A fast algorithm for adapted time-frequency tilings
type: Item
instance of: scholarly article
title: A fast algorithm for adapted time-frequency tilings
zbMATH Open document ID: 0857.65148
author: Christoph Thiele
author: Lars F. Villemoes
published in: Applied and Computational Harmonic Analysis
publication date: 1997-02-20T00:00:00Z
review text: Orthonormal bases of \(\mathbb{R}^N\), with \(N\) a power of 2, are considered which consist of discretized rescaled Walsh functions. A fast algorithm of order \(O(N\log N)\) is presented, for selecting the best basis among all these bases, given a signal and an additive cost function. Instead of relying on dyadic interval segmentations, the algorithm operates directly in the time-frequency plane by constructing a tiling of minimal cost among all possible tilings with dyadic rectangles of area 1. In the second part of the paper, generalizations replacing the Walsh group are dicussed. Libraries of bases attached to other finite Abelian groups are introduced, and an analoguous algorithm for picking the minimal cost function can be found. The basis elements in these libraries correspond to subsets of the plane that are no longer rectangles, but spread over the plane. The main example involves the fast Fourier transform.
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 897661
zbMATH Keywords: best basis algorithm
zbMATH Keywords: adapted time frequency tilings
zbMATH Keywords: Walsh functions
zbMATH Keywords: fast algorithm
zbMATH Keywords: finite Abelian groups
zbMATH Keywords: fast Fourier transform
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
full work available at URL: acha.1996.0009
OpenAlex ID: W1978691304
DOI: 10.1006/ACHA.1996.0009
description: scientific article; zbMATH DE number 897661