A Method for the Generation and Processing of Dyadic Indexed Data

Author

Besslich, P.W.

Author_Institution

Department of Electrical Engineering, University of Bremen

Issue

5

fYear

1983

fDate

5/1/1983 12:00:00 AM

Firstpage

487

Lastpage

494

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.

Keywords

Boolean function minimization; Hamming distance; Walsh–Hadamard transform; dyadic index system; dyadic shift; fast in-place radix-2 transformation; fuzzy function minimization; weighting transform; Boolean functions; Discrete transforms; Frequency; Fuzzy systems; Hamming distance; Image analysis; Indexing; Logic arrays; Minimization methods; Shape; Boolean function minimization; Hamming distance; Walsh–Hadamard transform; dyadic index system; dyadic shift; fast in-place radix-2 transformation; fuzzy function minimization; weighting transform;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/TC.1983.1676260

Filename

1676260