Filter bank tree and M-band wavelet packet algorithms in audio signal processing

This correspondence investigates M -band wavelet packets and a generalized framework for the design and efficient utilization of multirate filter bank trees (FBTs). While the increased flexibility of M -band wavelet packets over the standard 2-band wavelet packets is desirable in many signal processing applications, the possibilities in time-frequency design using arbitrary filter bank cascades are even greater. We show how to construct FBTs for arbitrary given tree-like splits of the time-frequency plane. Furthermore we give an explicit construction for efficient simultaneous subband and spectral analysis in the general FBT case. Results from audio signal processing applications show that the proposed methods in many cases yield better results than those using standard wavelet packets. Wavelet transforms constitute a well established tool in signal processing. Yet, as with many general tools, specific applications require suitable adaptations. Popular extensions to the wavelet transforms are the wavelet packet transforms [1] and the M -band wavelet transforms [2]. While the former allow binary timefrequency tilings (TFTs) [3], the latter correspond to M -adic logarithmic splits of the time-frequency axis. Like many extensions to wavelet theory that were initially inspired by certain applications, our investigations were started by the search for more flexible TFTs for analysis and denoising of severely distorted high fidelity audio signals. In contrast to M -band wavelet decompositions, M -band wavelet packets allow for TFTs as depicted in Fig. 1. Also there is no nonlinear phase restriction as with nontrivial 2-band orthonormal wavelets [4]. Several approaches to model human perception as well as analysis of audio signals suggest that even arbitrary M -adic TFTs may be too restrictive for reasonable audio signal processing. Probably the most popular of those approaches is the partition of the frequency axis into critical bands [5] of human auditory perception, used in many applications such as MPEG-audio coding. Another model for sound analysis comes Permission to publish this abstract separately is granted