A 2‐D digital filter design technique using separate approximation of phase and magnitude responses by denominator and numerator

Abstract

AbstractThis paper discusses a design of two‐dimensional HR digital filter in the frequency domain, where the magnitude and the phase responses are assigned separately to the denominator and the numerator, respectively, and are designed independently. the design procedure is as follows. Considering only the phase, the all‐pole filter (denominator polynomial) is designed. Then the numerator is designed from the 2‐D mirror‐ image polynomial as a correction for the magnitude. In earlier methods of this kind, a nonlinear problem is encountered in the design of the all‐pole filter in approximating the phase. By contrast, in this paper, the 2‐D group‐delay (phase) approximation is reduced to the 2‐D spectral approximation by using the cepstrum, and the derivation of the parameters is reduced to the solution of the 2‐D normal equation. From the viewpoint of ensuring the stability, an approximation by three‐term separable all‐pole filter is also shown, which makes the stability test easy. an algorithm is shown which solves the ap proximation problem for this case by iteratively solving the linear problem. the proposed design method features smaller computational complexity, since the denominator and the numerator polynomials are derived independently. In addition, the design is made easy since the linear problems are handled throughout the filter design.