Extracting Reverberant Sound Using a Linearly Constrained Minimum Variance Spatial Filter

O. Thiergart and E.A.P. Habets

Published in the IEEE Signal Processing Letters, 2014.


Microphone arrays are typically used to extract the direct sound of sound sources while suppressing noise and reverberation. Applications such as immersive spatial sound reproduction commonly also require an estimate of the reverberant sound. A linearly constrained minimum variance filter, of which one of the constraints is related to the spatial coherence of the assumed reverberant sound field, is proposed to obtain an estimate of the sound pressure of the reverberant field. The proposed spatial filter provides an almost omnidirectional directivity pattern with spatial nulls for the directions-of-arrival of the direct sound. The filter is computationally efficient and outperforms existing methods.

Listening Examples (Stereo)

Details of the simulation setup are described in [1]. A shoebox room (7 x 9 x 3.5m, RT60 = 390ms) was simulated. The sound was captured with an uniform linear array with M=8 omnidirectional microphones. Two sound sources were located at 51 degrees and 97 degrees in a distance of 1.7m from the microphone array. Microphone self-noise was added to the microphone signals (36dB segSNR).

The following filters for extracting the reverberant sound were computed:

  1. Single-Channel: State-of-the-art single-channel Wiener filter, e.g. as in [2]. The required information on the diffuse sound power was provided as a priori information (temporally averaged over 50ms)
  2. Multi-Channel MMSE: MMSE filter described in [1], Eq. (10). All required information to compute the filter was provided as a priori information (temporally averaged over 50ms)
  3. Multi-Channel LCMV: Average LCMV filter (first-order Taylor approximation) proposed in [1], Eq. (14). The required DOAs of the direct sound were provided.

All filters aim at extracting the diffuse sound while supressing the direct sound of the sound sources. In the following sound examples, the extracted diffuse sound is reproduced from all directions. In contrast, the direct sound, which could not be suppressed by the filters, is reproduced from the front. This makes it more audible when the filter fails.

Example 1: Two speech sources

Example 2: Castanets and one speech source


  1. O. Thiergart and E. Habets, "Extracting Reverberant Sound Using a Linearly Constrained Minimum Variance Spatial Filter," to appear in IEEE Signal Processing Letters, 2013
  2. O. Thiergart, G. Del Galdo, M. Taseska, and E. Habets, "Geometry-based spatial sound acquisition using distributed microphone arrays," Audio, Speech, and Language Processing, IEEE Transactions on, vol. 21, no. 12, pp. 2583-2594, December 2013.