Experiments in dimensionally-optimum Gabor representations

Series expansions of signals in which significant features of the signal are captured in a few large coefficients are desirable. It is shown that, given a collection of signals, it is possible to find Gabor representations for these that are maximally concentrated in time-frequency space. The following problem is addressed: given a signal set, find the window function of the Gabor expansion that minimizes an ´average dimension´ of the signal representations relative to that window. The dimension measure employed is entropy based and related to the quantum-mechanical technique where one interprets expansion coefficients as probabilities. An iterative algorithm based on partial derivatives of the signal set dimension with respect to the expansion function was used to evaluate the effectiveness of several nonlinear optimization algorithms in finding an optimum window.<>