Robust audio precompensation with probabilistic modeling of transfer function variability

A new approach to the single-channel loudspeaker equalization problem is presented. A scalar discrete-time mixed-phase precompensation filter is designed to be spatially robust, meaning that equalization performance should be insensitive to listener movements within a predefined spatial region. The problem is posed in a single-input multiple-output (SIMO) feedforward control framework and a polynomial solution is derived, based on a set of room transfer functions (RTFs) measured at a number of control points in the region, and a multipoint mean-square error (MSE) criterion. Spatial robustness is obtained by the introduction of two novel strategies. Firstly, a probabilistic model is used to describe the RTF variability around each control point, and the MSE criterion is averaged with respect to this variability. Secondly, the pre-response errors, normally associated with mixed-phase equalizer design, are alleviated by restricting the compensator to have a certain structure. The proposed method is shown to produce filters with excellent time-and frequency-domain performance.