Design and Implementation of Linear-Phase and/or Pairwise-Symmetric Perfect-Reconstruction FIR Multirate Filter Banks

Citation

Nguyen, Truong Quang (1989) Design and Implementation of Linear-Phase and/or Pairwise-Symmetric Perfect-Reconstruction FIR Multirate Filter Banks. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8z2n-y592. https://resolver.caltech.edu/CaltechETD:etd-11102005-091115

Abstract

This thesis studies the structures, design procedures and implementations of FIR perfect-reconstruction digital filter banks. The first part of the thesis deals with the structures and the design procedures of the perfect-reconstruction filter banks where the polyphase transfer matrices are lossless. These structures are parameterized by a set of rotation angles [37]. The usual procedure is to blindly optimize these angles to minimize an objective function where the objective function consists of all the stopband energies of the filters which we would like to design. This procedure is very time-consuming because of the nonlinear objective function and the large number of parameters to be optimized. The pairwise-symmetry property is imposed on these perfect reconstruction systems as a means of decreasing the number of parameters (rotation angles). The pairwise-symmetric property together with a method to initialize these rotation angles gives a very efficient design procedure. Design examples and complexity of the pairwise-symmetric, perfect-reconstruction FIR filter banks have compared well with the approximate perfect-reconstruction systems.

The second part of the thesis studies the structures and the design procedures of perfect-reconstruction filter banks which yield linear-phase filters. By confining the problem to a class, we are able to count exactly the number of linear-phase, perfect-reconstruction filter banks in this class. For the two-channel filter banks, we have obtained structures and design procedures for all nontrivial systems. Comparison with the approximated perfect-reconstruction systems in terms of complexity and performance is made. In our subclass of linear-phase, perfect-reconstruction, there are three structures for the case of three-channel filter banks. By limiting the problem to one of these systems, we obtain structures which yield linear-phase, perfect-reconstruct ion filters. The implementation complexity is studied. Design examples for all new methods presented here are included, along with tabulation of lattice and filter coefficients.

[37] Z. Doganata, P. P. Vaidyanathan, and T. Q. Nguyen, "General Synthesis procedures for FIR lossless transfer matrices for perfect-reconstruction multirate filter bank applications," IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. ASSP-36, 1561-1574, Oct. 1988.

Thesis Files