Low-pass filters, martingales, and multiresolution analyses
type: Item
instance of: scholarly article
title: Low-pass filters, martingales, and multiresolution analyses
zbMATH Open document ID: 0980.42033
author: R. Gundy
published in: Applied and Computational Harmonic Analysis
publication date: 2002-02-19T00:00:00Z
review text: Necessary and sufficient conditions for a trigonometric polynomial to be a low-pass filter have been given by \textit{A. Cohen} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 5, 439-459 (1990; Zbl 0736.42021)] and \textit{W. M. Lawton} [J. Math. Phys. 31, No. 8, 1898-1901 (1990; Zbl 0708.46020)]. In the paper under review the author gives necessary and sufficient conditions for an arbitrary periodic function to be a low--pass filter, following the approach of Lawton. The technique also applies to functions that give rise to a Riesz basis.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 60G46
zbMATH DE Number: 1512547
zbMATH Keywords: low-pass filters
zbMATH Keywords: martingales
zbMATH Keywords: multiresolution analyses
zbMATH Keywords: Riesz basis
reviewed by: Richard A. Zalik
MaRDI profile type: Publication
full work available at URL: acha.2000.0320
OpenAlex ID: W2033571861
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DOI: 10.1006/ACHA.2000.0320
description: scientific article; zbMATH DE number 1512547