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49
ModulationScale Analysis for Content Identification
 IEEE Transactions on Signal Processing
, 2004
"... For nonstationary signal classification, e.g., speech or music, features are traditionally extracted from a timeshifted, yet short data window. For many applications, these shortterm features do not efficiently capture or represent longer term signal variation. Partially motivated by human auditio ..."
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Cited by 11 (0 self)
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For nonstationary signal classification, e.g., speech or music, features are traditionally extracted from a timeshifted, yet short data window. For many applications, these shortterm features do not efficiently capture or represent longer term signal variation. Partially motivated by human audition, we overcome the deficiencies of shortterm features by employing modulationscale analysis for longterm feature analysis. Our analysis, which uses timefrequency theory integrated with psychoacoustic results on modulation frequency perception, not only contains shortterm information about the signals, but also provides longterm information representing patterns of time variation. This paper describes these features and their normalization. We demonstrate the effectiveness of our longterm features over conventional shortterm features in contentbased audio identification. A simulated study using a large data set, including nearly 10 000 songs and requiring over a billion audio pairwise comparisons, shows that modulationscale features improves content identification accuracy substantially, especially when time and frequency distortions are imposed. Index TermsAudio fingerprinting, audio identification, audio retrieval, auditory classification, content identification, feature extraction, feature normalization, longterm features, modulation features, modulation scale, modulation spectrum, pattern recognition, shortterm features, 2D features.
Joint Distributions of Arbitrary Variables Made Easy
 IEEE Signal Processing Letters
, 1996
"... In this paper, we propose a simple framework for studying certain distributions of variables beyond timefrequency and timescale. When applicable, our results turn the theory of joint distributions of arbitrary variables into an easy exercise of coordinate transformation. While straightforward, the ..."
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Cited by 9 (4 self)
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In this paper, we propose a simple framework for studying certain distributions of variables beyond timefrequency and timescale. When applicable, our results turn the theory of joint distributions of arbitrary variables into an easy exercise of coordinate transformation. While straightforward, the method can generate many distributions previously attainable only by the general construction of Cohen, including time versus inverse frequency, time versus Mellin transform (scale), and time versus chirp distributions. In addition to providing insight into these new signal analysis tools, warpbased distributions have efficient implementations for potential use in applications. This work was supported by the National Science Foundation, grant no. MIP9457438, and by the Office of Naval Research, grant no. N000149510849. 1 Introduction The successful application of joint timefrequency distributions to problems in timevarying spectral analysis has stimulated considerable recent...
Covariant TimeFrequency Representations Through Unitary Equivalence
 IEEE Signal Processing Letters
, 1996
"... We propose a straightforward characterization of all quadratic timefrequency representations covariant to an important class of unitary signal transforms (namely, those having two continuousvalued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie ..."
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Cited by 9 (2 self)
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We propose a straightforward characterization of all quadratic timefrequency representations covariant to an important class of unitary signal transforms (namely, those having two continuousvalued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie groups, we can describe these representations simply in terms of unitary transformations of the wellknown Cohen's and affine classes. This work was supported by the National Science Foundation, grant no. MIP9457438, the Office of Naval Research, grant no. N000149510849, and the Texas Advanced Technology Program, grant no. TXATP 003604 002. I. Introduction Quadratic timefrequency representations (TFRs) have found wide application in problems requiring timevarying spectral analysis [1, 2]. Since the distribution of signal energy jointly over time and frequency coordinates does not have a unique representation, there exist many different TFRs and many different ways to obtai...
Multiband modulation energy tracking for noisy speech detection
 IEEE Trans. Audio, Speech, Language Process
, 2006
"... Abstract—The ability to accurately locate the boundaries of speech activity is an important attribute of any modern speech recognition, processing, or transmission system. The effort in this paper is the development of efficient, sophisticated features for speech detection in noisy environments, usi ..."
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Cited by 9 (7 self)
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Abstract—The ability to accurately locate the boundaries of speech activity is an important attribute of any modern speech recognition, processing, or transmission system. The effort in this paper is the development of efficient, sophisticated features for speech detection in noisy environments, using ideas and techniques from recent advances in speech modeling and analysis, like presence of modulations in speech formants, energy separation and multiband filtering. First we present a method, conceptually based on a classic speech–silence discrimination procedure, that uses some newly developed, shorttime signal analysis tools and provide for it a detection theoretic motivation. The new energy and spectral content representations are derived through filtering the signal in various frequency bands, estimating the Teager–Kaiser Energy for each and demodulating the most active one in order to derive the signal’s dominant AM–FM components. This modulation approach demonstrated an improved robustness in noise over the classic algorithm, reaching an average error reduction of 33.5 % under 5–30dB noise. Second, by incorporating alternative modulation energy features in voice activity detection, improvement in overall misclassification error of a high hit rate detector reached 7.5 % and 9.5 % on different benchmarks. Index Terms—Detector evaluation, energy separation algorithm (ESA), modulations, multiband demodulation, speech analysis, speech endpoint detection, Teager energy, voice activity detection (VAD). I.
Nonstationary spectral analysis based on timefrequency operator symbols and underspread approximations
 IEEE TRANS. INF. THEORY
, 2006
"... We present a unified framework for timevarying or time–frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all m ..."
