Flexible time segmentations for time-varying wavelet packets

We examine the problem of how to choose a time-varying filter bank representation for a signal, which is optimal for a rate-distortion cost function. This involves deciding which filter tree to use, (frequency segmentation) and deciding when to prune or add branches to the tree, (time segmentation), For optimality the time and frequency segmentations must be done jointly and not sequentially. Herley et al. (see IEEE Trans. Signal Processing, vol.41, no.12, p.3341-60, 1993) described an algorithm to find the best binary time-frequency split of a signal. In this work, we remove the constraint of binary time segmentation and study the adaptive wavelet packets expansion of a signal with arbitrary segmentation. A fast dynamic programming based algorithm is proposed to solve the optimal segmentation problem. Experimental results on different classes of sources are provided