Recursive digital filters with optimum equiripple passband magnitude characteristic

Abstract

The paper investigates, for the first time, the design of recursive digital filters that exhibit optimum equiripple passband magnitude characteristics. After a brief description of the optimum equiripple filters in the analog domain, digital optimum C (Chebyshev) tan and sine filters are derived directly in the digital domain through the minimization of the area under the passband characteristic function. The influence of the truncated coefficients is also considered and its effects are demonstrated through an example proving the robustness of the magnitude function. Furthermore, a design procedure is proposed for the optimum C tan half-band filter. To highlight the effectiveness of the proposed approximation, a comparative analysis is conducted with the staircase digital filter, as both filters optimize passband responses by minimizing the area under the characteristic function. The results of comparison demonstrate that the optimum equiripple approximation surpasses the staircase approximation, not only in the analog but also in the digital domain.