Spatial Subtraction of Reflections from Room Impulse Responses Measured with a Spherical Microphone Array

Abstract

We propose a method for the decomposition of measured directional room impulse responses (DRIRs) into prominent reflections and a residual. The method comprises obtaining a fingerprint of the timefrequency signal that a given reflection carries, imposing this timefrequency fingerprint on a plane-wave prototype that exhibits the same propagation direction as the reflection, and finally subtracting this plane-wave prototype from the DRIR. Our main contributions are the formulation of the problem as a spatial subtraction as well as the incorporation of order truncation, spatial aliasing and regularization of the radial filters into the definition of the underlying beamforming problem. We demonstrate, based on simulated as well as measured array impulse responses, that our method increases the accuracy of the model of the reflection under test and consequently decreases the energy of the residual that remains in a measured DRIR after the spatial subtraction.

Signal Compaction Using Polynomial EVD for Spherical Array Processing With Applications

“…Further, for a sufficiently large SH order L, instead of using Q microphones, a lower dimension of L eigenbeams can be used to represent the sound field. In terms of compaction, particularly for sound sources arriving at the spherical microphone array from well-defined directions, the SHT outputs can be linearly combined via beamforming to further compact the source's power, and is therefore widely regarded as a tool for dimensionality reduction of spherical microphone array data [25], [51], [52]. This compaction is difficult to assess via the coding gain, since the SHT is not a unitary transform or otherwise norm-preserving.…”

Direct and Residual Subspace Decomposition of Spatial Room Impulse Responses

“…This leads to the typical assumption that spherical arrays in SH-domain processing have frequency-independent steering vectors so that, as with narrow-band signals, a multiplicative signal model is sufficient. However, the necessary regularization of the radial filters and spatial aliasing in practice limit this property to a narrow frequency region [27]. Thus, these assumptions are not made in the proposed broadband algorithm so that it can either be directly applied to the microphone signals or to an SH decomposition thereof.…”

“…In this section, the norms of the spectra χ s (f ) of two of the ground truth reflections from Fig. 4 (a) are compared to extracted spectra from the direct part x s (t) obtained either via the spatial subtraction method [27] or the subspace decomposition. The frequency-domain vector χ s (f ) contains the spectrum of all SH-domain signal channels during the presence of a reflection.…”

“…While most of the renderers are designed to accurately reproduce salient reflections and diffuse reverberation, none of the existing methods achieves an explicit separation of salient reflections from the SRIR while preserving the spatio-temporal properties of both the reflections and the residual. To overcome this limitation, the authors recently proposed to use the spatial subtraction method to subtract salient reflections from an SRIR by using a beamformer and a plane-wave prototype [27]. The spatial subtraction method was initially proposed for the separation of direct and diffuse parts in sound scenes [28] and was extended in [27] by employing a comprehensive microphone-array signal model that includes the impacts of scattering and spatial aliasing, which improved the separation performance when applied to SRIRs.…”

“…To overcome this limitation, the authors recently proposed to use the spatial subtraction method to subtract salient reflections from an SRIR by using a beamformer and a plane-wave prototype [27]. The spatial subtraction method was initially proposed for the separation of direct and diffuse parts in sound scenes [28] and was extended in [27] by employing a comprehensive microphone-array signal model that includes the impacts of scattering and spatial aliasing, which improved the separation performance when applied to SRIRs.…”