Singleton Wavelet Packet Matrix

Abstract

Wavelet Packet Transform (WPT) is one of the generalized forms of the wavelet transform that has been a subject of interest for a variety of researchers. Owing to the multi-resolution characteristic of WPT, it has stepped into various research fields. The literature presents WPT as an iterative filtering and sub-sampling procedure, generally applied over a set of input feature vectors. In this work, we propose WPT as a linear encoder that packs the iterative process in the form of a transformation matrix. This results in a one-step matrix realization of complex and iterative WPT. The proposed matrix implementation is compared with state-of-the-art iterative DWT and Wavelet Packet Decomposition used in a variety of hardware- and software-defined languages. The proposed Wavelet Packet Matrix surpasses the baseline methods in terms of increased speed and reduction in process complexity. The generated sparse matrix can be a rapid transformation stage in real-time systems. It becomes handy in compressed sensing, harmonic analysis of signal and other applications involving iterative WPT analysis.