Dolph-Chebyshev radial filter for the near-field spherical microphone array

Separation of coincident speech sources using microphone arrays is a challenging problem. Radial filters can be designed in the spherical harmonic domain to separate coincident speech sources effectively. Limited studies have been conducted on polynomial based near-field radial filter design in the spherical harmonic domain earlier. In this paper, a radial filter design method using a frequency domain Kaiser window function is proposed. The magnitude response of the Kaiser window function exhibits sharp notches, making it a good candidate for the design of radial notch filters. The polynomial expansion of the Kaiser window can be utilized for modeling the spherical array beamformer output. Improved white noise gain and directivity index are noted in the radial filters designed using the Kaiser window function. The radial filter is also used to separate co-incident speech sources. Experimental results on coincident speech source separation indicate better LSD, PESQ, and SDR scores than existing approaches.

Radial filter design for processing near field speech sources over a spherical microphone array is challenging. Polynomial based radial filter design procedures have been proposed in earlier work. In this paper we address the issue of radial filter design using a family of orthogonal polynomials called the Gegenbauer polynomials. The radial filters designed using this approach indicate an improved radial response and greater efficiency in attenuating distant sources. Improved white noise gain and directivity index are also noted from experimental evaluations. The radial filters hence designed are used to separate directionally co-incident near field speech sources. Subjective evaluation is conducted on separated sources using measures like LSD, PESQ, and SDR. The subjective evaluation scores are motivating enough to be considered for practical speech and audio applications.

The area of sound field synthesis has significantly advanced in the past decade, facilitated by the development of high-quality sound-field capturing and re-synthesis systems. Spherical microphone arrays are among the most recently developed systems for sound field capturing, enabling processing and analysis of three-dimensional sound fields in the spherical harmonics domain. In spite of these developments, a clear relation between sound fields recorded by spherical microphone arrays and their perception with a re-synthesis system has not yet been established, although some relation to scalar measures of spatial perception was recently presented. This paper presents an experimental study of spatial sound perception with the use of a spherical microphone array for sound recording and headphone-based binaural sound synthesis. Sound field analysis and processing is performed in the spherical harmonics domain with the use of head-related transfer functions and simulated enclosed sound fields. The effect of several factors, such as spherical harmonics order, frequency bandwidth, and spatial sampling, are investigated by applying the repertory grid technique to the results of the experiment, forming a clearer relation between sound-field capture with a spherical microphone array and its perception using binaural synthesis regarding space, frequency, and additional artifacts. The experimental study clearly shows that a source will be perceived more spatially sharp and more externalized when represented by a binaural stimuli reconstructed with a higher spherical harmonics order. This effect is apparent from low spherical harmonics orders. Spatial aliasing, as a result of sound field capturing with a finite number of microphones, introduces unpleasant artifacts which increased with the degree of aliasing error.

Low-pass filtering of sinograms in the radial direction is the most common practice to limit noise amplification in filtered back projection (FBP) reconstruction of positron emission tomography studies. Other filtering strategies have been proposed to prevent the loss in resolution due to low-pass radial filters, although results have been diverse. Using the well-known properties of the Fourier transform of a sinogram, the authors defined a binary mask that matches the expected shape of the support region in the Fourier domain of the sinogram ("bow tie"). This mask was smoothed by a convolution with a ten-point Gaussian kernel which not only avoids ringing but also introduces a pre-emphasis at low frequencies. A new filtering scheme for FBP is proposed, comprising this smoothed bow-tie filter combined with a standard radial filter and an axial filter. The authors compared the performance of the bow-tie filtering scheme with that of other previously reported methods: Standard radial filtering, angular filtering, and stackgram-domain filtering. All the quantitative data in the comparisons refer to a baseline reconstruction using a ramp filter only. When using the smallest size of the Gaussian kernel in the stackgram domain, the authors achieved a noise reduction of 33% at the cost of degrading radial and tangential resolutions (14.5% and 16%, respectively, for cubic interpolation). To reduce the noise by 30%, the angular filter produced a larger degradation of contrast (3%) and tangential resolution (46% at 10 mm from the center of the field of view) and showed noticeable artifacts in the form of circular blurring dependent on the distance to the center of the field of view. For a similar noise reduction (33%), the proposed bow-tie filtering scheme yielded optimum results in resolution (gain in radial resolution of 10%) and contrast (1% increase) when compared with any of the other filters alone. Experiments with rodent images showed noticeable image quality enhancement when using the proposed bow-tie filtering scheme.

