are also indebted to the accelerated evolution of signal processing methods. Today, a major challenge in this domain is the development of fast and efficient algorithms capable of dealing with the huge amount of data provided by the modern sensor technology. This book intends to provide highlights of the current research in signal processing area, to offer a snapshot of the recent advances in this field. This work is mainly destined to researchers in the signal processing related areas but it is also accessible to anyone with a scientific background desiring to have an up-to-date overview of this domain. The twenty-five chapters present methodological advances and recent applications of signal processing algorithms in various domains as telecommunications, array processing, biology, cryptography, image and speech processing. The methodologies illustrated in this book, such as sparse signal recovery, are hot topics in the signal processing community at this moment. The editor would like to thank all the authors for their excellent contributions in the different areas of signal processing and hopes that this book will be of valuable help to the readers. January 2010 Editor Sebastian MIRON Centre de Recherche en Automatique de Nancy Nancy-Université, CNRS VI VII Contents Preface V 1. New Adaptive Algorithms for the Rapid Identification of Sparse Impulse Responses 001 Mariane R. Petraglia 2. Vector sensor array processing for polarized sources using a quadrilinear representation of the data covariance 019 Sebastian Miron, Xijing Guo and David Brie 3. New Trends in Biologically-Inspired Audio Coding 037 Ramin Pichevar, Hossein Najaf-Zadeh, Louis Thibault and Hassan Lahdili 4. Constructing wavelet frames and orthogonal wavelet bases on the sphere 059 Daniela Roşca and Jean-Pierre Antoine 5. MIMO Channel Modelling 077 Faisal Darbari, Robert W. Stewart and Ian A. Glover 6. Finite-context models for DNA coding* 117 Armando J. Pinho, António J. R. Neves, Daniel A. Martins, Carlos A. C. Bastos and Paulo J. S. G. Ferreira 7. Space-filling Curves in Generating Equidistrubuted Sequences and Their Properties in Sampling of Images 131 Ewa Skubalska-Rafajłowicz and Ewaryst Rafajłowicz 8. Sparse signal decomposition for periodic signal mixtures 151 Makoto Nakashizuka 9. Wavelet-based techniques in MRS 167 A. Suvichakorn, H. Ratiney, S. Cavassila, and J.-P Antoine 10. Recent Fingerprinting Techniques with Cryptographic Protocol 197 Minoru Kuribayashi 11. Semiparametric curve alignment and shift density estimation: ECG data processing revisited 217 T. Trigano, U. Isserles, T. Montagu and Y. Ritov VIII 12. Spatial prediction in the H.264/AVC FRExt coder and its optimization 241 Simone Milani 13. Detection of Signals in Nonstationary Noise via Kalman Filter-Based Stationarization Approach 263 Hiroshi Ijima and Akira Ohsumi 14. Direct Design of Infinite Impulse Response Filters based on Allpole Filters 275 Alfonso Fernandez-Vazquez and Gordana Jovanovic Dolecek 15. Robust Unsupervised Speaker Segmentation for Audio Diarization 307 Hachem Kadri, Manuel Davy and Noureddine Ellouze 16. New directions in lattice based lossy compression 321 Adriana Vasilache 17. Segmented Online Neural Filtering System Based On Independent Components Of Pre-Processed Information 337 Rodrigo Torres, Eduardo Simas Filho, Danilo de Lima and José de Seixas 18. Practical Source Coding with Side