Some algebraic relations between involutions, convolutions, and correlations, with applications to holographic memories
type: Item
instance of: scholarly article
title: Some algebraic relations between involutions, convolutions, and correlations, with applications to holographic memories
zbMATH Open document ID: 0637.92022
DOI: 10.1007/BF00319516
published in: Biological Cybernetics
publication date: 1987-01-01T00:00:00Z
review text: Some of the basic definitions of the convolution and correlation operation are reviewed. The non-commutativity and non-associativity of the correlation are avoided by introducing a simple involution (which consists in reversing the order of the elements). It is shown that in the finite case, convolutions and correlations can be computed as standard matrix products. Some implications for holographic memory models are discussed.
Mathematics Subject Classification ID: 91E99
Mathematics Subject Classification ID: 00A05
Mathematics Subject Classification ID: 68R99
zbMATH DE Number: 4039704
zbMATH Keywords: spaces of doubly infinite sequences
zbMATH Keywords: non-commutativity
zbMATH Keywords: non-associativity
zbMATH Keywords: involution
zbMATH Keywords: convolutions
zbMATH Keywords: correlations
zbMATH Keywords: matrix products
zbMATH Keywords: holographic memory models
Wikidata QID: Q52134210
author: Peter H. Schönemann
reviewed by: R. Andonie
MaRDI profile type: Publication
cites work: Non-associative algebras. I: Fundamental concepts and isotopy
cites work: Q4061081
cites work: Convolution and correlation algebras
cites work: Self-organization and associative memory
description: scientific article; zbMATH DE number 4039704