A new transform for time-frequency analysis

Author

Kumar, Arun ; Fuhrmann, Daniel R. ; Frazier, Michael ; Jawerth, Björn D.

Author_Institution

Southwestern Bell Technol. Resources Inc., St. Louis, MO, USA

Volume

40

Issue

7

fYear

1992

fDate

7/1/1992 12:00:00 AM

Firstpage

1697

Lastpage

1707

Abstract

The psi-decomposition of a signal, in which the signal is written as a weighted sum of certain elementary synthesizing functions, is described. The set S of synthesizing functions consists of dilated and translated copies of two parent functions, which are concentrated in both the time and the frequency domains. The weighting constants in the psi-decomposition define a transform called the phi-transform. The phi-transform of a signal captures both the frequency content and the temporal evolution of a nonstationary signal. The phi-transform is linear, continuous, and continuously invertible. The set S of synthesizing functions used in the psi-decomposition is nonorthogonal, hence considerable flexibility is permitted in its construction. It is shown with the help of two examples that the set S is easy to construct

Keywords

frequency-domain analysis; signal processing; time-domain analysis; transforms; continuously invertible transform; elementary synthesizing functions; frequency domain; nonstationary signal; phi-transform; psi-decomposition; signal processing; temporal evolution; time domain; time-frequency analysis; translated copies; weighting constants; Fourier transforms; Frequency domain analysis; Helium; Mathematics; Signal analysis; Signal processing; Signal synthesis; Time frequency analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.143442

Filename

143442