Derivation of fast algorithms via binary filtering of signals

Derivation of fast algorithms via binary filtering of signals We present a new way to derive a fast algorithm realizing the discrete Walsh transform (DWT), which can be applied both in the traditional form, i.e., to a one-dimensional numerical array, and to a multi-dimensional array, as well as for a signal of a continuous argument in the form of a function or an image. The algorithm is presented as iterated application of the primitive discrete Haar transform (DHT) over two variables. Two standard ways of arranging the results of this simplest transform lead to the fast DWT in the Hadamard or Paley enumeration in the case of splitting the signal into equal parts. Application of the algorithm to analogous shifts of the periodic source signal results in longitudinal filtering of a signal via decomposing it into a sum of simpler signals. In an incomplete version of the last algorithm, we come to an analog of the fast DHT. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Derivation of fast algorithms via binary filtering of signals

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946016040049
Publisher site
See Article on Publisher Site

Abstract

We present a new way to derive a fast algorithm realizing the discrete Walsh transform (DWT), which can be applied both in the traditional form, i.e., to a one-dimensional numerical array, and to a multi-dimensional array, as well as for a signal of a continuous argument in the form of a function or an image. The algorithm is presented as iterated application of the primitive discrete Haar transform (DHT) over two variables. Two standard ways of arranging the results of this simplest transform lead to the fast DWT in the Hadamard or Paley enumeration in the case of splitting the signal into equal parts. Application of the algorithm to analogous shifts of the periodic source signal results in longitudinal filtering of a signal via decomposing it into a sum of simpler signals. In an incomplete version of the last algorithm, we come to an analog of the fast DHT.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 6, 2017

References

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