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Problemy Peredachi Informatsii, 2016, Volume 52, Issue 4, Pages 49–63
(Mi ppi2221)
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This article is cited in 2 scientific papers (total in 2 papers)
Methods of Signal Processing
Derivation of fast algorithms via binary filtering of signals
M. S. Bespalov, A. S. Golubev, A. S. Pochenchuk Vladimir State University, Vladimir, Russia
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.
Received: 04.04.2016 Revised: 08.06.2016
Citation:
M. S. Bespalov, A. S. Golubev, A. S. Pochenchuk, “Derivation of fast algorithms via binary filtering of signals”, Probl. Peredachi Inf., 52:4 (2016), 49–63; Problems Inform. Transmission, 52:4 (2016), 359–372
Linking options:
https://www.mathnet.ru/eng/ppi2221 https://www.mathnet.ru/eng/ppi/v52/i4/p49
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Abstract page: | 1247 | Full-text PDF : | 49 | References: | 52 | First page: | 26 |
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