对合、卷积和相关之间的一些代数关系及其在全息存储器中的应用。

Some algebraic relations between involutions, convolutions, and correlations, with applications to holographic memories.

作者信息

Schönemann P H

出版信息

Biol Cybern. 1987;56(5-6):367-74. doi: 10.1007/BF00319516.

DOI:10.1007/BF00319516

PMID:3620535

Abstract

Convolutions and correlations # in spaces H of doubly infinite sequences are related by a # b = S(a Sb), where S is an involution which reflects the order in the integral domain Z on which the sequences are defined. This relation can be used to represent a non-associative correlation algebra (H, #) by an associative convolution algebra equipped with the involution S which, as is shown, greatly simplifies derivations. Related matrix representations of #, S are given for sequences with finite support in Ren. Some implications for holographic memory models are discussed.

摘要

双无穷序列空间(H)中的卷积和相关性通过(a#b = S(a Sb))相关联，其中(S)是一个对合，它反映了定义序列的整数域(Z)中的顺序。这种关系可用于通过配备对合(S)的结合卷积代数来表示非结合相关代数((H, #))，如所示，这极大地简化了推导过程。给出了(\mathbb{R}^n)中具有有限支撑的序列的(#)、(S)的相关矩阵表示。讨论了对全息记忆模型的一些影响。