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 $n\to +\infty$. If $f$ is holderian, the convergence rate is exponential.