Causal IIR Audio Precompensator Filters Subject to Quadratic Constraints

Abstract

Infinite impulse response (IIR) Wiener precompensator design, with constraints on causality, is here also extended to incorporate general quadratic constraints. A method for finding a linear quadratic optimal, causal discrete-time multiple-input multiple-output filter subject to a set of user defined constraints is proposed and analyzed. A method for designing causal filters subject to constraints on the power gains in a large number of small frequency intervals is also proposed. The resulting set of methods provide constrained stable IIR filters with optimal parameterization. Compared to finite impulse response Wiener filtering, the computational complexity is much lower; and compared to noncausal frequency domain designs, we gain control of the time-domain properties of the compensated system. The design methods are applied to a room compensation audio problem subject to filter power gain constraint(s) and are compared to a corresponding noncausal per-frequency method. The results are presented with audio filtering and sound field control as main motivating applications but the methods extend to other areas of linear feedforward controller design and Wiener filtering.