acoustic research

A main thread of research activity is to design sensor arrays to realize a broadband and/or nearfield design specification. In acoustics design the frequency range of interest is typically multi-octave making the design problem truly broadband. The lower frequencies correspond to long wavelengths tending to make any signal sources nearfield. Simultaneously the higher frequencies are farfield. The mix of nearfield and farfield properties creates a design challenge.

acoustic papers

Papers dealing with broadband and nearfield arrays, and beamforming with particular application in acoustics such as microphone arrays, multispeaker systems and the like.

Keywords: Arrays; Beamforming; Broadband Arrays; Nearfield Arrays; Acoustic Transducers; Sensors; Antenna Radiation Patterns; Array Signal Processing; Direction-of-arrival Estimation; Linear Antenna Arrays; Array Design; Array Processing; Beamformer Design; Broadband Nearfield Beamforming; Farfield Beampattern; Frequency Invariant Beampattern; Nearfield Broadband Beampattern; Radial Beampattern Transformation; Spherical Harmonic Solution; Wave Equation; Acoustic Reverberant Environment; Equalized Room Response; Robustness; Architectural Acoustics

W. Zhang, T. D. Abhayapala, R. A. Kennedy, and R. Duraiswami, "Modal Expansion of HRTFs: Continuous Representation in Frequency-Range-Angle", Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'2009, pp. 4, April 2009 (to appear).
Abstract BibTeX
PDF: 2009_icassp.pdf
Abstract: This paper proposes a continuous HRTF representation in both 3D spatial and frequency domains. The method is based on the acoustic reciprocity principle and a modal expansion of the wave equation solution to represent the HRTF variations with different variables in separate basis functions. The derived spatial basis modes can achieve HRTF near-field and far-field representation in one formulation. The HRTF frequency components are expanded using Fourier Spherical Bessel series for compact representation. The proposed model can be used to reconstruct HRTFs at any arbitrary position in space and at any frequency point from a finite number of measurements. Analytical simulated and measured HRTFs from a KEMAR are used to validate the model.
@inproceedings{KennedyC2009a,
    title = {Modal Expansion of {HRTF}s: Continuous Representation in Frequency-Range-Angle},
    author = {Zhang, W. and Abhayapala, T. D. and Kennedy, R. A. and Duraiswami, R.},
    booktitle = {Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'2009},
    pages = {4},
    month = {April},
    year = {2009 (to appear)}}
W. Zhang, R. A. Kennedy, and T. D. Abhayapala, "Efficient continuous head-related transfer function model using data independent basis functions: Experimentally guided approach", IEEE Trans. on Audio, Speech and Language Process., no. T-ASL-01753-2007, 2009 (to appear).
Abstract BibTeX
PDF: 2DHRTF_ieee.pdf
Abstract: A continuous functional model is proposed for head-related transfer functions (HRTFs) in a two dimensional auditory scene (azimuth and frequency). The model is based on a separable representation which uses a Fourier Bessel Series expansion for the spectral cues and a conventional Fourier Series expansion for the spatial cues. Being independent of the data, these two sets of basis functions make HRTF reconstruction, especially interpolation, very easy. The continuous functional model is also developed in the time domain. Two sets of HRTF measurements, one from a KEMAR manikin and the other from 43 different subjects, are used to investigate the model performance. The performance of the model in accurately approximating experimentally measured HRTFs has been assessed in both frequency and time domains. The average mean square error between measured and model reconstructed HRTFs is less than two percent. The predictive capabilities of our proposed model is also validated. The usefulness of the proposed model in representing and particularly synthesizing the spatial sound is discussed.
@article{KennedyJ2009_SpeechAudio,
    title = {Efficient continuous head-related transfer function model using data independent basis functions: Experimentally guided approach},
    author = {Zhang, W. and Kennedy, R. A. and Abhayapala, T. D.},
    journal = {IEEE Trans. on Audio, Speech and Language Process.},
    year = {2009 (to appear)}}
D. B. Ward, R. A. Kennedy, and R. C. Williamson, "Constant Directivity Beamforming", Microphone Arrays, pp. 3-17, 2001.
Abstract BibTeX
PDF: KennedyBC2001c.pdf Google-Scholar: [15]
Abstract: Beamforming, or spatial filtering, is one of the simplest methods for discriminating between different signals based on the physical location of the sources. Because speech is a very wideband signal, covering some four octaves, traditional narrowband beamforming techniques are inappropriate for hands-free speech acquisition. One class of broadband beamformers, called constant directivity beamformers, aim to produce a constant spatial response over a broad frequency range. In this chapter we review such beamformers, and discuss implementation issues related to their use in microphone arrays.
@inproceedings{KennedyBC2001c,
    title = {Constant Directivity Beamforming},
    author = {Ward, D. B. and Kennedy, R. A. and Williamson, R. C.},
    booktitle = {Microphone Arrays},
    pages = {3-17},
    year = {2001}}
B. D. Radlović and R. A. Kennedy, "Non-minimum Phase Equalization and its Subjective Importance in Room Acoustics", IEEE Trans. Speech and Audio Processing, vol. 8, no. 6, pp. 728-737, November 2000.
Abstract BibTeX
Official: Link DOI: 10.1109/89.876311 PDF: 00876311.pdf Google-Scholar: [32]
