Design of three‐dimensional IIR digital filters with complex coefficients using spectral transformations
Takashi Sekiguchi, Shinichi Takahashi · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1990
Abstract This paper describes a design method of three‐dimensional recursive digital filters with complex coefficients by means of spectral transformations applied to one‐dimensional recursive digital filters with complex coefficients. In multidimensional filters with complex coefficients having an analytic input signal, characteristics can be made arbitrary in the regions in which an input signal frequency component does not exist. Therefore, the degrees of freedom in design increase significantly. Since complex coefficient filters are introduced in the one‐dimensional prototype filter and the spectral transformation function (subfilter), there is no restriction on the cutoff radius in the spherically symmetric filters. In three‐dimensional recursive symmetric fan filters, (cone filters) the design of a passband with an almost arbitrary solid angle becomes possible by the direct transformation from one dimension to three. Also, the stability of the resulting filters is always guaranteed.