I.I.R. digital filter design using constrained optimisation techniques

A new design method for all-pole infinite impulse response (i.i.r.) digital filters is introduced. The method involves minimising the area between the ideal lowpass filter response in the passhand and the actual passband response, subject to a quadratic constraint which ensures filter realisability. A unique solution is obtained to the minimisation which relates the filter weights to the eigenvector of a Toeplitz matrix. The filters are seen to have a small ripple in the passhand and a sharp cutoff in the stopband.