Equalization of Multichannel Acoustic Systems in Oversampled Subbands

Abstract

Abstract-Equalization of room transfer functions (RTFs) is an important topic with several applications in acoustic signal processing. RTFs are often modeled as finite-impulse response filters, characterized by orders of thousands of taps and non-minimum phase. In practice, only approximate estimates of the actual RTFs are available due to measurement noise, limited estimation accuracy, and temporal variation of source-receiver position. These issues make equalization a difficult problem. In this paper, we discuss multichannel equalization with focus on inexact RTF estimates. We present a multichannel method for the equalization filter design utilizing decimated and oversampled subbands, where the fullband acoustic impulse response is decomposed into equivalent subband filters prior to equalization. This technique is not only more computationally efficient but also more robust to impulse response inaccuracies compared with the full-band counterpart.

Adaptive inverse filtering of room acoustics

“…For the case that multichannel RTFs have common zeros, or Li < Lc, (4) gives an MCLS inverse system [4].…”

“…T , where Li = Lc, is obtained by using (4). By applying g to h = [h1 h2], an equalized impulse response can be obtained,…”

“…From a theoretical perspective, reverberation can be completely removed by using multiple microphones and techniques based on MINT in the case that the multichannel room transfer functions (RTFs) do not share any common zeros [2]. In practice, MINT is computationally expensive [4], and this motivates the use of the subband algorithm [4]. On the other hand, multichannel adaptive systems have been used for acoustic system equalization [5] [6], and it is shown that an identical inverse filtering system to MINT can be obtained [7].…”

“…However, the existence of common and near-common zeros [8] causes problems in both closed-form and adaptive inverse filtering algorithms. MINT has been generalized to a multichannel least squares (MCLS) method [4], and it can overcome the problems due to the existence of common zeros. In adaptive inverse filtering, we will show that near-common zeros slow down the convergence rate of the adaptive algorithms.…”

Improving the conditioning of the optimization criterion in acoustic multi-channel equalization using shorter reshaping filters

“…In [26], it has been proposed to use a signaldependent penalty function to promote sparsity in the output signal and reduce artifacts generated by nonrobust techniques. In [31,32], it has been proposed to relax the constraints on the filter design by constructing approximate reshaping filters in the subband domain. In [33], it has been proposed to relax the constraints on the filter design by using a shorter reshaping filter length than conventionally used.…”