Multi-channel low-frequency room equalization using perceptually motivated constrained optimization

We consider the problem of multiple-loudspeaker low-frequency room equalization for a wide listening area, where the equalized loudspeaker is helped using the remaining ones. Using a spatial discretization of the listening area, we formulate the problem as a multipoint error minimization between desired and synthesized magnitude frequency responses. The desired response and cost function are formulated with a goal of capturing the room's spectral power profile, and penalizing strong resonances. Considering physical and psychoacoustical observations, we argue for the use of gain-limited, short, and well-localized equalization filters, with an additional delay for loudspeakers that help the equalized one. We propose a convex optimization framework for computing room equalization filters, where the mentioned filter requirements are incorporated as convex constraints. We verify the effectiveness of our equalization approach through simulations.