Regularity and unitarity of affine and hyperbolic time-frequency representations

Franz Hlawatsch; Antonia Papandreou; G. Faye Boudreaux-Bartels

Regularity and unitarity of affine and hyperbolic time-frequency representations

Franz Hlawatsch, Antonia Papandreou, G. Faye Boudreaux-Bartels

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

Abstract

The affine and hyperbolic classes of quadratic time-frequency representations (QTFRs) provide frameworks for multiresolution or constant-Q time-frequency analysis. This paper studies the QTFR properties of regularity (QTFR reversibility) and unitarity (preservation of inner products, Moyal's formula) in the context of affine and hyperbolic QTFRs. We develop the calculus of inverse kernels and discuss important implications of regularity and unitarity, such as signal recovery, the derivation of other quadratic signal representations, optimum detection, least-squares signal synthesis, the effect of linear signal transforms, and the construction of QTFR basis systems.

Original language	English (US)
Title of host publication	Digital Speech Processing
Publisher	Publ by IEEE
Pages	111.245-248
ISBN (Print)	0780309464
State	Published - Jan 1 1993
Externally published	Yes
Event	1993 IEEE International Conference on Acoustics, Speech and Signal Processing - Minneapolis, MN, USA Duration: Apr 27 1993 → Apr 30 1993

Publication series

Name	Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
Volume	3
ISSN (Print)	0736-7791

Other

Other	1993 IEEE International Conference on Acoustics, Speech and Signal Processing
City	Minneapolis, MN, USA
Period	4/27/93 → 4/30/93

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

Cite this

Regularity and unitarity of affine and hyperbolic time-frequency representations. / Hlawatsch, Franz; Papandreou, Antonia; Boudreaux-Bartels, G. Faye.
Digital Speech Processing. Publ by IEEE, 1993. p. 111.245-248 (Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing; Vol. 3).

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

Hlawatsch, F, Papandreou, A & Boudreaux-Bartels, GF 1993, Regularity and unitarity of affine and hyperbolic time-frequency representations. in Digital Speech Processing. Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 3, Publ by IEEE, pp. 111.245-248, 1993 IEEE International Conference on Acoustics, Speech and Signal Processing, Minneapolis, MN, USA, 4/27/93.

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M3 - Conference contribution

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ER -

Regularity and unitarity of affine and hyperbolic time-frequency representations

Abstract

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ASJC Scopus subject areas

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