Hindawi Publishing CorporationEURASIP Journal on Advances in Signal ProcessingVolume 2011, Article ID 963642, 3 pagesdoi:10.1155/2011/963642

Editorial

Recent Advances in Theory and Methods forNonstationary Signal Analysis

Patrick Flandrin (EURASIP Member),1 Antonio Napolitano (EURASIP Member),2

Haldun M. Ozaktas,3 and David J. Thomson4

1 Departement de Physique (UMR CNRS 5672), Ecole Normale Superieure de Lyon, 69364 Lyon Cedex 07, France2 Department of Technology, University of Napoli “Parthenope”, 80143 Napoli, Italy3 Department of Electrical Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey4 Department of Mathematics and Statistics, Queen’s University, Kingston, ON, Canada K7L 3N6

Correspondence should be addressed to Antonio Napolitano, antonio.napolitano@uniparthenope.it

Received 3 March 2011; Accepted 3 March 2011

Copyright © 2011 Patrick Flandrin et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

All physical processes are nonstationary. When analyzingtime series, it should be remembered that nature canbe amazingly complex and that many of the theoreticalconstructs used in stochastic process theory, for example,linearity, ergodicity, normality, and particularly stationarity,are mathematical fairy tales. There are no stationary timeseries in the strict mathematical sense; at the very least, every-thing has a beginning and an end. Thus, while it is necessaryto know the theory of stationary processes, one should notadhere to it dogmatically when analyzing data from physicalsources, particularly when the observations span an extendedperiod. Nonstationary signals are appropriate models forsignals arising in several fields of applications includingcommunications, speech and audio, mechanics, geophysics,climatology, solar and space physics, optics, and biomedicalengineering. Nonstationary models account for possible timevariations of statistical functions and/or spectral characteris-tics of signals. Thus, they provide analysis tools more generalthan the classical Fourier transform for finite-energy signalsor the power spectrum for finite-power stationary signals.Nonstationarity, being a “nonproperty” has been analyzedfrom several different points of view. Several approachesthat generalize the traditional concepts of Fourier analysishave been considered, including time-frequency, time-scale,and wavelet analysis, and fractional Fourier and linearcanonical transforms. Approaches that generalize the power-spectrum analysis include cyclostationary signal analysis,multitaper spectral estimation, and evolutionary spectralanalysis. In addition, techniques such as adaptive system and

signal analysis, empirical mode decomposition, and otherdata-driven methods have been used with the purpose ofmodeling nonstationary phenomena.

In this special issue, recent advances in the theoryand methodologies for nonstationary signal analysis areaddressed, different approaches are compared, emerging ornew techniques are proposed, and new application fields areexplored. Of the 51 papers submitted, only 19 were acceptedafter the review process.

Four papers are related to basic topics of nonstationarysignal analysis such as instantaneous frequency estimation,time-frequency detection, Zak transform, and AM-FM anal-ysis.

In the paper “An efficient algorithm for instantaneousfrequency estimation of nonstationary multicomponent signalsin low SNR” by J. Lerga et al., a method for componentsinstantaneous frequency (IF) estimation of multicomponentsignals in low signal-to-noise ratio (SNR) is proposed. Themethod combines a new modification of a blind sourceseparation algorithm for components separation, with theimproved adaptive IF estimation procedure based on themodified sliding pairwise intersection of confidence intervalsrule.

In the paper “Time-frequency detection of slowly varyingperiodic signals with harmonics: methods and performanceevaluation” by J. O’Toole and B. Boashash, two methodsto detect slowly varying periodic signals with harmoniccomponents are presented. Both methods are based ondifferent modifications of the time-frequency-matched filter

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and attempt to overcome the problem of predefining thetemplate set for the matched filter. The ambiguity filtermethod reduces the number of required templates by onehalf; the time-frequency correlator method does not requirea predefined template set at all.

