The influence of regularization on anechoic performance and robustness of sound zone methods

Abstract

Recent attention to the problem of controlling multiple loudspeakers to create sound zones has been directed towards practical issues arising from system robustness concerns. In this study, the effects of regularization are analyzed for three representative sound zoning methods. Regularization governs the control effort required to drive the loudspeaker array, via a constraint in each optimization cost function. Simulations show that regularization has a significant effect on the sound zone performance, both under ideal anechoic conditions and when systematic errors are introduced between calculation of the source weights and their application to the system. Results are obtained for speed of sound variations and loudspeaker positioning errors with respect to the source weights calculated. Judicious selection of the regularization parameter is shown to be a primary concern for sound zone system designers -the acoustic contrast can be increased by up to 50dB with proper regularization in the presence of errors. A frequency-dependent minimum regularization parameter is determined based on the conditioning of the matrix inverse. The regularization parameter can be further increased to improve performance depending on the effort constraints, expected magnitude of errors, and desired sound field properties of the system.

Time Domain Optimization of Filters Used in a Loudspeaker Array for Personal Audio

“…Conversely, it can be seen that when the differences in response in the bright zone are limited to be less than 5 dB. This result is similar to that obtained by comparing the least squares method with the acoustic contrast maximization method in the frequency domain, where the acoustic contrast maximization method is able to obtain a higher contrast at the expense of a more uneven reproduction in the listening zone [2], [8], [22], [23]. The array effort needed for the filters is similar for both values of , except at around 300 Hz.…”

“…In this case, the acoustic contrast is calculated at a single frequency as (19) where and are obtained by Fourier transformation of and . It should be emphasized that the acoustic contrast is used here only as a metric to quantify the performance, rather than as a cost function, as it is known than maximizing the contrast can result in a very uneven pressure in the bright zone, which is not as subjectively pleasing as minimizing the difference between the pressure at each point in the bright zone and a smooth-varying target pressure [2], [8], [22], [23]. Acoustic contrast and array effort are dimensionless quantities, whose levels are generally plotted in dB.…”

“…This problem has been mitigated by the introduction of a modified cost function which takes into account the uniformity of the frequency response [20]. Furthermore, the acoustic contrast maximization method does not generally provide a uniform spatial distribution of the pressure over the bright zone [2], [8], [22], [23], which is not good in terms of the perceived audio quality. Another characteristic of the superdirective control filters created in the frequency domain is the need for a modeling delay, which is generally chosen to be about half of the filter length, since otherwise the obtained time responses are non-causal.…”

An analytical model for wedge-shaped acoustic arrays

“…The most classic form is probably the generation of a sound field in a dedicated reproduction area with holophony as the objective [2,3,8]. Acoustic contrast control and pressure matching, as well as acoustic beamforming are also forms of sound field control [6,[17][18][19][20]. All these techniques can (but do not have to) be derived on the basis of wave propagation models, between which the physical accuracy may vary for a given environment.…”

Combining Artificial and Natural Background Noise in Personal Audio Systems

“…This line of enquiry, i.e. consideration of the perceptual relevance of sound leaking from one zone into another, has been taken by contributors to the POSZ Project [7] to inform loudspeaker positioning, [8], [9] and the choice of sound zoning methods [10]- [12]. A recent article by Donley et.…”