Study on compuationally efficient FIR filters with prefilter-equalizer structure ans those with powers-of-two coefficients

Abstract

In this thesis, a systematic design algorithm for the cascade filter with the Cyclotomic Polynomial (CP) prefilter-equalizer structure and an efficient implementation method for programmable multiplierless filters are proposed. The CP prefilter-equalizer structure is composed of the CP prefilter, that is a cascade connection of CP``s, followed by a conventional FIR filter. We found that the design problem of the CP prefilter can be formulated as an optimization problem with linear objective functions by applying the logarithm to the transfer function of the CP prefilter. Then this problem is solved by linear programming (LP). In addition, we show that the uniformly spaced and the nonuniformly spaced equalizer design problems can be optimally solved by using LP. The resulting prefilter-equalizer design methods show better performance than existing ones. We also develop a method for simultaneous design of the prefilter and the equalizer. By representing the frequency response of the equalizer as a product of some polynomials, we can design equalizers following the prefilter design method. In this thesis, observing the characteristics of FIR filters, a set of polynomials which is useful for representing the equalizer is determined. Then the filter with the prefilter-equalizer structure is composed of the cascade connection of the CP``s and the equalizer polynomials. Using the proposed prefilter design method mentioned above, the prefilter and the equalizer can be designed simultaneously. In our design examples, the proposed filters show better performance than the filters designed separately. Finally, an efficient programmable multiplierless FIR filter with sums and differences of powers-of-two coefficients, usually called 2PFIR filter, is described. We made an observation that the exponents of 2PFIR filter coefficients representable by the canonical signed digit (CSD) code with M ternary digits can be chosen from some subsets of {0, 1, …, M-1}. This observation...