Lars-Johan Brännmark

Compensation of Loudspeaker–Room Responses in a Robust MIMO Control Framework

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.

Spatially Robust Audio Compensation Based on SIMO Feedforward Control

This paper introduces a single-input multiple-output (SIMO) feedforward approach to the single-channel loudspeaker equalization problem. Using a polynomial multivariable control framework, a spatially robust equalizer is derived based on a set of room transfer functions (RTFs) and a multipoint mean-square error (MSE) criterion. In contrast to earlier multipoint methods, the polynomial approach provides analytical expressions for the optimum filter, involving the RTF polynomials and certain spatial averages thereof. However, a direct use of the optimum solution is questionable from a perceptual point of view. Despite its multipoint MSE optimality, the filter exhibits similar, albeit less severe, problems as those encountered in nonrobust single-point designs. First, in the case of mixed phase design it is shown to cause residual ldquopre-ringingsrdquo and undesirable magnitude distortion in the equalized system. Second, due to insufficient spatial averaging when using a limited number of RTFs in the design, the filter is overfitted to the chosen set of measurement points, thus providing insufficient robustness. A remedy to these two problems is proposed, based on a constrained MSE design and a method for clustering of RTF zeros. The outcome is a mixed phase compensator with a time-domain performance preferable to that of the original unconstrained design.

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.

Design and analysis of linear quadratic Gaussian feedforward controllers for active noise control

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.

Improved loudspeaker-room equalization using multiple loudspeakers and MIMO feedforward control

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.

Symmetric Loudspeaker-Room Equalization Utilizing a Pairwise Channel Similarity Criterion

Similarity of the room transfer functions (RTFs) of symmetric channel pairs is crucial for correct sound reproduction of, for example, stereophonic or 5.1 surround multichannel recordings. This physical and psychoacoustical insight yielded the filter design framework presented in this paper. The filter design framework introduced is based on MIMO feedforward control. It has the aim of pairwise equalization of two audio channels and incorporates two features. In the first place, each channel is individually equalized by minimizing the difference between a desired target response and the original RTF by means of support loudspeakers. The second and novel feature represents the similarity requirement and aims at minimizing the difference between the compensated RTFs of the two channels. In order to asses the proposed method a measure of RTF similarity is proposed. Tests with measurements of two different multichannel audio systems proved the method to be able to significantly improve the similarity of two RTFs.

Improved loudspeaker-room equalization for stereo systems regarding channel similarity

In this paper, a new approach to robust single-channel loudspeaker - room equalization for stereo systems based on psychoacoustic insights is presented. Traditionally, in single-channel equalization each channel is equalized individually according to a desired target. In case the target cannot be reached for at least one of the two channels, this approach results in different loudspeaker - room transfer functions of the two channels at the listening position. However, reproducing the intended sound image of stereo recordings requires equal acoustic transfer functions from the input to the two loudspeakers to the listening region. In this paper we aim not only at equalizing the individual channels according to a desired target, but also at explicitly requiring symmetry between the two channels of a stereo system. To this end we propose a two-channel similarity SIMO controller structure, which is an extension to an earlier approach by the authors. The new approach is evaluated based on measurements in a room and is found to reduce differences between the room transfer functions of the two channels in both frequency and time domain.

Multiple-point statistical room correction for audio reproduction: minimum mean squared error correction filtering.

This paper treats the problem of correction of loudspeaker and room responses using a single source. The objective is to obtain a linear correction filter, which is robust with respect to listener movement within a predefined region-of-interest. The correction filter is based on estimated impulse responses, obtained at several positions, and a linear minimum mean squared error criteria. The impulse responses are estimated using a Bayesian approach that takes both model errors and measurement noise into account, which results in reliable impulse response estimates and a measure of the estimation errors. The correction filter is then constructed by using information from both the estimated impulse response coefficients and their associated estimation errors. Furthermore, in the optimization criteria a time-dependent reflection filter is introduced, which attenuates the high frequency parts of the reflected responses, that is, the parts of the responses that cannot be compensated with a single source system. The resulting correction filter is shown to significantly improve both the temporal and spectral properties of the responses compared to the uncorrected system, and, furthermore, the obtained correction filter has a low level of pre-ringing.

Variable control of the pre-response error in mixed phase audio precompensation

We introduce a method for controlling the spatial robustness of a mixed phase loudspeaker equalizer design. The emphasis is on time domain behaviour and the pre-response error that is always present in mixed phase design. Based on measurements from a small spatial region, a mixed phase compensator is regularized to be valid also over a large spatial region. The regularization can be applied gradually to match any size of listener region, while fulfilling a set of constraints for the pre-response error. The compensation thus avoids the unacceptably high pre-response error levels that generally occur outside the measurement region. The proposed compensator design, which is validated on measurements in both small and large spatial regions, is shown to produce excellent results.