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A Fast Algorithm for Adapted Time–Frequency Tilings

✍ Scribed by Christoph M. Thiele; Lars F. Villemoes

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
221 KB
Volume
3
Category
Article
ISSN
1063-5203

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✦ Synopsis

We first consider orthonormal bases of R N 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.

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