The approximation of arbitrary complex filter responses

Approximation and design methods of a general class of IIR complex functions without any required symmetrical property are examined. A set of routines has been developed to allow arbitrary amplitude approximation of such asymmetrical functions. Approximation routines will include such features as high-order touch points in both passband and stopband regions, fixed poles and zeros and arbitrary frequency template shaping. These features, in conjunction with a Remez approximation algorithm, will permit the development of functions that realise any reasonable arbitrary shape and form of the transfer function. Approximation routines have been implemented in the XFILTER design software and a number of examples, demonstrating efficiency and flexibility of the proposed approximation method