Automatic order selection in the design of IIR filters

J.F. Kaiser´s empirical formula for FIR filter length as a function of transition width and rejection loss provides a simple FIR design algorithm. Recent developments in time serles analysis provide a procedure for selecting the orders of an IIR but fails to provide a simultaneous estimate of the quality of the approximation. By relating the order selection algorithm to Levinson recursion, this paper removes this difficulty. As an added benefit, analysis of the resulting relationship provides a highly automatic procedure for order selection and approximation by an IIR of any ideal transfer function.