Spherical microphone arrays (SMAs) are widely used to capture spatial sound fields that can then be rendered in various ways as a virtual acoustic environment (VAE) including headphone-based binaural synthesis. Several practical limitations have a significant impact on the fidelity of the rendered VAE. The finite number of microphones of SMAs leads to spatial undersampling of the captured sound field, which, on the one hand, induces spatial aliasing artifacts and, on the other hand, limits the order of the spherical harmonics (SH) representation. Several approaches have been presented in the literature that aim to mitigate the perceptual impairments due to these limitations. In this article, we present a listening experiment evaluating the perceptual improvements of binaural rendering of undersampled SMA data that can be achieved using state-of-the-art mitigation approaches. In particular, we examined the Magnitude Least-Squares algorithm, the Bandwidth Extraction Algorithm for Microphone Arrays, Spherical Head Filters, SH Tapering, and a newly proposed equalization filter. In the experiment, subjects rated the perceived differences between a dummy head and the corresponding SMA auralization. We found that most mitigation approaches lead to significant perceptual improvements, even though audible differences to the reference remain.

Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

Estimation of the direction of arrival (DOA) of reflections in a room using spherical microphone arrays can be performed using several methods such as plane-wave decomposition, and delay-and-sum beamforming, for which the resolution of the estimation process is usually bounded by the array order, or the number of microphones. In this paper a method for DOA estimation of the reflections in a room using room impulse-response data and spherical microphone arrays is presented, in which only a first order microphone array is required. The proposed method uses signal processing in the spherical harmonics domain, utilizing an analytical dependence of the spherical harmonic coefficients on different acoustics parameters. It is shown that the zero order spherical harmonics coefficients is a function of the time delays and amplitudes of the planes waves composing the sound field, while the first order coefficients are a function of the time delays, amplitudes and the elevation and azimuth components of the wave arrival direction. Using this property leads to the development of an estimator based on the least-squares approach, in which each order is used to estimate a single sound-field parameter.

Room impulse responses (RIRs) play an important role in acoustical signal processing and room acoustics analysis. The problem of estimating the directions-of-arrival (DOA) of a source in a room and its reflections using RIR data and microphone arrays, is considered. Optimal array processing methods proposed for sound field analysis using spherical microphone array are utilized. Because of the possible coherence between the signals, these methods cannot be used directly, and a preprocessing technique is typically needed. Recently, frequency smoothing (FS) as a preprocessing technique has been developed for spherical microphone arrays. Although FS has already been developed for the general case, the study of its performance in a comprehensive manner, for spherical microphone arrays with RIR data has not been previously presented. Therefore, theoretical analysis of the signal matrix structure using RIR data is performed. The conclusions from this analysis may lead to an optimization of the smoothing process. A method for an optimal selection of frequencies in the smoothing process for the case of one reflection is presented, followed by formulations for smoothing in the more general case. Finally, FS and its relation to SVD of the array data matrix are also presented and discussed.

Using spherical microphone arrays to form directed beams is becoming an important technology in sound field analysis, teleconferencing, and surveillance systems. Moreover, in scenarios for capturing musical content, the recording and post-production process could be simplified through flexible beamforming technology. Often, audio engineers favor the use of conventional recording microphones over spherical microphone arrays which might be due to the engineer's preference for distinct spatial and timbral characteristics of different microphone types and brands. We present an approach to create beamforming pattern using a 144 channel spherical microphone array, which aims to match the distinct spatial and timbral characteristics of classic microphones. For this, we first measured the spatial and timbral characteristics of several classic microphones types as well as the characteristics of our spherical microphone array in an anechoic chamber. Using a regularized least-square approach, these data were then used for computing the filters for the spherical microphone array that forms the desired beams. We show the results of several microphone-beam simulations and compare them with the impulse responses of the original classic microphones. Advantages and limitations of our approach will be discussed.

We propose a method to reproduce 3D auditory scenes captured by spherical microphone arrays over headphones. This algorithm employs expansions of the captured sound and the head related transfer function over the sphere and uses the orthonormality of the spherical harmonics. Using a spherical microphone array, we first record the 3D auditory scene, then the recordings are spatially filtered and reproduced through headphones in the orthogonal beam-space of the head related transfer functions (HRTFs). We use the KEMAR HRTF measurements to verify our algorithm. In experiments, we use a hemispherical array for recording. The reproduction results are posted online.

