Generalized Phase Shifting for $M$ -Band Discrete Wavelet Packet Transforms

This correspondence presents a novel method for the construction of translation-invariant discrete wavelet packet (TIDWP) transforms for any decomposition level k, starting from any phase of a critically sampled discrete wavelet-packet representation of level k. The process is performed by phase shifting, i.e., the direct recovering of the wavelet coefficients omitted by the downsampling operations of each decomposition level without reconstructing the input signal. The proposed method enables tradeoffs between memory utilization and computational efficiency for the construction of translation-invariant representations. Hence, it is useful in resource-constrained TIDWP-based applications of digital signal compression, image segmentation and detection of transients