Daniel P. Jarrett

Rigid sphere room impulse response simulation: Algorithm and applications

Simulated room impulse responses have been proven to be both useful and indispensable for comprehensive testing of acoustic signal processing algorithms while controlling parameters such as the reverberation time, room dimensions, and source-array distance. In this work, a method is proposed for simulating the room impulse responses between a sound source and the microphones positioned on a spherical array. The method takes into account specular reflections of the source by employing the well-known image method, and scattering from the rigid sphere by employing spherical harmonic decomposition. Pseudocode for the proposed method is provided, taking into account various optimizations to reduce the computational complexity. The magnitude and phase errors that result from the finite order spherical harmonic decomposition are analyzed and general guidelines for the order selection are provided. Three examples are presented: an analysis of a diffuse reverberant sound field, a study of binaural cues in the presence of reverberation, and an illustration of the algorithms use as a mouth simulator.

Coherence-based diffuseness estimation in the spherical harmonic domain

The diffuseness of sound fields has previously been estimated in the spatial domain using the spatial coherence between a pair of microphones (omnidirectional or first-order). In this paper, we propose a diffuseness estimator for spherical microphone arrays based on the coherence between eigenbeams, which result from a spherical harmonic decomposition of the sound field. The weighted averaging of the diffuseness estimates over all eigenbeam pairs is shown to significantly reduce the variance of the estimates, particularly in fields with low diffuseness.

On the Noise Reduction Performance of a Spherical Harmonic Domain Tradeoff Beamformer

In this letter, we derive an expression for the expected incoherent noise reduction factor of a spherical harmonic domain (SHD) tradeoff beamformer. The tradeoff beamformer attempts to reduce noise while minimizing speech distortion, and includes the minimum variance distortionless response (MVDR) and multichannel Wiener filters as special cases. For the open spherical microphone array, we find a number of analogies between the expressions for the expected noise reduction factor of the SHD and spatial domain MVDR beamformers. In an anechoic environment we find that the performance of the SHD MVDR beamformer with an open array depends almost entirely on the number of microphones, as in the spatial domain.

Simulating room impulse responses for spherical microphone arrays

A method is proposed for simulating the sound pressure signals on a spherical microphone array in a reverberant enclosure. The method employs spherical harmonic decomposition and takes into account scattering from a solid sphere. An analysis shows that the error in the decomposition can be made arbitrarily small given a sufficient number of spherical harmonics.

Dereverberation performance of rigid and open spherical microphone arrays: Theory & simulation

Linear microphone arrays have been extensively used for dereverberation. In this paper we look at the dereverberation performance of two types of spherical microphone array: the open array (microphones suspended in free space) and the rigid array (microphones mounted on a rigid baffle). Dereverberation is performed in the spherical harmonic domain using a technique similar to the commonly used delay-and-sum beamformer (DSB). We analyse the theoretical performance with respect to the direct-to-reverberant ratio (DRR), and we also present simulation results obtained using a simulation tool for spherical arrays. The performance of the spherical DSB is found to increase with the radius of the sphere, and to be 1–2 dB higher for the rigid array. These results serve as a baseline for evaluating the performance of future dereverberation algorithms for spherical arrays.

Noise reduction in the spherical harmonic domain using a tradeoff beamformer and narrowband DOA estimates

In noise reduction, a common approach is to use a microphone array with a beamformer that combines the individual microphone signals to extract a desired speech signal. The beamformer weights usually depend on the statistics of the noise and desired speech signals, which cannot be directly observed and must be estimated. Estimators based on the speech presence probability (SPP) seek to update the statistics estimates only when desired speech is known to be absent or present. However, they do not normally distinguish between desired and undesired speech sources. In this contribution, an algorithm is proposed to distinguish between these two types of sources using additional spatial information, by estimating a desired speech presence probability based on the combination of a multichannel SPP and a direction of arrival (DOA) based probability. The DOA-based probability is computed using DOA estimates for each time-frequency bin. The estimated statistics are then used to compute the weights of a spherical harmonic domain tradeoff beamformer, which achieves a balance between noise reduction and speech distortion. The performance evaluation demonstrates the effectiveness of the proposed approach at suppressing both background noise and spatially coherent noise. A number of audio examples and sample spectrograms are also provided.

Spherical harmonic domain noise reduction using an MVDR beamformer and DOA-based second-order statistics estimation

Most beamformers used for noise reduction rely on the accurate estimation of the second-order statistics of the noise, and in some cases, of the desired signal. Speech presence probability (SPP) based statistics estimators seek to update the estimates only when speech is absent/present, however, when used with a fixed a priori SPP, they cannot distinguish between a coherent desired source and coherent noise sources. We propose to distinguish between desired and noise sources by estimating the second-order statistics with a direction of arrival dependent a priori SPP, which we then use to compute the weights of a spherical harmonic domain minimum variance distortionless response filter.

Eigenbeam-based acoustic source tracking in noisy reverberant environments

In this work, an adaptive acoustic source tracking algorithm is proposed. It is based on eigenbeams which perform spatial decomposition of the sound field, works in two dimensions for tracking of azimuth and elevation, has low computational complexity, and is robust to noise and room reverberation. The tracking is performed using an adaptive principal component analysis of the particle velocity vector, which points from the acoustic source to the sensor. The particle velocity vector is estimated using a spherical microphone array, and is formed by combining the first-order eigenbeams.

An informed spatial filter for dereverberation in the spherical harmonic domain

In speech communication systems the received microphone signals are commonly degraded by reverberation and ambient noise that can decrease the fidelity and intelligibility of a desired speaker. Reverberation can be modeled as non-stationary diffuse sound which is not directly observable. In this work, we derive a multichannel Wiener filter in the spherical harmonic domain to reduce both reverberation and noise. The filter depends on the direction-of-arrival of the direct sound of the desired speaker and an interference power spectral density matrix for which an estimator is developed. The resulting informed spatial filter incorporates instantaneous information about the diffuseness of the sound field into the design of the filter. In addition, it is shown how the proposed filter relates to the well-known robust minimum variance distortionless response filter that is also used for comparison in the evaluation. Experimental results show that the proposed spatial filter provides a tradeoff between noise reduction and dereverberation depending on the diffuse sound PSD.

Signal-Dependent Array Processing

In this chapter, we derive spherical harmonic domain signal-dependent beamformers, whose weights depend on the second-order statistics of the desired signal and/or of the noise to be suppressed. These beamformers adaptively seek to achieve optimal performance in terms of noise reduction and speech distortion.