In the paper “Construction of sparse representations ofperfect polyphase sequences in Zak space with applications toradar and communication” by A. K. Brodzik, it is shownthat the Zak space analysis of a chirp produces a highlycompactified chirp, with support restricted to an algebraicline. In contrast, discrete Fourier transform of a chirp is,essentially, a chirp, with support similar to the support of thetime-domain signal. Further investigation leads to relaxationof the original restriction to chirps, permitting constructionof a wide range of polyphase sequence families with idealcorrelation properties. The paper also contains an elemen-tary introduction to the Zak transform methods, a survey ofrecent results in Zak space sequence design and analysis, anda discussion of the main open problems in this area.

In the paper “Tree image growth analysis using instan-taneous phase modulation” by J. Ramachandran et al., theuse of Amplitude-Modulation Frequency-Modulation (AM-FM) methods for tree growth analysis is proposed. For thisapplication the authors introduce the use of fast filter bankfilter coefficient computation based on piecewise linear poly-nomials and radial frequency magnitude estimation usinginteger-based Savitzky-Golay filters for derivative estimation.

Two papers address the problem of spectrum andcovariance function estimation for nonstationary processes.In both papers the class of the locally stationary processes isconsidered in detail.

In the paper “Optimal multitaper Wigner spectrum esti-mation of a class of locally stationary processes using Hermitefunctions” M. Hansson-Sandsten investigates discrete-timemultitapers that give an optimal Wigner spectrum estimatefor a class of locally stationary processes. It is shown thatthe optimal multitapers are well approximated by Hermitefunctions (which is computationally efficient) and thata limited number of windows can be used for a meansquare error optimal spectrogram estimate. Comparisonswith other frequently used methods are provided.

In the paper “Optimal nonparametric covariance functionestimation for any family of nonstationary random processes”by J. Sandberg and M. Hansson-Sandsten, the covariancefunction estimate of a zero-mean nonstationary randomprocess in discrete time is accomplished from one observedrealization by weighting observations with a kernel function.Several kernel functions have been proposed in the literature.The authors prove that the mean square error (MSE) optimalkernel function for any parameterized family of randomprocesses can be computed as the solution to a systemof linear equations. Even though the resulting kernel isoptimized for members of the chosen family, it seems to berobust in the sense that it is often close to optimal for manyother random processes as well.

Three papers are concerned with applications of waveletand wideband signal processing.

In the paper “Nonstationary system analysis methods forunderwater communications” by N. Josso et al., following

a linear time-varying wideband system representation, twomethods for estimating the underwater communicationenvironment are proposed. The first one is based on estimat-ing discrete wideband spreading function (WSF) coefficientsfrom a canonical time-scale system representation. Thesecond one follows a ray system model and estimates a highlylocalized WSF using the matching pursuit decompositionalgorithm by extracting time-scale features for different raypaths.

In the paper “Synthesis of an optimal wavelet basedon auditory perception criterion” by A. Karmakar et al., amethod is proposed for synthesizing an optimal waveletbased on auditory perception criterion for dyadic filter bankimplementation. The design method of this perceptuallyoptimized wavelet is based on the critical band structureand the temporal resolution of human auditory system. Theconstruction of this compactly supported wavelet is done bydesigning the corresponding optimal finite impulse responsequadrature mirror filter (QMF).

In the paper “A signal-specific QMF bank design tech-nique using Karhunen-Loeve transform approximation” by M.Dogan and O. N. Gerek, a signal-specific method of QMFbank design is proposed. The method uses the Karhunen-Loeve transform (KLT) matrix which is specific for thestatistical characteristics of the signal and compresses thesignal with the maximum coding gain. A block wavelettransform (BWT) inversion method is proposed whichdesigns the QMF banks by matching the BWT matrix to theKLT matrix.

Since its introduction some ten years ago, the techniqueof “Empirical Mode Decomposition” (EMD) has gained anincreased popularity in the analysis of nonstationary signals.Two papers of this special issue are concerned with EMD.

