Design of two-dimensional FIR filter using hybrid domain approximation

Abstract

This paper proposes a zero-phase, two-dimensional (2-D) FIR filter design using a hybrid domain where a spatial variable and frequency variable are mixed. For a desired amplitude response given in 2-D frequency plane, the approximation method of 1-D FIR filter design is applied in two steps and the desired response is approximated. First, the approximation coefficients in the hybrid domain are obtained by min-max approximation for one of the frequency variables. Then filter coefficients are obtained by the frequency sampling method or inconsistent Čhebyshev approximation method for another of the variables. Moreover, the error distribution of the designed 2-D filter is evaluated; and, when the magnitude of the error is uneven in the frequency domain, then the method of redesigning is proposed to obtain good approximation. Since this method decomposes the calculation of the 2-D filter into the 1-D case, its design is very simple. Moreover, this method has the advantage of free setting the magnitude of error in the passband and stopband of filter.