Wavelet transform for time-frequency representation and filtration of discrete signals

Waldemar Popiński

Applicationes Mathematicae (1996)

  • Volume: 23, Issue: 4, page 433-448
  • ISSN: 1233-7234

Abstract

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A method to analyse and filter real-valued discrete signals of finite duration s(n), n=0,1,...,N-1, where N = 2 p , p>0, by means of time-frequency representation is presented. This is achieved by defining an invertible discrete transform representing a signal either in the time or in the time-frequency domain, which is based on decomposition of a signal with respect to a system of basic orthonormal discrete wavelet functions. Such discrete wavelet functions are defined using the Meyer generating wavelet spectrum and the classical discrete Fourier transform between the time and the frequency domains.

How to cite

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Popiński, Waldemar. "Wavelet transform for time-frequency representation and filtration of discrete signals." Applicationes Mathematicae 23.4 (1996): 433-448. <http://eudml.org/doc/219144>.

@article{Popiński1996,
abstract = {A method to analyse and filter real-valued discrete signals of finite duration s(n), n=0,1,...,N-1, where $N=2^p$, p>0, by means of time-frequency representation is presented. This is achieved by defining an invertible discrete transform representing a signal either in the time or in the time-frequency domain, which is based on decomposition of a signal with respect to a system of basic orthonormal discrete wavelet functions. Such discrete wavelet functions are defined using the Meyer generating wavelet spectrum and the classical discrete Fourier transform between the time and the frequency domains.},
author = {Popiński, Waldemar},
journal = {Applicationes Mathematicae},
keywords = {spectro-temporal filtration; orthonormal wavelet base; Discrete Fourier Transform; finite duration signals; wavelet transform; discrete signals; discrete Fourier transform; time-frequency analysis; orthonormal discrete wavelet functions},
language = {eng},
number = {4},
pages = {433-448},
title = {Wavelet transform for time-frequency representation and filtration of discrete signals},
url = {http://eudml.org/doc/219144},
volume = {23},
year = {1996},
}

TY - JOUR
AU - Popiński, Waldemar
TI - Wavelet transform for time-frequency representation and filtration of discrete signals
JO - Applicationes Mathematicae
PY - 1996
VL - 23
IS - 4
SP - 433
EP - 448
AB - A method to analyse and filter real-valued discrete signals of finite duration s(n), n=0,1,...,N-1, where $N=2^p$, p>0, by means of time-frequency representation is presented. This is achieved by defining an invertible discrete transform representing a signal either in the time or in the time-frequency domain, which is based on decomposition of a signal with respect to a system of basic orthonormal discrete wavelet functions. Such discrete wavelet functions are defined using the Meyer generating wavelet spectrum and the classical discrete Fourier transform between the time and the frequency domains.
LA - eng
KW - spectro-temporal filtration; orthonormal wavelet base; Discrete Fourier Transform; finite duration signals; wavelet transform; discrete signals; discrete Fourier transform; time-frequency analysis; orthonormal discrete wavelet functions
UR - http://eudml.org/doc/219144
ER -

References

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  1. [1] C. K. Chui, An Introduction to Wavelets, Academic Press, San Diego, 1992. Zbl0925.42016
  2. [2] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996. Zbl0644.42026
  3. [3] K. Flornes, A. Grossmann, M. Holschneider and B. Torresani, Wavelets on discrete fields, Appl. Comput. Harmonic Anal. 1 (1994), 137-146. Zbl0798.42021
  4. [4] C. Gasquet et P. Witomski, Analyse de Fourier et applications, filtrage, calcul numérique, ondelettes, Masson, Paris, 1990. 
  5. [5] L. H. Koopmans, The Spectral Analysis of Time Series, Academic Press, New York, 1974. Zbl0289.62056
  6. [6] Y. Meyer, Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs, Séminaire Bourbaki 662 (1985-1986). 
  7. [7] Y. Meyer, Ondelettes et opérateurs I, Hermann, Paris, 1990, 109-120. Zbl0694.41037
  8. [8] W. H. Press, B. P. Flannery, S. A. Teukolsky and W. Vetterling, Numerical Recipes-The Art of Scientific Computing, Cambridge University Press, 1992. Zbl0845.65001
  9. [9] R. C. Singleton, An algorithm for computing the mixed radix fast Fourier transform, IEEE Trans. Audio Electroacoustics AU-17 (2) (1969). 

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