In the first one, “Multivariate empirical mode decompo-sition for quantifying multivariate phase synchronization” A.Y. Mutlu and S. Aviyente make use of a recent extension ofEMD to multivariate data for getting a robust descriptionof time-varying phase synchrony between channels. Theyevidence that their approach can be used for quantifyingmultivariate synchronization within a network of oscillators,with an application to electroencephalogram (EEG) data.

In the second paper, “Evaluation of empirical modedecomposition for event-related potential analysis” N.Williams et al. investigate the potentiality of EMD fordenoising those EEG signals that correspond to weakmodifications due to a stimulus. They show in particularthe gain offered by the new technique, as compared to moreclassical filtering operations assuming a form of stationarity.

One paper exploits cyclostationary signal analysis formechanical applications.

In the paper “Electrical noise cancelation for bearingsdamage detection using stator current and voltage” by A.Ibrahim et al., the problem of detection of a bearing defect inan asynchronous machine is addressed. For this purpose, it isconsidered that the voltage is imposed and is independent ofmechanical aspects and that the mechanical defect appearsonly in the current signal via the impedance variation.Cyclostationary signal analysis and Wiener filtering areused to extract mechanical information contained into the

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electrical current signal. Then statistical indicators such askurtosis are adopted to highlight the presence of a defect.

Theoretical results and applications are presented inseveral fields such as DNA sequence analysis, biomedicalsignal analysis, system identification, mechanical systems,communications.

In the paper “Short exon detection in DNA sequencesbased on multifeature spectral analysis” by N. Y. Songand H. Yan, DNA bending stiffness, disrupt energy, freeenergy, and propeller twist properties are analyzed by anautoregressive (AR) model. The linear prediction matricesfor the four features are combined to find the same set oflinear prediction coefficients, from which the spectrum of theDNA sequence is estimated and exons are detected based onthe 1/3 frequency component. Moving windows of differentsizes in the AR model are used to account for the non-stationarity of DNA sequences.

In the paper “Selection of nonstationary dynamic featuresfor obstructive sleep apnea detection in children” by L. M.Cano et al., a methodology for selecting a set of relevantnonstationary features to increase the specificity of theobstructive sleep apnea detector is proposed. Specifically,dynamic features are extracted from time-evolving spectralrepresentation of photoplethysmography envelope record-ings.

In the paper “A self-adaptive approach for the detectionand correction of stripes in the sinogram: suppression of ringartifacts in CT imaging” by A. N. M. A. N. M. Ashrafuzzamanet al., novel techniques are proposed for the detection andsuppression of ring artifacts in computed tomography (CT)imaging. First-and second-order derivatives of the sinogramare exploited. In addition, a new method for the detectionof wideband contiguous stripes using the mean curve andmultilevel polyphase decomposition of the given sinogram isalso proposed.

In the paper “Mean-square performance analysis of thefamily of selective partial update NLMS and affine projectionadaptive filter algorithms in nonstationary environment” byM. S. E. Abadi and F. Moradiani, a general framework ispresented for mean-square performance analysis in nonsta-tionary environment of the selective partial update affineprojection algorithm (SPU-APA) and the family of SPUnormalized least mean-squares (SPU-NLMSs) adaptive filteralgorithms.

In “An improved flowchart for Gabor order tracking withGaussian window as the analysis window” by Y. Jin andZ.-Y. Hao, an improved flowchart for Gabor order trackingis proposed, which eliminates the try-and-error process ofanalysis parameters.

In the paper “Performance of post-demodulator adaptivefilters for FSK signals in a multipath environment” S.-T. Leeet al. extend understanding of the post-demodulator filterand demonstrate that the statistical assumptions that alignbit error rate (BER) performance with MSE performance donot apply in this context and that simply decreasing the MSEmight increase the BER rather than decrease it. An alternativepost demodulator adaptive filter with similar complexity tothe least mean square (LMS) filter is proposed which showsimproved BER performance.

