Design issues in multirate digital filter banks, including transmultiplexers

Citation

Koilpillai, Ravinder David (1991) Design issues in multirate digital filter banks, including transmultiplexers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/C6MF-3A43. https://resolver.caltech.edu/CaltechETD:etd-06272007-082624

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Several aspects of the theory and design of FIR digital filter banks for analysis/synthesis systems are studied in this thesis. In particular, we focus on filter banks satisfying the perfect reconstruction (PR) property. We present a new approach to design PR filter banks wherein the filter bank is obtained by cosine-modulation of a linear-phase prototype filter of length N = 2mM, m [...] 1 (where M is the number of channels). The PR property is satisfied because the polyphase component matrix of the modulated filter bank is lossless. This is achieved by satisfying the necessary and sufficient condition - a pairwise power complementary property between the 2M polyphase components of the prototype. In this approach, regardless of the number of channels, we still design only the prototype. The design procedure involves the two-channel lossless lattice. This approach compares favorably (in terms of the number of parameters to be optimized and the ease of design) with other design techniques. Design examples and detailed comparisons are presented. The existing approaches for designing PR filter banks include the lattice based methods, which structurally force the polyphase component matrix to be lossless. New initialization procedures, which can be used to initialize the values of all the lattice parameters (prior to optimization), are presented. The main advantage is that we can get 'good' initializations by using conventional Quadrature Mirror Filter (QMF) banks and pseudo-QMF banks (which can be readily designed, but do not satisfy PR). It is shown that these filter banks have polyphase component matrices that are 'approximately' lossless. The initialization also enables the design of a family of PR filter banks. In conventional approaches to pseudo-QMF design, the prototype filter is obtained by optimization, wherein lies the main computational effort. We present a new approach in which the prototype of a M-channel filter bank is obtained by spectral factorization (of a 2Mth band filter), thereby eliminating the need for optimization. The overall transfer function T(z) has linear-phase and an approximate 'flat' magnitude response in the region [epsilon][...][omega][...] ([pi] - [epsilon] where [epsilon] depends on the transition bandwidth of the prototype [...]. A new spectral factorization algorithm (non-iterative) which is based on the Inverse Linear Predictive Coding (LPC) technique is presented. Design examples for the above method are obtained by using this algorithm. Finally, we consider a dual of the QMF circuit - the transmultiplexer (TMUX). Traditional TMUX designs suppress the undesirable crosstalk. The crosstalk-free transmultiplexer (CF-TMUX) focuses on crosstalk cancellation, rather that suppression. It is shown that the filters of a CF-TMUX are the same as the filters of a 1-skewed AF-QMF bank. In addition, if the QMF bank satisfies PR, then the TMUX also achieves PR.

Thesis Files