Design of linear-phase recursive filters by optimization of model reduced non-recursive filters

This paper presents a linear-phase IIR filter design approach, based on optimization of IIR filters obtained via model reduction of symmetric-coefficient FIR filters. The desired IIR filter is reached by minimizing the L ₂ error between the frequency response of the model reduced IIR filter and an almost-ideal frequency response. The objective function is constructed as the squared spectral norm of an interconnection of filters. The gradient of the objective function with respect to the IIR filter´s parameters is derived and used to apply Quasi-Newton algorithms. A design example is carried to illustrate the potential of the proposed approach.