In the paper “A study on conjugate quadrature filters” byJ.-S. Leng and T.-Z. Huang, a general method to constructa (J + 1)-length conjugate quadrature filter (CQF) withmultiplicity r and scale a starting from a J-length CQFis obtained. As a special case, the authors address theconstruction of a (J + 1)-length CQF with multiplicity 2and scale 2 which can generate a compactly supportedsymmetric-antisymmetric orthonormal multiwavelet systemstarting from a J-length CQF.

Acknowledgment

H. M. Ozaktas acknowledges partial support of the TurkishAcademy of Sciences.

Patrick FlandrinAntonio NapolitanoHaldun M. Ozaktas

David J. Thomson

Photograph © Turisme de Barcelona / J. Trullàs

Preliminary call for papers

The 2011 European Signal Processing Conference (EUSIPCO 2011) is thenineteenth in a series of conferences promoted by the European Association forSignal Processing (EURASIP, www.eurasip.org). This year edition will take placein Barcelona, capital city of Catalonia (Spain), and will be jointly organized by theCentre Tecnològic de Telecomunicacions de Catalunya (CTTC) and theUniversitat Politècnica de Catalunya (UPC).EUSIPCO 2011 will focus on key aspects of signal processing theory and

li ti li t d b l A t f b i i ill b b d lit

Organizing Committee

Honorary ChairMiguel A. Lagunas (CTTC)

General ChairAna I. Pérez Neira (UPC)

General Vice ChairCarles Antón Haro (CTTC)

Technical Program ChairXavier Mestre (CTTC)

Technical Program Co Chairsapplications as listed below. Acceptance of submissions will be based on quality,relevance and originality. Accepted papers will be published in the EUSIPCOproceedings and presented during the conference. Paper submissions, proposalsfor tutorials and proposals for special sessions are invited in, but not limited to,the following areas of interest.

Areas of Interest

• Audio and electro acoustics.• Design, implementation, and applications of signal processing systems.

l d l d d

Technical Program Co ChairsJavier Hernando (UPC)Montserrat Pardàs (UPC)

Plenary TalksFerran Marqués (UPC)Yonina Eldar (Technion)

Special SessionsIgnacio Santamaría (Unversidadde Cantabria)Mats Bengtsson (KTH)

FinancesMontserrat Nájar (UPC)• Multimedia signal processing and coding.

• Image and multidimensional signal processing.• Signal detection and estimation.• Sensor array and multi channel signal processing.• Sensor fusion in networked systems.• Signal processing for communications.• Medical imaging and image analysis.• Non stationary, non linear and non Gaussian signal processing.

Submissions

Montserrat Nájar (UPC)

TutorialsDaniel P. Palomar(Hong Kong UST)Beatrice Pesquet Popescu (ENST)

PublicityStephan Pfletschinger (CTTC)Mònica Navarro (CTTC)

PublicationsAntonio Pascual (UPC)Carles Fernández (CTTC)

I d i l Li i & E hibiSubmissions

Procedures to submit a paper and proposals for special sessions and tutorials willbe detailed at www.eusipco2011.org. Submitted papers must be camera ready, nomore than 5 pages long, and conforming to the standard specified on theEUSIPCO 2011 web site. First authors who are registered students can participatein the best student paper competition.

Important Deadlines:

P l f i l i 15 D 2010

Industrial Liaison & ExhibitsAngeliki Alexiou(University of Piraeus)Albert Sitjà (CTTC)

International LiaisonJu Liu (Shandong University China)Jinhong Yuan (UNSW Australia)Tamas Sziranyi (SZTAKI Hungary)Rich Stern (CMU USA)Ricardo L. de Queiroz (UNB Brazil)

Webpage: www.eusipco2011.org

Proposals for special sessions 15 Dec 2010Proposals for tutorials 18 Feb 2011Electronic submission of full papers 21 Feb 2011Notification of acceptance 23 May 2011Submission of camera ready papers 6 Jun 2011