Time-variant filtering of signals in the mixed time frequency domain

Saleh, Bahaa E. A.; Subotic, Nikola S.

doi:10.1109/tassp.1985.1164753

Cited by 41 publications

(8 citation statements)

References 11 publications

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“…Section IV considers the property of unitarity (preservation of inner products, Moyal's formula). Important implications of unitarity include a method for least-squares signal synthesis [38], [39], [42], [44]- [48]. The application of the results of Sections III and IV to the -distribution yields interesting new relations.…”

Section: Wherementioning

confidence: 99%

The hyperbolic class of quadratic time-frequency representations. II. Subclasses, intersection with the affine and power classes, regularity, and unitarity

Hlawatsch

Papandreou-Suppappola

Boudreaux-Bartels

1997

IEEE Trans. Signal Process.

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Part I of this paper introduced the hyperbolic class (HC) of quadratic/bilinear time-frequency representations (QTFR's) as a new framework for constant-Q time-frequency analysis. The present Part II defines and studies the following four subclasses of the HC: • The localized-kernel subclass of the HC is related to a timefrequency concentration property of QTFR's. It is analogous to the localized-kernel subclass of the affine QTFR class. • The affine subclass of the HC (affine HC) consists of all HC QTFR's that satisfy the conventional time-shift 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 time-shift" covariance property. They form the intersection of the HC with the recently introduced power classes. • The power-warp subclass of the HC consists of all HC QTFR's that satisfy a covariance to power-law frequency warpings. It is the HC counterpart of the shift-scale covariant subclass of Cohen's class. All of these subclasses are characterized by 1-D kernel functions. It is shown that the affine HC is contained in both the localizedkernel hyperbolic subclass and the localized-kernel affine subclass and that any affine HC QTFR can be derived from the Bertrand unitary P 0-distribution 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 least-squares signal synthesis and new relations for the Altes-Marinovich Q-distribution.

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Section: Wherementioning

confidence: 99%

The hyperbolic class of quadratic time-frequency representations. II. Subclasses, intersection with the affine and power classes, regularity, and unitarity

Hlawatsch

Papandreou-Suppappola

Boudreaux-Bartels

1997

IEEE Trans. Signal Process.

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“…More recently frequency-domain techniques have been applied to shift-variant discrete-time systems [91 and to time-varying filtering [10]. In this section, we review basic time-varying, linear-systems theory and use it to interpret the results of section 2.…”

Section: Time-varying Linear Systemsmentioning

confidence: 99%

Characterization and Simulation of an Acoustic Source Moving through an Oceanic Waveguide

Reuter¹

1994

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EXECUTIVE SUMMARYThe processing of acousti,; energy produced in an oceanic waveguide by a moving source in a near-field scenario is a challenging task statistically due to the nonstationarity of the data induced by the source motion. Many techniques of time series analysis require the estimation of at least second-order moments of the data received at a sensor or an array of sensors. The inherent assumption is made that statistically consistent estimates can be determined from sufficiently long segments of data. However, data of adequate length may not be available in the near-field scenario and so reliable estimates are difficult to obtain.In the first part of this report, we introduce a statistical characterization of the moving source via a time-varying linear-syste" :;.,_:'retation that inherently accounts for source motion. This approach demonstrates how sp% ,-.-. ,erence, which is indicative of temporally nonstationary data, is dependent on various envirn -mertal and source parameters. In the second part, wc present a technique that uses this interpretatioa to simulate the acoustic time series received at a sensor or an array of sensors of arbitrary geometry due to an acoustic source moving through an oceanic waveguide. This simulation can be L~ed tn test how source motion affects the performance of signal and array processing algorithms. We further ciLmonstrate the utility of this algorithm by comparing simulation results with experimental data.Ao6s3t1on 7OUW

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“…Whereas many of the treatments that are performed on signals can be viewed as a filter, there are several proposals in this direction such as time-variant filtering [21][22][23], filtering in fractional domains [24][25][26] and optimal filtering in fractional domain [17,[27][28][29]. Recently, applications of these developments have been reported in areas such as seismic signals [23,30,31] and biological signals [32], showing with this the relevance of the fractional Fourier analysis in processing of non-stationary signals.…”

Section: Introductionmentioning

confidence: 99%

“…The works [21][22][23] are based on a convolution operation, but, its representation in a fractional domain is not studied, only its implementation in the time domain and the frequency domain are analyzed. Among the works on filtering in fractional domains, the works by [24] and [26] emerge as the seminal ones, paving the way for new developments.…”

Section: Introductionmentioning

confidence: 99%

A time-variant filtering approach for non-stationary random signals based on the fractional convolution

2016

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Time-variant filtering of signals in the mixed time frequency domain

Cited by 41 publications

References 11 publications

The hyperbolic class of quadratic time-frequency representations. II. Subclasses, intersection with the affine and power classes, regularity, and unitarity

The hyperbolic class of quadratic time-frequency representations. II. Subclasses, intersection with the affine and power classes, regularity, and unitarity

Characterization and Simulation of an Acoustic Source Moving through an Oceanic Waveguide

A time-variant filtering approach for non-stationary random signals based on the fractional convolution

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