Title :
Tunable FIR and IIR Fractional-Delay Filter Design and Structure Based on Complex Cepstrum
Author :
Pei, Soo-Chang ; Lin, Huei-Shan
Author_Institution :
Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan
Abstract :
A cepstrum-based approach is proposed to design finite- and infinite-impulse-response (IIR) fractional-delay (FD) filters. The maximal-flatness criteria on frequency responses are formulated as a system of linear equations to solve the truncated complex cepstrum. The closed-form solutions to cepstrum sequences can be derived. Moreover, it is very attractive that the resultant cepstrum coefficients are directly proportional to the desired FD. Under a fixed filter order, the set of normalized complex cepstra needs to be computed once and stored, and the specific set for an arbitrary FD is obtained by simply multiplying the stored set with the delay value. According to this observation, we also design two kinds of tunable filter structures consisting of several linear-phase filters, in which it is more flexible to obtain better performance by adding the extra substructure without modifying the present one. Moreover, the tunable FD is simply controlled by a single parameter, and the usage of linear-phase filters saves half of the multipliers, largely reducing the cost of hardware implementation. In addition, we obtain an IIR all-pass filter with a wider useful band than that based on Thiran´s design.
Keywords :
FIR filters; IIR filters; all-pass filters; circuit tuning; frequency response; linear phase filters; IIR fractional-delay filter design; all-pass filter; closed-form solutions; frequency response; linear-phase filter; maximal-flatness criteria; normalized complex cepstra; tunable FIR filter; All-pass filter; Farrow structure; complex cepstrum; fractional-delay (FD) filter; linear-phase filter; tunable structure;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2009.2015212