The gamma transform: a local time-frequency analysis method

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 (while the wavelet transform adapts according to the frequency). The discretized version of the gamma transform produces a gamma frame, and in fact a tight gamma frame for L/sup 2/(0,T) provided the frequency sampling interval /spl omega//sub 0/ is /spl les/2/spl pi//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.