Information 359 Lorenzo Cappellari 19. Crystal-like Symmetric Sensor Arrangements for Blind Decorrelation of Isotropic Wavefield 385 Nobutaka Ono and Shigeki Sagayama 20. Phase Scrambling for Image Matching in the Scrambled Domain 397 Hitoshi Kiya and Izumi Ito 21. Fast Algorithms for Inventory Based Speech Enhancement 415 Robert M. Nickel, Tomohiro Sugimoto and Xiaoqiang Xiao 22. Compression of microarray images 429 António J. R. Neves and Armando J. Pinho 23. Roundoff Noise Minimization for State-Estimate Feedback Digital Controllers Using Joint Optimization of Error Feedback and Realization 449 Takao Hinamoto, Keijiro Kawai, Masayoshi Nakamoto andWu-Sheng Lu 24. Signal processing for non-invasive brain biomarkers of sensorimotor performance and brain monitoring 461 Rodolphe J. Gentili, Hyuk Oh, Trent J. Bradberry, Bradley D. Hatfield and José L. Contreras-Vidal 25. The use of low-frequency ultrasonics in speech processing 503 Farzaneh Ahmadi and Ian Mcloughlin New Adaptive Algorithms for the Rapid Identification of Sparse Impulse Responses 1 New Adaptive Algorithms for the Rapid Identification of Sparse Impulse 01 Responses Mariane R. Petraglia New Adaptive Algorithms for the Rapid Identification of Sparse Impulse Responses MarianeR.Petraglia FederalUniversityofRiodeJaneiro Brazil 1. Introduction Itiswellknownthattheconvergenceoftheadaptivefilteringalgorithmsbecomesslowwhen thenumberofcoefficientsisverylarge. However,inmanyapplications,suchasdigitalnet- work and acoustical echo cancelers, the system being modeled presents sparse impulse re- sponse, that is, mostof itscoefficientshave smallmagnitudes. The classicaladaptation ap- proaches,suchastheleast-meansquare(LMS)andrecursiveleastsquares(RLS)algorithms, donottakeintoaccountthesparsenesscharacteristicsofsuchsystems. Inordertoimprovetheconvergencefortheseapplications,severalalgorithmshavebeenpro- posed recently, which employ individual step-sizes for the updating of the differentcoeffi- cients. Theadaptationstep-sizesaremadelargerforthecoefficientswithlargermagnitudes, resultinginafasterconvergenceforthemostsignificantcoefficients. Suchideawasfirstin- troducedin(Duttweiler,2000)resultingintheso-calledproportionatenormalizedleastmean square(PNLMS)algorithm.However,theperformanceofthePNLMSalgorithmfortheiden- tificationofnon-sparseimpulseresponsecanbeverypoor,evenslowerthanthatofthecon- ventionalLMSalgorithm. Animprovedversionofsuchalgorithm,whichemploysanextra parametertocontrolthe amountofproportionalityinthestep-sizenormalization, was pro- posedin(Benesty&Gay,2002). AnobservedcharacteristicofthePNLMSalgorithmisarapidinitialconvergence,duetothe fastadaptationspeedofthelargevaluecoefficients,followedbyanexpressiveperformance degradation, owing to the small adaptation speed of the small value coefficients. Such be- haviorismoresignificantinthemodelingofnotverysparseimpulseresponses. Inorderto reducethisproblem,theapplicationofanon-linearfunctiontothecoefficientsinthestep-size normalizationwasproposedin(Deng&Doroslovacki,2006). The well-known slow convergence of the gradient algorithms for colored input signals is also observed in the proportionate-type NLMS algorithms. Implementations that combine theideasofthePNLMSandtransform-domainadaptivealgorithmswereproposedin(Deng & Doroslovacki,2007) and (Petraglia & Barboza, 2008) for accelerating the convergence for coloredinputsignals. In this chapter, we give an overviewof the mostimportantadaptive algorithmsdeveloped forthefastidentificationofsystemswithsparseimpulseresponses. Theconvergenceofthe proposedalgorithmsarecomparedthroughcomputersimulationsfortheidentificationofthe channelimpulseresponsesinadigitalnetworkechocancellationapplication. 