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Cited by 8 (4 self)
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We present a unified framework for timevarying or time–frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all major existing TF spectra such as the Wigner–Ville, evolutionary, instantaneous power, and physical spectrum. Our subsequent analysis focuses on the practically important case of nonstationary processes with negligible highlag TF correlations (socalled underspread processes). We demonstrate that for underspread processes all TF spectra yield effectively identical results and satisfy several desirable properties at least approximately. We also show that Gabor frames provide approximate Karhunen–Loève (KL) functions of underspread processes and TF spectra provide a corresponding approximate KL spectrum. Finally, we formulate simple approximate input–output relations for the TF spectra of underspread processes that are passed through underspread linear timevarying systems. All approximations are substantiated mathematically by upper bounds on the associated approximation errors. Our results establish a TF calculus for the secondorder analysis and timevarying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes.
Multiple Window TimeFrequency Analysis
 in Proc. IEEE Int. Symp. TimeFrequency and TimeScale Analysis
, 1996
"... We propose a robust method for estimating the timevarying spectrum of a nonstationary random process. Our approach extends Thomson's powerful multiple window spectrum estimation scheme to the timefrequency and timescale planes. The method refines previous extensions of Thomson's method through op ..."
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Cited by 8 (1 self)
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We propose a robust method for estimating the timevarying spectrum of a nonstationary random process. Our approach extends Thomson's powerful multiple window spectrum estimation scheme to the timefrequency and timescale planes. The method refines previous extensions of Thomson's method through optimally concentrated window and wavelet functions and a statistical test for extracting chirping line components. 1. INTRODUCTION Many methods exist for estimating the power spectrum of stationary signals. However, these methods are insufficient for the nonstationary signals that occur in important applications such as radar, sonar, acoustics, biology, and geophysics. These applications demand timefrequency representations that indicate how the power spectrum changes over time. To date research in timefrequency analysis has focused on deterministic signals. Only recently has attention turned to nonstationary random processes [14]. Unlike the power spectrum for stationary random proc...
On the Instantaneous Frequencies of Multicomponent AMFM Signals
 IEEE Signal Processing Lett
, 1998
"... We study the instantaneous frequencies (IF's) of multicomponent AMFM signals by extending the recent work on the twocomponent case by Loughlin and Tacer to the more general Mcomponent case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegatively wei ..."
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Cited by 7 (2 self)
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We study the instantaneous frequencies (IF's) of multicomponent AMFM signals by extending the recent work on the twocomponent case by Loughlin and Tacer to the more general Mcomponent case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegatively weighted average of the IF's of the components is proposed, which we apply as a method of interpreting the IF's of signals having no more than three dominant components at each time. Our quantitative study shows that in general, the IFbased monocomponent AMFM decomposition is not appropriate for the modeling and analysis of multicomponent AMFM signals unless all the components are well separated in the time domain. Index TermsAmplitude modulation, frequency domain analysis, frequency modulation, modulation/demodulation.
The discrete harmonic oscillator, Harper’s equation, and the discrete fractional Fourier transform
 J. Phys. A
, 2000
"... Abstract. Certain solutions to Harper’s equation are discrete analogues of (and approximations to) the Hermite–Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform ..."
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Cited by 6 (3 self)
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Abstract. Certain solutions to Harper’s equation are discrete analogues of (and approximations to) the Hermite–Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the timeevolution operator of the discrete harmonic oscillator. 1.
Stochastic timefrequency analysis using the analytic signal: Why the complementary distribution matters
 IEEE Trans. Signal Process
, 2003
"... Abstract—We challenge the perception that we live in a “proper world, ” where complex random signals can always be assumed to be proper (also called circularly symmetric). Rather, we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper, which m ..."
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Cited by 6 (1 self)
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Abstract—We challenge the perception that we live in a “proper world, ” where complex random signals can always be assumed to be proper (also called circularly symmetric). Rather, we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper, which means that its complementary correlation function is nonzero. We explore the consequences of this finding in the context of stochastic timefrequency analysis in Cohen’s class. There, the analytic signal plays a prominent role because it reduces interference terms. However, the usual timefrequency representation (TFR) based on the analytic signal gives only an incomplete signal description. It must be augmented by a complementary TFR whose properties are developed in detail in this paper. We show why it is still advantageous to use the pair of standard and complementary TFRs of the analytic signal rather than the TFR of the corresponding real signal. Index Terms—Complementary correlation, improper complex random process, interference reduction, nonstationary analytic signal, timefrequency distribution. I.
Adaptive TimeVarying Cancellation of Wideband Interferences in SpreadSpectrum Communications Based on TimeFrequency Distributions
 IEEE Trans. Signal Processing
, 1999
"... The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the timefrequency representation of the received signal from which the parameters of an adaptive timevarying interference excision ..."
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Cited by 6 (0 self)
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The aim of this paper is to propose an adaptive method for suppressing wideband interferences in spread spectrum (SS) communications. The proposed method is based on the timefrequency representation of the received signal from which the parameters of an adaptive timevarying interference excision filter are estimated. The approach is based on the generalized WignerHough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise. The performance of the proposed approach is evaluated in the presence of linear and sinusoidal FM interferences plus white Gaussian noise in terms of SNR improvement factor and bit error rate (BER).