Wavelet packet transform of stationary signals: Asymptotic behaviour of spectral densities
Summary: 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 hölderian, the convergence rate is exponential.
scientific article; zbMATH DE number 1002167