The Gamma Transform: A Local Time-Frequency Analysis Method.
Technical rept. 1 Oct-31 Oct 95,
COLORADO UNIV AT BOULDER
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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 L2O,T provided the frequency sampling interval w0 is less than or equal to 2piT. 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.
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