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

• Autorzy: Waldemar Popiński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

spectro-temporal filtration; orthonormal wavelet base; Discrete Fourier Transform; finite duration signals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1995-1996
• Tom: 23
• Numer: 4
• Strony: 433-448

Daty

wydano

1996

otrzymano

1995-03-09

Twórcy

autor

Waldemar Popiński

• Research and Development Center of Statistics, al. Niepodległości 208, 00-925 Warszawa, Poland

Bibliografia

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