A New Transform For Time-Frequency Analysis

Authors

Arun Kumar, Washington University in St Louis
Daniel R. Fuhrmann, Washington University in St Louis
Michael Frazier, Washington University in St Louis
Bjorn Jawerth, University of South Carolina

Document Type

Technical Report

Publication Date

1990-07-30

Filename

WUCS-90-26.pdf

Technical Report Number

WUCS-90-26

Abstract

This paper describes the Psi-decomposition of a signal, in which the signal is written as a weighted sum of certain elementary synthesizing functions. The set S of synthesizing functions consists of dilated and translated versions of two parent functions, which are concentrated in both the time and frequency domains. The weighting constant 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 non stationary signal. The Phil-transform is linear, continuous, and continuously invertible. The set S of synthesizing functions used in the Psi-decomposition is non-orthogonal, hence considerable flexibility is permitted in its construction. We will show with the help of two examples that the set S is easy to construct.

Comments

Permanent URL: http://dx.doi.org/10.7936/K7F18X35

Recommended Citation

Kumar, Arun; Fuhrmann, Daniel R.; Frazier, Michael; and Jawerth, Bjorn, "A New Transform For Time-Frequency Analysis" Report Number: WUCS-90-26 (1990). All Computer Science and Engineering Research.
https://openscholarship.wustl.edu/cse_research/701