Design of Complex IIR Digital Filters using Transformed Variables

The design of real IIR digital filters using conformal transform variables has been extensively researched; this paper deals with the design of complex IIR digital filters having non-symmetric transfer functions, and directly designed using transformed variables. The transformation used is an extension of a transform used previously for continuous-time complex filters; the extension adds a bilinear function which enables the transform to be used for designing discrete-time transfer functions. Approximations having equiripple and monotonically decreasing passbands are supported. Methods for improving numerical accuracy and minimizing coefficient sensitivities are described. A high-order cascade filter example simulated using Monte Carlo analysis demonstrates almost ideal accuracy.