Perfect-reconstruction multiplierless low delay filter bank design

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Electrical and Computer Engineering

First Committee Member

Claude S. Lindquist - Committee Chair


Perfect Reconstruction (PR) filter banks are a useful tool in speech processing especially if system delay, operations count and power consumption are minimal. There is considerable interest in casual IIR PR filter banks because of the potential reduction in number of operations for a desired selectivity. This dissertation studies the effect of delay on filter behavior and obtains IIR PR filter banks with minimal delay.The filter bank polyphase matrix determinant is equal to a delay or a minimum phase rational transfer function. It is shown that both cases for the matrix determinant are found from the same solution of the Bezout identity matrix-vector equation. The IIR filter bank is shown to decouple into an arbitrary PR FIR bank followed by independent optimization of the poles and a parameterizing polynomial which is not wholly arbitrary. Causal IIR filter banks for which filter structure and system delay trade-offs can be made are found. The IIR system delay can be reduced considerably with acceptable filters. The poles contribute selectivity and delay reduction by moving the zeros forced by the perfect reconstruction condition to better locations.A filter cascade structure is proposed such that regularity is maintained when the filter coefficients are coded in Canonical Signed Digit (CSD) form. A post-processing Inverse Filtering method is introduced which cancels the reconstruction error due to coefficient coding. In general this error canceling inverse filter is split into a casual and an anti-causal part which forces extra delay. By properly coding some filter coefficients, however, the error is recovered without delay penalty. The post-processing inverse filter can be used selectively on critical signal portions, minimizing the operations overhead.


Engineering, Electronics and Electrical

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