Comprehensive room acoustic characterization requires resolving reflection behavior across time, frequency, and space. The recently proposed eigenbeam–vMF-based analyzer provides a framework for this by modeling the reflection field as a time–frequency-dependent directional power distribution, estimated via spatial correlation of eigenbeams (ambisonics) and parameterized using von Mises–Fisher clustering. This formulation enables a unified and interpretable description of anisotropic early reflections, their transition into diffuse reverberation, and frequency-dependent acoustic behavior. Prior work showed that the analyzer reliably captures these features using higher-order ambisonics from a 32-channel spherical microphone array (SMA) and that constraining the same array to the first order still led to retaining the dominant features. This paper investigates whether this capability extends to first-order microphone arrays with sparser spatial sampling for more economical and practical deployment. A comparative study is conducted in a recording studio with variable wall panels (wood and felt), evaluating a four-channel first-order array against a 32-channel SMA. The results reveal distinct acoustic differences between panel settings, which are consistent across both arrays. While the SMA captures finer spatial detail and prolonged anisotropic reflections more effectively, the first-order array demonstrates potential for preliminary room acoustic assessments by identifying room mode frequencies, dominant reflection directions, and highly reflective surfaces.

The capture of the spatial structure of a sound field and analysis is important in many fields including creating virtual environments, source localization and detection, noise suppression, and beamforming. Spherical microphone arrays are a promising development to help achieve such capture and analysis, and have been studied by several groups. We develop a practical spherical microphone array and demonstrate its utility in applications for sound capture, room measurement and for beamforming and tracking. To accommodate equipment failure and manufacturing imprecision we extend their theory to handle arbitrary microphone placement. To handle speech capture and surveillance we describe the development of a new sensor, the hemispherical microphone array. For each array the practical performance follows that predicted by theory. Future applications and improvements are also discussed. [Work supported by NSF.]

Spatial impression is an important acoustic quality of concert halls. An accepted objective measure for spatial impression is the interaural cross-correlation (IACC) coefficient. Recently, spherical microphone arrays have been studied for room acoustics analysis and music recordings. This study presents a theoretical formulation for the computation of IACC using spherical-harmonics representations of the sound field, as measured by spherical microphone arrays, and spherical-harmonics representation of head-related transfer functions (HRTFs), taken from HRTF databases. As spherical microphone arrays typically use a finite number of microphones, they may not be able to capture the complete spatial information in a sound field. Therefore, the effect of limited spherical-harmonics order on the accuracy of IACC approximation using the proposed method is studied using simulated and measured data. The method presented in this paper can be further used to study the effect of limited spatial information on the spatial perception of sound fields.

This document illustrates how to process the signals from the microphones of a rigid-sphere higher-order ambisonic microphone array so that they are encoded with N3D normalization and ACN channel order and thereby can be used with the standard ambisonic software tools such as SPARTA and the IEM Plugin Suite. A MATLAB script is provided.

Conversion of microphone array signals into loudspeaker array signals is an essential process in high-definition spatial audio. This paper presents the theory of boundary matching filters (BMFs) for spherical array signal conversion. BMFs adapt the physical boundary conditions used during recording to the ones required for reproduction by relying on a theoretical framework provided by the Kirchhoff–Helmholtz integral equation (KHIE). Computationally, array signal conversion is performed in a transform domain where sound fields are represented in terms of spherical harmonic functions. Related research on transform-domain signal conversion filters is interpreted in the context of the KHIE. The case of a rigid recording boundary and an open reproduction boundary is addressed. The proposed rigid-to-open BMFs provide a suitable basis for designing gain-limited filters to deal with the problem of excessive gains at certain frequency bands, observed when using high-resolution arrays. Spatial, spectral, and temporal effects in sound field reconstruction when finite numbers of transducers are used in anechoic conditions are investigated analytically and exemplified numerically. Results show that the proposed gain-limited rigid-to-open BMFs outperform the existing gain-limited filters based on Tikhonov regularization because they reduce the spatial discretization effects and yield impulse responses that are more localized around their main peaks.