A method for sound field control applied to active noise control is presented and evaluated. The method uses Linear Quadratic Gaussian (LQG) feedforward control to find a Minimal Mean Square Error (MMSE)-optimal linear sound field controller under a causality constraint. It is obtained by solving a polynomial matrix spectral factorization and a linear (Diophantine) polynomial matrix equation. An important component in the design is the control signal penalty term of the criterion. Its use and influence is here discussed and evaluated using measured room impulse responses. The results indicate that the use of a relatively simple, frequency-weighted penalty on individual control signals provides most of the benefits obtainable by the considered more advanced alternative. We also introduce and illustrate several tools for performance analysis. An analytical expression for the attainable performance clearly reveals the performance loss generated by having to use a causal controller instead of the ideal noncausal controller. This loss is largest at low frequencies. Furthermore, we introduce a measure of the reproducibility of the target noise sound field with given control loudspeaker setups and room transfer functions. It describes how well a controller that uses an input subspace of dimension equal to the effective rank of the system is able to reproduce a target sound field. This performance measure can e.g. be used to support the selection of good combinations of placements of control loudspeakers.

A new multichannel approach to robust broadband loudspeaker-room equalization is presented. Traditionally, the equalization (or room correction) problem has been treated primarily by single-channel methods, where loudspeaker input signals are prefiltered individually by separate scalar filters. Single-channel methods are generally able to improve the average spectral flatness of the acoustic transfer functions in a listening region, but they cannot reduce the variability of the transfer functions within the region. Most modern audio reproduction systems, however, contain two or more loudspeakers, and in this paper we aim at improving the equalization performance by using all available loudspeakers jointly. To this end we propose a polynomial based MIMO formulation of the equalization problem. The new approach, which is a generalization of an earlier single-channel approach by the authors, is found to reduce the average reproduction error and the transfer function variability over a region in space. Moreover, pre-ringing artifacts are avoided, and the reproduction error below 1000 Hz is significantly reduced with an amount that scales with the number of loudspeakers used.

In this paper, a new multichannel approach to robust loudspeaker-room equalization is presented. Traditionally, the equalization (or room correction) problem has been treated mostly by single-channel methods, with loudspeaker signals being prefiltered individually by separate scalar filters. Single-channel methods can generally improve the average spectral flatness of the acoustic transfer functions in a listening region, but the variability of the transfer functions within the region cannot be affected. Most modern audio reproduction systems, however, contain two or more loudspeakers, and in this paper we aim at improving the equalization performance by using all available loudspeakers jointly. To this end we propose a general MIMO formulation of the problem, which is a multichannel generalization of an earlier single-channel approach by the authors. The new approach is found to reduce the average reproduction error and the spatial variability of the acoustic transfer functions. Moreover, pre-ringing artifacts are avoided, and the reproduction error below 1000 Hz is significantly reduced with an amount that scales with the number of loudspeakers used.

A well known problem in loudspeaker equalization is that mixed phase design of the inverse filter causes residual "pre-ringings" in the equalized system, due to the spatial variability of loudspeaker- room transfer functions. A common strategy for robust and perceptually acceptable equalization is therefore to use minimum phase filters only. In this paper, a method for cautious mixed phase equalization is proposed. By analysis of a set of room transfer functions, it is concluded that some non-minimum phase zeros are insensitive to receiver position, and can therefore be robustly inverted. The method improves upon a minimum phase equalization by extending the minimum phase model with a robustly invertible all pass link. Validation measurements show that the time-domain aspect of equalization is improved throughout the spatial region of interest, while pre-ringings are kept at a very low and prespecified level.