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 filter-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 filter-banks. 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 closed-form and numerical designs for the synthesis filter-bank are introduced, which aim for different 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. Finally, an efficient implementation for the special case of an allpass transformed filter-bank without subsampling is derived. This system, termed as filter-bank equalizer, allows to perform adaptive subband filtering with a low signal delay. It is shown how this filter-bank can be used for noise reduction, speech dereverberation, or speech intelligibility improvement in noisy environments. These low delay speech enhancement systems are of particular interest for applications within cell phones, hands-free devices, or digital hearing aids.