Allpass-Based Analysis-Synthesis Filter-Banks

Filter-banks are an essential component of many algorithms for digital signal processing, which are nowadays employed in a variety of ubiquitous devices. Filter-banks enable signal processing in the frequency-domain and their design has often a significant influence on the performance of a system with regard to its computational complexity, signal quality and delay. In this thesis, novel design approaches for different types of allpass-based analysis-synthesis filter-banks are devised. A substantial benefit of these recursive filter-banks is that they can achieve a high frequency selectivity and/or a non-uniform time-frequency resolution with a low signal delay. One focus of this work is the design of allpass-based quadrature-mirror filter-banks (QMF-banks) with near-perfect reconstruction. New synthesis filter-banks are presented which consist of allpass polyphase filters. They are designed by simple analytical expressions such that the trade-off between reconstruction error and signal delay of the filter-bank can be controlled in a simple manner. The devised QMF-bank has been employed in a candidate proposal for a new ITU-T speech and audio codec and has helped to achieve a high speech and audio quality with a low signal delay. A key issue in the design of allpass-based filter-banks is to compensate non-linear phase distortions caused by the recursive analysis fillter-bank. Therefore, known as well as novel phase equalizer designs for this purpose are presented and analyzed. Another focus of this work is the design of allpass transformed analysis-synthesis fillterbanks. They can achieve a non-uniform time-frequency resolution similar to that of the human
auditory system, which is beneficial for speech and audio processing systems. Novel closedform and numerical designs for the synthesis filter-bank are introduced, which aim for dfferent design objectives. A benefit of the closed-form designs is their simplicity, while the numerical designs allow the explicit control of specific properties of the filter-bank such as signal delay, reconstruction error, bandpass characteristic of the synthesis filters etc. The new numerical designs are all stated as a convex optimization problem which can be solved rather easily.