Low-pass filters, martingales, and multiresolution analyses

被引：23

作者：

Gundy, RE ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Stat, Piscataway, NJ 08854 USA

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2000年 / 9卷 / 02期

关键词：

low-pass filters; martingales; multiresolution analyses;

D O I：

10.1006/acha.2000.0320

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Necessary and sufficient conditions for a trigonometric polynomial to be a lowpass filter have been given by A. Cohen (Ann.. Inst. H. Poincare Anal. Nonlineaire 7 (1990), 439-459) and W. Lawton (J. Math. Phys. 31 (1990), 1898-1901). We give 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. (C) 2000 Academic Press.

引用

页码：204 / 219

页数：16

共 15 条

[1] BIORTHOGONAL BASES OF COMPACTLY SUPPORTED WAVELETS [J].

COHEN, A ;

DAUBECHIES, I ;

FEAUVEAU, JC .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (05) :485-560

[2] WAVELETS, MULTISCALE ANALYSIS AND QUADRATURE MIRROR FILTERS [J].

COHEN, A .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1990, 7 (05) :439-459

[3] HARMONIC-FUNCTIONS FOR A TRANSITION OPERATOR AND APPLICATIONS [J].

CONZE, JP ;

RAUGI, A .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1990, 118 (03) :273-310

[4]

DAUBECHIES I, 1995, 10 LECTURES WAVELETS

[5]

DOBRIC V, 2000, J GEOM ANAL, V10, P413

[6]

GUNDY RF, 1999, CONT MATH, V247, P249

[7]

HERNANDEZ E, 1996, 1 COURSE WAVELET

[8]

JAMISON B, 1964, J MATH ANAL APPL, V9, P203

[9] STRONGLY MIXING G-MEASURES [J].

KEANE, M .

INVENTIONES MATHEMATICAE, 1972, 16 (04) :309-&

[10] NECESSARY AND SUFFICIENT CONDITIONS FOR CONSTRUCTING ORTHONORMAL WAVELET BASES [J].

LAWTON, WM .

JOURNAL OF MATHEMATICAL PHYSICS, 1991, 32 (01) :57-61

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