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An Implementation of the “algorithme à trous” to Compute the Wavelet Transform

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Wavelets

Part of the book series: Inverse Problems and Theoretical Imaging ((IPTI))

Abstract

The computation of the wavelet transform involves the computation of the convolution product of the signal to be analysed by the analysing wavelet. It will be shown that the computation load grows with the scale factor of the analysis. We are interested in musical sounds lasting a few seconds. Using a straightforward algorithm leads to a prohibitive computation time, so we need a more effective computation procedure.

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References

  1. M. HOLSCHNEIDER. R. KRONLAND-MARTINET, J. MORLET and Ph. TCHAMITCHIAN: A real time algorithm for signal analysis with the help of the wavelet transform. Preprint, CPT, CNRS-Luminy, Marseille, France.

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  2. R. KRONLAND-MARTINET. J. MORLET and A. GROSSMANN: Analysis of sound patterns through wavelet transforms. International Journal of Pattern Recognition and Artificial Intelligence, Special issue on expert systems and pattern analysis, Vol 1 n°2. World Scientific Publishing Company. 97–126.

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  3. R. KRONLAND-MARTINET: The use of the wavelet transform for the analysis, synthesis and processing of speech and music sounds. Preprint. LMA CNRS. 31 Chemin Joseph Aiguier, 13402 Marseille CEDEX 9, France.

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  4. J. F. ALLOUIS: Use of High Speed Microprocessors for Digital Synthesis, in Foundations of Computer Music, Article 18, Edited by C. ROADS and J. STRAWN, The MIT Press. 1985.

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© 1989 Springer-Verlag Berlin Heidelberg

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Dutilleux, P. (1989). An Implementation of the “algorithme à trous” to Compute the Wavelet Transform. In: Combes, JM., Grossmann, A., Tchamitchian, P. (eds) Wavelets. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97177-8_29

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  • DOI: https://doi.org/10.1007/978-3-642-97177-8_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-97179-2

  • Online ISBN: 978-3-642-97177-8

  • eBook Packages: Springer Book Archive

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