Regularity and unitarity of affine and hyperbolic time-frequency representations

Authors

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

Document Type

Conference Proceeding

Date of Original Version

1-1-1993

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.

Publication Title, e.g., Journal

Proceedings ICASSP IEEE International Conference on Acoustics Speech and Signal Processing

Volume

3

Citation/Publisher Attribution

Hlawatsch, Franz, Antonia Papandreou, and G. Faye Boudreaux-Bartels. "Regularity and unitarity of affine and hyperbolic time-frequency representations." Proceedings ICASSP IEEE International Conference on Acoustics Speech and Signal Processing 3, (1993). https://digitalcommons.uri.edu/ele_facpubs/1602