Wavelet packet transform of stationary signals: Asymptotic behaviour of spectral densities
type: Item
instance of: scholarly article
title: Wavelet packet transform of stationary signals: Asymptotic behaviour of spectral densities
zbMATH Open document ID: 0867.94004
DOI: 10.4171/RMI/210
author: Loïc Hervé
published in: Revista Matemática Iberoamericana
publication date: 1997-05-31T00:00:00Z
full work available at URL: https://eudml.org/doc/39523
review text: Summary: We consider quadrature mirror filters, and the associated wavelet packet transform. Let \(X=\{X_n\}_{n\in\mathbb{Z}}\) be a stationary signal which has a continuous spectral density \(f\). We prove that the \(2^n\) signals, obtained from \(X\) by \(n\) iterations of the transform, ``converge'' to white noises when \(n\to+\infty\). If \(f\) is hölderian, the convergence rate is exponential.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 1002167
zbMATH Keywords: quadrature mirror filters
zbMATH Keywords: wavelet packet transform
zbMATH Keywords: stationary signal
zbMATH Keywords: white noise
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1002167