Abstract
The wavelet analysis, introduced by J. MORLET and Y. MEYER in the middle of the eighties, is a processus of time-frequency (or time-scale) analysis which consists of decomposing a signal into a basis of functions (ø jk ) called wavelets. These wavelets are in turn deduced from the analyzing wavelet ø by dilatations and translations. More precisely:
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the changing of the index k is mathematically realized by a time dilatation; the index k is a scale index corresponding to a range of frequency;
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for each k, the wavelets (ø jk ) are deduced one from the others by translation in time space, leading to a time analysis in the range of frequency corresponding to k. The higher the frequency, the better is the time resolution, in such a way that changing the index k makes a zoom effect.
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© 1991 Birkhäuser Boston
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Bonnet, P., Remond, D. (1991). Discrete Wavelets and Fast Wavelet Transform. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_8
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_8
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