Least pth optimization for the design of 1-D filters with arbitrary amplitude and phase responses

Closed-form formulas for the evaluation of the gradient vector and the Hessian matrix of an IIR (infinite impulse response) transfer function are presented. These formulas are used in a modified Newton optimization algorithm for the optimal design of IIR digital filters in the L/sub p/-norm sense. The method is expected to be useful in designing digital filters with arbitrary amplitude and phase responses. Issues concerning the selection of the initial point and stability of the filter designed are addressed. Design examples are included to illustrate the use of the proposed closed-form formulas.<>