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A generalized reverse jacket transform. (English) Zbl 1014.65150

Summary: Generalizations of the well-known Walsh-Hadamard transform (WHT), namely the center-weighted Hadamard transform (CWHT) and the complex reverse-jacket transform (CRJT) have been proposed, and their fast implementation and simple index generation algorithms have recently been reported. These transforms are of size 2 r ×2 r for integral values or r, and defined in terms of the binary radix representation of integers.

In this paper, using an appropriate mixed-radix representation of integers, we present a generalized transform called the general reverse jacket transform (GRJT) that unifies all the three classes of transforms, WHT, CWHT, and CRJT, and that is also applicable for any even length vectors, that is of size 2r×2r. A subclass of GRJT which includes CRJT (but not CWHT) is applicable for finite fields and useful for constructing error control codes.

MSC:
65T50Discrete and fast Fourier transforms (numerical methods)
94A08Image processing (compression, reconstruction, etc.)