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The hyperbolic class of quadratic timefrequency representations  Part II: Subclasses . . .
 IEEE TRANS. SIGNAL PROCESSING
, 1997
"... Part I of this paper introduced the hyperbolic class (HC) of quadratic/bilinear timefrequency representations (QTFR’s) as a new framework for constantQ timefrequency analysis. The present Part II defines and studies the following four subclasses of the HC: • The localizedkernel subclass of the ..."
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Cited by 18 (3 self)
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Part I of this paper introduced the hyperbolic class (HC) of quadratic/bilinear timefrequency representations (QTFR’s) as a new framework for constantQ timefrequency analysis. The present Part II defines and studies the following four subclasses of the HC: • The localizedkernel subclass of the HC is related to a timefrequency concentration property of QTFR’s. It is analogous to the localizedkernel subclass of the affine QTFR class. • The affine subclass of the HC (affine HC) consists of all HC QTFR’s that satisfy the conventional timeshift covariance property. It forms the intersection of the HC with the affine QTFR class. • The power subclasses of the HC consist of all HC QTFR’s that satisfy a “power timeshift ” covariance property. They form the intersection of the HC with the recently introduced power classes. • The powerwarp subclass of the HC consists of all HC QTFR’s that satisfy a covariance to powerlaw frequency warpings. It is the HC counterpart of the shiftscale covariant subclass of Cohen’s class. All of these subclasses are characterized by 1D kernel functions. It is shown that the affine HC is contained in both the localizedkernel hyperbolic subclass and the localizedkernel affine subclass and that any affine HC QTFR can be derived from the Bertrand unitary P 0distribution by a convolution. We furthermore consider the properties of regularity (invertibility of a QTFR) and unitarity (preservation of inner products, Moyal’s formula) in the HC. The calculus of inverse kernels is developed, and important implications of regularity and unitarity are summarized. The results comprise a general method for leastsquares signal synthesis and new relations for the AltesMarinovich Qdistribution.
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 14 (6 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.
Timefrequency subspace detectors and application to knock detection
 JOURNAL OF ELECTRONICS AND COMMUNICATIONS
, 1999
"... We consider a composite hypotheses detection problem involving a subspace and an energy level, and we show that for this problem the matched subspace detector is uniformly most powerful and the generalized likelihood ratio detector. We present a generalization of the matched subspace detector and ti ..."
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Cited by 7 (3 self)
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We consider a composite hypotheses detection problem involving a subspace and an energy level, and we show that for this problem the matched subspace detector is uniformly most powerful and the generalized likelihood ratio detector. We present a generalization of the matched subspace detector and timefrequency methods for the formulation and design of subspace detectors. Finally, we apply the various detectors to the problem of detecting knock in car engines, and we demonstrate the potential advantages of timefrequency detectors.
Time–frequency signal processing: a statistical perspective
 in: Proceedings of the Workshop on Circuits, Systems and Signal Processing, Mierlo, The
, 1998
"... Abstract—Timefrequency methods are capable of analyzing and/or processing nonstationary signals and systems in an intuitively appealing and physically meaningful manner. This tutorial paper presents an overview of some timefrequency methods for the analysis and processing of nonstationary random s ..."
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Cited by 1 (1 self)
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Abstract—Timefrequency methods are capable of analyzing and/or processing nonstationary signals and systems in an intuitively appealing and physically meaningful manner. This tutorial paper presents an overview of some timefrequency methods for the analysis and processing of nonstationary random signals, with emphasis placed on timevarying power spectra and techniques for signal estimation and detection. We discuss two major definitions of timedependent power spectra— the generalized WignerVille spectrum and the generalized evolutionary spectrum—and show their approximate equivalence for underspread random processes. Timedependent power spectra are then applied to nonstationary signal estimation and detection. Specifically, simple expressions and designs of signal estimators (Wiener filters) and signal detectors in the stationary case are extended to underspread nonstationary processes. This results in timefrequency techniques for nonstationary signal estimation and detection which are intuitively meaningful as well as efficient and stable. I.
unknown title
, 2002
"... A learning approach to the detection of gravitational wave transients ..."
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Tempsfréquence et décision — Une introduction
"... C’est une évidence et une banalite ́ de dire que le monde qui nous entoure est “non stationnaire”. Si s’offrent bien sûr a ̀ notre observation des phénomènes empreints d’une grande régularite ́ (du moins rapportés a ̀ une échelle temporelle humaine, comme par exemple le mouvement des astres ..."
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C’est une évidence et une banalite ́ de dire que le monde qui nous entoure est “non stationnaire”. Si s’offrent bien sûr a ̀ notre observation des phénomènes empreints d’une grande régularite ́ (du moins rapportés a ̀ une échelle temporelle humaine, comme par exemple le mouvement des astres), ce par quoi le monde nâıt