Least square digital filter design in the frequency domain

[摘要] This thesis develops new methods for obtaining optimal frequency domain approximation in the design of digital filters. The approach uses a squared error approximation criterion and allows a transition band in the desired frequency response specification. Four particular cases are considered. The first case considers FIR filters whose frequency responses include transition bands and whose errors are uniformly weighted. The new technique defines the exact transition edges, maintains optimality, reduces the Gibbs;; phenomenon, and has low computational requirement. Two error measures are investigated, the discrete squared error and the integral squared error. The second case involves the near-singularity problems which occur in the design of FIR filter with zero transition band error. A new approach is developed and a considerable improvement over the existing techniques is obtained. This new design method could accommodate almost any weighting function, and has computational complexity comparable to those of the existing ones. The third case includes a complex frequency domain approximation in the IIR filter design. A technique based on the quasilinearization method is developed, and comparison shows that in most design examples the new approach appears to converge more rapidly than other competitive algorithms. Unlike other frequency domain linearization methods, the new algorithm does not modify the error criterion. The fourth case includes an IIR filter design method with magnitude specification in the frequency domain. The problem is formulated as a successive complex frequency domain approximation. A new algorithm to solve this problem is developed, and experiments indicate that the algorithm converges faster than the other competitors do for most of filter design examples.

[发布机构] Rice University

[效力级别] Electrical engineering