Sound-field reproduction in-room using optimal control techniques: Simulations in the frequency domain

Abstract

This paper describes the simulations and results obtained when applying optimal control to progressive sound-field reproduction (mainly for audio applications) over an area using multiple monopole loudspeakers. The model simulates a reproduction system that operates either in free field or in a closed space approaching a typical listening room, and is based on optimal control in the frequency domain. This rather simple approach is chosen for the purpose of physical investigation, especially in terms of sensing microphones and reproduction loudspeakers configurations. Other issues of interest concern the comparison with wave-field synthesis and the control mechanisms. The results suggest that in-room reproduction of sound field using active control can be achieved with a residual normalized squared error significantly lower than open-loop wave-field synthesis in the same situation. Active reproduction techniques have the advantage of automatically compensating for the room's natural dynamics. For the considered cases, the simulations show that optimal control results are not sensitive (in terms of reproduction error) to wall absorption in the reproduction room. A special surrounding configuration of sensors is introduced for a sensor-free listening area in free field.

Power-output regularization in global sound equalization

“…7 Classical WFS assumes that the reproduction environment is anechoic and therefore does not perform well in a real reproduction environment. 8 Nevertheless, the mechanisms of power output minimization and power absorption 9 between the reproduction sources still hold for sound field reproduction in closed spaces, as pointed out by Gauthier et al, who observed that sound absorption becomes important in reverberant enclosures when using optimal control techniques. 8 It was also observed that, at frequencies where the modal density is low, optimal control acts to create a sound energy flow over the sensor array and mainly prevents a pure standing wave pattern.…”

“…8 Nevertheless, the mechanisms of power output minimization and power absorption 9 between the reproduction sources still hold for sound field reproduction in closed spaces, as pointed out by Gauthier et al, who observed that sound absorption becomes important in reverberant enclosures when using optimal control techniques. 8 It was also observed that, at frequencies where the modal density is low, optimal control acts to create a sound energy flow over the sensor array and mainly prevents a pure standing wave pattern. This relation between spatial sound field reproduction and the suppression of the standing wave pattern that is likely to occur is also related to Santillán's work, where the reproduction of a plane wave serves as a solution for global equalization in a rectangular room.…”

Map estimation of driving signals of loudspeakers for sound field reproduction from pressure measurements

“…Sound pressure control methods based on a numerical algorithm, such as least squares method, can be applied as SP-DS conversion [4,5]. In this context, sound pressures at the planar or linear distribution of control points are controlled to correspond with those obtained with the microphones.…”

Regularization in global sound equalization based on effort variation

“…When the number of sensors is less than the number of sources the linear problem is underdetermined and reconstruction of the source strengths requires the use of a regularization technique. One of the most common techniques used in active control is effort regularization, which is based on the standard form of Tikhonov regularization [14][15][16] and the cost function…”