Order selection for and design of IIR filters

The design of infinite impulse response digital filters can be viewed as a spectral factorization problem. When one knows what the numerator and denominator orders are, this design problem is greatly simplified. Selection of the appropriate orders has long been a significant problem in recursive filter design. Recent work by Gray et al. suggests a general method by which the orders may be selected prior to design. In this paper, infinite impulse response digital filters are designed from finite impulse response prototypes using the Gray technique to first select the order. Once the order has been determined, the recursive filter coefficients are determined directly from the finite Impulse filter. Because of the wealth of knowledge available concerning order lengths for nonrecursive filters, the procedures used here permit direct comparison between the two filter methods.