DESIGN AND SYNTHESIS OF CASCADED AND MULTIRATE FIR DIGITAL FILTERS

Abstract

This research work is focusing on the design and synthesis of computationally efficient FIR digital filters operating in the cascade form and/ or in the multirate environment. A novel method for the synthesis of half-band filters using the frequency-response-masking technique is presented. This method leads to a new implementation architecture which can be exploited for multirate or multistage implementations of half-band filters. Several variations of the frequency response-masking technique structure are developed. Five possible implementation schemes are proposed for synthesizing five different classes of sharp bandstop filters. It is demonstrated in this thesis that one of the variations is particularly suitable for synthesizing multirate filters. This is because variation preserves all the hardware complexity advantages available in a multirate system. A new joint-optimization method is developed for designing cascaded FIR filters. In this joint-optimization method, two cascaded filters are jointly optimized using linear programming technique so that the frequency response ripple of one filter is 180° out of phase with that of another filter. The individual filters can therefore have a larger passband ripple magnitude than the maximum allowable overall ripple magnitude and yet the overall filter does not violate its tolerance limit. Finally, the design of decimation and interpolation filters for a 128-time oversampling Delta-Sigma data converter is chosen as examples to illustrate the design technique. The design technique involved is a combination of several techniques presented in this thesis.