A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions

A. Papandreou; F. Hlawatsch; G. F. Boudreaux-Bartels

doi:10.1109/TFTSA.1992.274241

A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions

A. Papandreou, F. Hlawatsch, G. F. Boudreaux-Bartels

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

8 Scopus citations

Abstract

We study the Bertrand distribution which is a member of the affine class of time-frequency distributions (TFDs), and the Altes distribution which does not belong to any known class of TFDs. We show that both TFDs are closely related to a "hyperbolic time-frequency geometry." Based on this geometry, we define and study a new "hyperbolic class" of TFDs which contains both the Bertrand distribution and the Altes distribution. We show that the hyperbolic class can be derived from the well-known Cohen's class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.

Original language	English (US)
Title of host publication	Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	27-30
Number of pages	4
ISBN (Electronic)	0780308050, 9780780308053
DOIs	https://doi.org/10.1109/TFTSA.1992.274241
State	Published - 1992
Externally published	Yes
Event	1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Victoria, Canada Duration: Oct 4 1992 → Oct 6 1992

Publication series

Name	Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis

Conference

Conference	1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
Country/Territory	Canada
City	Victoria
Period	10/4/92 → 10/6/92

ASJC Scopus subject areas

Signal Processing

Access to Document

10.1109/TFTSA.1992.274241

Cite this

Papandreou, A., Hlawatsch, F., & Boudreaux-Bartels, G. F. (1992). A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions. In Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (pp. 27-30). [274241] (Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/TFTSA.1992.274241

A unified framework for the Bertrand distribution and the Altes distribution : The new hyperbolic class of quadratic time-frequency distributions. / Papandreou, A.; Hlawatsch, F.; Boudreaux-Bartels, G. F.

Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis. Institute of Electrical and Electronics Engineers Inc., 1992. p. 27-30 274241 (Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Papandreou, A, Hlawatsch, F & Boudreaux-Bartels, GF 1992, A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions. in Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis., 274241, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Institute of Electrical and Electronics Engineers Inc., pp. 27-30, 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Victoria, Canada, 10/4/92. https://doi.org/10.1109/TFTSA.1992.274241

Papandreou A, Hlawatsch F, Boudreaux-Bartels GF. A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions. In Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis. Institute of Electrical and Electronics Engineers Inc. 1992. p. 27-30. 274241. (Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis). doi: 10.1109/TFTSA.1992.274241

Papandreou, A. ; Hlawatsch, F. ; Boudreaux-Bartels, G. F. / A unified framework for the Bertrand distribution and the Altes distribution : The new hyperbolic class of quadratic time-frequency distributions. Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis. Institute of Electrical and Electronics Engineers Inc., 1992. pp. 27-30 (Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis).

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title = "A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions",

abstract = "We study the Bertrand distribution which is a member of the affine class of time-frequency distributions (TFDs), and the Altes distribution which does not belong to any known class of TFDs. We show that both TFDs are closely related to a {"}hyperbolic time-frequency geometry.{"} Based on this geometry, we define and study a new {"}hyperbolic class{"} of TFDs which contains both the Bertrand distribution and the Altes distribution. We show that the hyperbolic class can be derived from the well-known Cohen's class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.",

author = "A. Papandreou and F. Hlawatsch and Boudreaux-Bartels, {G. F.}",

note = "Publisher Copyright: {\textcopyright} 1992 IEEE.; 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis ; Conference date: 04-10-1992 Through 06-10-1992",

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AB - We study the Bertrand distribution which is a member of the affine class of time-frequency distributions (TFDs), and the Altes distribution which does not belong to any known class of TFDs. We show that both TFDs are closely related to a "hyperbolic time-frequency geometry." Based on this geometry, we define and study a new "hyperbolic class" of TFDs which contains both the Bertrand distribution and the Altes distribution. We show that the hyperbolic class can be derived from the well-known Cohen's class of TFDs by a frequency-warping procedure that potentially results in a constant-Q time-frequency analysis.

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A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions

Abstract

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ASJC Scopus subject areas

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