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Revista Matemática Iberoamericana
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Published online: 1996-12-31
Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales
Loïc Hervé[1] (1) Université de Rennes I, FranceWe consider quadrature mirror filters, and the associated wavelet packet transform. Let $X = \{X_n \} _{n \in \mathbb Z}$ be a stationary signal which has a continuous spectral density, $f$. We prove that the $2^n$ signals, obtained from $X$ by $n$ iterations of the transform, " converge" to white noises when $n \rightarrow + \infty$. If $f$ is holderian, the convergence rate is exponential.
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Hervé Loïc: Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales. Rev. Mat. Iberoam. 12 (1996), 653-667. doi: 10.4171/RMI/210