Limit distributions for wavelet packet coefficients of band-limited stationary random processes

This paper addresses the limit distribution of wavelet packet coefficients obtained by decomposing band-limited random processes. When the wavelet decomposition filters satisfy a certain property of regularity, strictly stationary band-limited random processes yield wavelet packet coefficients that are asymptotically uncorrelated and Gaussian distributed when the resolution level increases. For any given path, the variance of the limit distribution is the value of the power spectral density of the input process at a specific frequency. Experimental results are presented to assess the convergence rate when Daubechies filters are used.