Eigenspaces of the discrete Walsh transform

Eigenspaces of the discrete Walsh transform We refine the notion of a discrete Walsh function and generalize the notion of a discrete Walsh transform, for which we propose a method for generating a corresponding W-matrix. We propose spectral decompositions of the discrete Walsh transform operators in arbitrary enumerations, as well as methods for finding bases of eigenspaces, one of them using a new direct product of matrices. We propose a notation for the fast discrete Walsh transform algorithm in the Paley enumeration. We construct Parseval frames for eigenspaces of the discrete Walsh transform in the Paley enumeration and demonstrate methods for applying them in error detection and correction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Eigenspaces of the discrete Walsh transform

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946010030051
Publisher site
See Article on Publisher Site

Abstract

We refine the notion of a discrete Walsh function and generalize the notion of a discrete Walsh transform, for which we propose a method for generating a corresponding W-matrix. We propose spectral decompositions of the discrete Walsh transform operators in arbitrary enumerations, as well as methods for finding bases of eigenspaces, one of them using a new direct product of matrices. We propose a notation for the fast discrete Walsh transform algorithm in the Paley enumeration. We construct Parseval frames for eigenspaces of the discrete Walsh transform in the Paley enumeration and demonstrate methods for applying them in error detection and correction.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 19, 2010

References

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