Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales

Abstract

We 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.