Joint optimization of multiple behavioral and implementation properties of digital IIR filter designs

Abstract

This paper presents an extensible framework for the simultaneous constrained optimization of multiple properties of digital IIR filters. The framework optimizes the pole-zero locations for behavioral properties of magnitude and phase response, and the implementation property of quality factors, subject to constraints on the same properties. We formulate the constrained nonlinear optimization problem as a sequential quadratic programming (SQP) problem. SQP solvers are robust when providing formulas for the gradients of the objective function and constraints. We program Mathematica to compute the gradient formulas and convert the formulas into Matlab programs to perform the optimization, The automated approach eliminates errors in manipulating the algebraic equations and transcribing equations into software. The key contributions are (1) an automated, extensible, multicriteria digital IIR filter optimization framework, and (2) a novel filter design. We have released the source code on the Internet.