A fast algorithm for adapted time-frequency tilings

Abstract

We first consider orthonormal bases of ℝN consisting of discretized rescaled Walsh functions, where N is a power of two. Given a vector, the best basis with respect to an additive cost function is found with an algorithm of order O(N log N). The algorithm operates in the time-frequency plane by constructing a tiling of minimal cost among all possible tilings with dyadic rectangles of area one. Then we discuss generalizations replacing the Walsh group, which controls the structure of the time-frequency plane, by other finite abelian groups. The main example here involves the Fast Fourier Transform. © 1996 Academic Press, Inc.