Design of IIR eigenfilters in the frequency domain

In this work a method to apply the eigenfilter approach to the design of IIR filters in the frequency domain is described. The eigenfilter approach is an appealing way of designing digital filters, due mainly to the simplicity of its implementation: an error function is expressed as a quadratic form in the filter coefficients and the search of the eigenvector corresponding to the minimum eigenvalue yields the optimum solution. This technique has been successfully applied to the design of both FIR and IIR filters. In this work the IIR case is addressed: in our approach the error between a desired function and the response of a rational transfer function is expressed in the frequency domain. Some examples of numerical design are shown for different types of filters, lowpass and bandpass, to show the effectiveness of the presented method.