Issue No.05 - May (1983 vol.32)
P.W. Besslich , Department of Electrical Engineering, University of Bremen
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.
weighting transform, Boolean function minimization, dyadic index system, dyadic shift, fast in-place radix-2 transformation, fuzzy function minimization, Hamming distance, Walsh?Hadamard transform
P.W. Besslich, "A Method for the Generation and Processing of Dyadic Indexed Data", IEEE Transactions on Computers, vol.32, no. 5, pp. 487-494, May 1983, doi:10.1109/TC.1983.1676260