Design of two‐dimensional IIR digital filters with complex coefficients using spectral transformations

Abstract

AbstractThis paper describes a new method for designing two‐dimensional (2‐D) digital filters with complex coefficients having circularly symmetric and fan characteristics by applying variable transformation (spectral variable) to one‐dimensional (1‐D) IIR digital filters with complex coefficients. A 2‐D digital filter with complex coefficients has an advantage in that it can increase greatly the degree of freedom for design, since once it satisfies the design specification partly in the frequency plane, its characteristics can be arbitrary in other regions.Here, a design method is proposed which makes positive use of this property of the complex coefficient digital filters. Since we have introduced the complex coefficient filters into spectral transformation functions and 1‐D prototype filters, there is no constraint on cutoff frequency (radius) accomplishable in circularly symmetric filters. In fan filters even a characteristic that has been difficult to design unless one uses optimization techniques, has become easy to design by means of variable transformation without using any optimization techniques. Moreover, the stability of the resulting IIR filters is guaranteed in simple conditions.