The Gamma Transform: A Local Time-Frequency Analysis Method.
Abstract
In this paper we introduce the gamma transform, a local time-frequency analysis method which applies to causal signals. The gamma transform resolves the identity, has good time-frequency resolution, and adapts resolution windows according to the time delay. The discretized version of the gamma transform produces gamma frame and, in fact, a tight gamma frame for L2(O,T) provided the frequency sampling interval w0 is less than or equal to 2pi/T. We demonstrate the gamma frame decomposition and reconstruction with several numerical experiments using tight gamma frames and dual gamma frames. Finally, we give the four varieties of the gamma transform corresponding roughly to the four Fourier transforms.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 29, 1996
- Accession Number
- ADA312353
Entities
People
- Louis L. Scharf
- Neng-tsann Ueng
Organizations
- University of Colorado Boulder