Abstract
The elements of an array of 2n data are indexed so that adjacent elements have Hamming distance 1. Based on this indexing a class of invertible fast in-place transformations is developed. The transform coefficients depend on the Hamming distance between the indexes of input data. A class of similar transformations exists in the Walsh-Hadamard domain. Three transform operations are discussed in detail: dyadic shift transform, a subsuming and averaging transformation and a weighting operation. Applications of the method are in the processing of Boolean and fuzzy switching functions, image analysis, etc.
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