Robustness of multichannel equalization in an acoustic reverberant environment

Abstract

A theoretical framework is established, for the robustness of multichannel sound equalization in reverberant environments. Using results from statistical room acoustics, a closed-form expression is derived that predicts the degradation in performance of an equalization system as the sound source moves from its nominal position inside the enclosure. The presented analysis also provides means of identifying the performance bounds that can be expected when using such a system in an actual room. Using extensive computer simulations, the effect of physical parameters such as the relative positions of the source and the receivers, as well as effects of different design parameters are investigated. Based on the conditions imposed by these parameters, it is shown that, depending on the array geometry and the exact form of the equalizers, slight performance gains can be expected as the number of receivers is increased.

Equalization of Multichannel Acoustic Systems in Oversampled Subbands

“…[8] and [26], where the authors studied equalization of RTF measured at a different location to that at the point of processing.…”

“…Thus, the remaining problem is to solve for in (22). Decimating (22) by a factor of , the following approximation can be formed: (25) which in the time domain is equivalently written (26) where is the length of the analysis filters. The convolution on the left-hand side of (26) is of length , and consequently, the length of the subband filters is (27) The estimates of the subband filters are then found by solving the following optimization problem [31]: (28) The th subband, th channel filters are obtained in the least squares optimal sense according to (29) In summary, given a full-band RTF and -band filter-bank satisfying perfect reconstruction and aliasing suppression in the subbands, a set of subband filters of order can be found such that the overall subband transfer function is equivalent to the full-band filter response.…”

Spherical harmonic analysis of equalization in a reverberant room

“…The multi-channel case proposed in [7] shows promise. However, as the robustness analysis in this case was based on the single-channel analysis of Radlovic et al [2], results are restricted to the assumptions of statistical room acoustics and a first order approximation only valid in moderately reverberant rooms.…”

“…Even a change in the source or microphone position of a few tenths of a wavelength creates a large variation in the room channel response and large degradation in equalized output [2,3,4]. Techniques have been suggested to combat this robustness problem [5,6,7].…”

Robustness of Non-Exact Multi-Channel Equalization in Reverberant Environments

“…The assessment of the feasibility of acoustic equalization under reverberant conditions, has been previously addressed in [1] and [2] where we determined the robustness of multi-channel equalization systems, by means of a closed form expression that predicts the equalization error when the source is moved from its nominal position. The work of these papers generalizes the work of Radlovic et al in [4] that only considered one-channel systems.…”