Multichannel equalization in subbands

Abstract

For the dereverberation of acoustic channels or the rendering of a specific sound field, the inversion of acoustics is a central problem and generally involves multichannel techniques. In this paper, we introduce a subband approach to the adaptive solution of this equalization problem. The presented method generally allows for faster convergence at lower complexity. We also address limitations of the subband technique, potential error sources, and design specifications. Simulations are presented underlining the use of our method

Equalization of Multichannel Acoustic Systems in Oversampled Subbands

“…The former authors derive the relations between the full-band and subband filters for critically decimated cosine modulated filter banks [27], which are shown to require cross-band filtering. On the other hand, Reilly et al [31] show that good approximations can be obtained with a diagonal filtering matrix, involving only one filter per subband for complex oversampled filter-banks since these sufficiently suppress aliasing in adjacent subbands [30]. We now extend this approach to the multichannel case with application to RTF equalization.…”

“…In [19], a rigourous approach was taken and the relation between full-band and subband filters was studied for an AR model of the room impulse response. An adaptive method for multichannel equalization in oversampled subbands was proposed in [30] and was shown to provide significant improvement over the full-band counterpart.…”

“…Here, this is done utilizing the multichannel equalization filter design from (8), which now becomes (30) such that for each subband (31) Thus, equalization is achieved by applying the inverse filters to the subband signals of the reverberant observations in each subband , , and an equalized full-band signal is constructed. Assuming that exact equalization is achieved in each subband, the accuracy of the final result will depend on the reconstruction properties of the filter-bank, the level of aliasing suppression and, consequently, on the design of the prototype filter.…”

“…We consider the general optimization problem , which has a minimum norm solution , where is an arbitrary real valued matrix and is a real valued vector. The number of flops required to solve this problem using the normal equations is given by [22] The subband equalization filter design takes into consideration two separate calculations for each of the subbands: the cost of the subband inverse filter computation in (30) and the cost of the subband decomposition in (29). The data for these calculations is complex where, generally, one complex multiply requires four real multiplies and two real additions and one complex addition requires two real additions.…”

An Investigation of Delayless Subband Adaptive Filtering for Multi-Input Multi-Output Active Noise Control Applications

“…In the context of active noise and vibration control, the delayless subband adaptive filtering method has generally been investigated in the context of single-input, single-output (SISO) systems [15], [16], [17], [18]. Although in this case it has been shown that significant improvements in the convergence speed and reductions in the computational demand can be achieved, it has been acknowledged that the potential gains of employing a subband method are even greater for multi-input, multi-output (MIMO) systems and the increase in convergence speed has been investigated, for example, for the related application of room response equalisation [19].…”