A Fast Algorithm for Adapted Time–Frequency Tilings

Abstract

We first consider orthonormal bases of open face RNconsisting of discretized rescaled Walsh functions, whereNis a power of two. Given a vector, the best basis with respect to an additive cost function is found with an algorithm of orderO(NlogN). 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.