2 Signal Processing 2. SparseImpulseResponseSystems ofsuchalgorithmsdependsonhowsparsethe modeledimpulseresponseis. Asparseness measureofanN-lengthimpulseresponsewwasproposedin(Hoyer,2004)as Sparse impulse responses are encountered in several applications, such as in acoustic and digitalnetworkechocancelers.Theadaptivefiltersemployedinthemodelingoftheunknown N w systeminsuchapplicationspresentasmallnumberofcoefficientswithsignificantmagnitude. ξw = 1 || ||1 (1) Figure1illustratesthe modelingofanunknownsystemwo, whichisassumedtobe linear, N−√N (cid:31) − √N||w||2(cid:30) time-invariant and of finite impulse response length (N), by an adaptive filter. The vector aconndtaitisniinnpgutthveeacdtoarpatisvex(finl)te=rc[oxe(fnfi)cxie(nntsi1s)denoxt(endasNw+(n1))]=T. T[wh0e(and)awp1ti(vne)fi··lt·ewrNou−t1p(unt)]iTs wξwhe=re0||wwh||elnisatlhleelle-nmoernmtsooffthweavreecteoqruwal.inItmshaogunlidtubdeeo(bnsoenrv-sepdarthseatim0p≤ulξswer≤esp1o,nasned)tahnadt − ··· − ξw =1whenonlyoneelementofwisnon-zero(thesparsestimpulseresponse). denotedasy(n),thedesiredresponseasd(n)andtheestimationerrorase(n).Oneofthemost Inthesimulationspresentedthroughoutthischapter,theidentificationofthedigitalnetwork usedadaptationtechniquesisthenormalizedleastmean-square(NLMS)algorithm,shownin channelsofITU-TRecommendationG.168(G.168,2004),byanadaptivefilterwith N = 512 Table1,whereβisafixedstep-sizefactorandδisasmallconstantneededinordertoavoid coefficients,willbeconsidered.Figures2(a)and2(b)showtheimpulseresponsesofthemost divisionbyzero. and least sparse digital network channel models (gm1 and gm4, respectively) described in AsshowninTable1fortheNLMSalgorithm,typicalinitializationparametersaregivenfor (G.168,2004).Figure2(c)presentsthegm4channelimpulseresponsewithawhitenoise(uni- allalgorithmsstudiedinthischapter. formlydistributedin[-0.05,0.05]) addedtoit, suchastosimulateanon-sparsesystem. The v[n] correspondingsparsenessmeasuresareξw =0.8970forthegm1channel,ξw =0.7253forthe gm4channelandξw =0.2153forthegm4plusnoisechannel. d[n] wo x[n] e[n] 0.2 (a) Model gm1 0.1 w(n) y[n] mplitude 0 A −0.1 Fig.1.Systemidentificationthroughadaptivefiltering. −0.2 0 50 100 150 200 250 300 350 400 450 500 Samples (b) Model gm4 0.2 Iδn=itia0l.i0z1a,tiβon=(t0y.2p5icalvalues) mplitude 0.01 A −0.1 w(0)= w (0) w (0) w (0) T =0 0 1 ··· N−1 −0.20 50 100 150 200 250 300 350 400 450 500 Processin(cid:31)gandAdaptation (cid:30) Samples (c) Model gm4+noise For n=0,1,2, 0.2 ··· xy((nn))==(cid:31)xTx(n(n)w) (nx)(n−1) ··· x(n−N+1) (cid:30)T Amplitude 0.01 −0.1 e(n)=d(n) y(n) − −0.2 w(n+1)=w(n)+β x(n)e(n) 0 50 100 150 200 S2a5m0ples 300 350 400 450 500 xT(n)x(n)+δ End Fig.2.Channelimpulseresponses:(a)gm1,(b)gm4and(c)gm4+noise. Table1.NLMSAlgorithm 3. Proportionate-typeNLMSAlgorithms The proportionate-type NLMS algorithms employ a different step-size for each coefficient, Describedinthenextsections,adaptivealgorithmsthattakeintoaccountthesparsenessofthe suchthat largeradjustments areappliedtothe largercoefficients(oractive coefficients),re- unknownsystemimpulseresponsehavebeenrecentlydeveloped.Theconvergencebehavior