Abstract: This paper investigates the perceptual significance of residual phase distortion due to an approximate equalization of the nonminimum-phase room response from a sound source to a microphone in a reverberant room. It is shown that disrupted phase relationships introduced by a minimum-phase equalization filter may have a detrimental effect on perceived sound quality. The subjective assessment of phase distortion on speech signals is related to an objective error criterion, newly introduced in this paper. An alternative approach to the minimum-phase/all-pass decomposition based on iterative flattening of the room transfer function (RTF) magnitude is also presented, which overcomes potential numerical problems and provides more insight into subjective aspects of magnitude and phase equalization in the reduction of acoustic reverberation. Factors contributing to the results and practical implications for equalization are discussed.
@article{KennedyJ2000c,
    title = {Non-minimum Phase Equalization and its Subjective Importance in Room Acoustics},
    author = {Radlović, B. D. and Kennedy, R. A.},
    journal = {IEEE Trans. Speech and Audio Processing},
    volume = {8},
    pages = {728-737},
    month = {November},
    year = {2000}}
B. D. Radlović, R. C. Williamson, and R. A. Kennedy, "Equalization in an Acoustic Reverberant Environment: Robustness Results", IEEE Trans. Speech and Audio Processing, vol. 8, no. 3, pp. 311-319, May 2000.
Abstract BibTeX
Official: Link DOI: 10.1109/89.841213 PDF: 00841213.pdf Google-Scholar: [50]
Abstract: This paper investigates the robustness of sound equalization using a room response inverse filter with respect to changing or uncertain source or microphone positions. It is shown that due to the variations of the transfer function from point to point in a room, even small changes in the source or microphone position of just a few tenths of the acoustic wavelength can cause large degradations in the equalized room response. The robustness problem is especially acute at high frequencies, which are known to carry some important attributes of the speech signal. The spatial extent of equalization, derived from the statistical-average properties of sound transmission in rooms, is illustrated by computer simulations which corroborate the theoretical results presented.
@article{KennedyJ2000b,
    title = {Equalization in an Acoustic Reverberant Environment: Robustness Results},
    author = {Radlović, B. D. and Williamson, R. C. and Kennedy, R. A.},
    journal = {IEEE Trans. Speech and Audio Processing},
    volume = {8},
    pages = {311-319},
    month = {May},
    year = {2000}}
T. D. Abhayapala, R. A. Kennedy, and R. C. Williamson, "Nearfield Broadband Array Design Using a Radially Invariant Modal Expansion", J. Acoust. Soc. Am., vol. 107, no. 1, pp. 392-403, January 2000.
Abstract BibTeX
Official: Link DOI: 10.1121/1.428311 PDF: KennedyJ2000a.pdf Google-Scholar: [16]
Abstract: This paper introduces an efficient parameterization for the nearfield broadband beamforming problem with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the actual broadband beampattern shape. The parameterization is based on an orthogonal basis set of elementary beampatterns by which an arbitrary beampattern can be constructed. A set of elementary beamformers are then designed for each elementary beampattern and the desired beamformer is constructed by summing the elementary beamformers with frequency and source-array distance dependent weights. An important consequence of our result is that the beamformer can be factored into three levels of filtering: (i) beampattern independent elementary beamformers; (ii) beampattern shape dependent filters; and (iii) radial focusing filters where a single parameter can be adjusted to focus the array to a desired radial distance from the array origin. As an illustration the method is applied to the problem of producing a practical array design that achieves a frequency invariant beampattern over the frequency range of 1:10 (which is suitable for speech acquisition using a microphone array), and with the array focused either to farfield or nearfield where at the lowest frequency the radial distance to the source is only three wavelengths.
@article{KennedyJ2000a,
    title = {Nearfield Broadband Array Design Using a Radially Invariant Modal Expansion},
    author = {Abhayapala, T. D. and Kennedy, R. A. and Williamson, R. C.},
    journal = {J. Acoust. Soc. Am.},
    volume = {107},
    pages = {392-403},
    month = {January},
    year = {2000}}
R. A. Kennedy, T. D. Abhayapala, and D. B. Ward, "Broadband Nearfield Beamforming using a Radial Beampattern Transformation", IEEE Trans. Signal Processing, vol. 46, no. 8, pp. 2147-2156, August 1998.
Abstract BibTeX
Official: Link DOI: 10.1109/78.705426 PDF: 00705426.pdf Google-Scholar: [50]
Abstract: This paper presents a new method of designing a beamformer having a desired nearfield broadband beampattern. The methodology uses the spherical harmonic solution to the wave equation to transform the desired nearfield beampattern to an equivalent farfield beampattern. A farfield beamformer is then designed for a transformed farfield beampattern that, if achieved, gives the desired nearfield pattern exactly. Salient features of the new method are as follows. (i) The nearfield patterns can be achieved for all angles, not just the primary look direction. (ii) There is no theoretical restriction on the bandwidth. (iii) General array geometries may be used. As an illustration, we apply the method to the problem of producing a practical array design that achieves a nearfield beampattern that is frequency invariant over an octave bandwidth, where at the lowest frequency, the array-source separation is three wavelengths.
@article{KennedyJ1998e,
    title = {Broadband Nearfield Beamforming using a Radial Beampattern Transformation},
    author = {Kennedy, R. A. and Abhayapala, T. D. and Ward, D. B.},
    journal = {IEEE Trans. Signal Processing},
    volume = {46},
    pages = {2147-2156},
    month = {August},
    year = {1998}}
D. B. Ward, Z. Ding, and R. A. Kennedy, "Broadband DOA Estimation Using Frequency Invariant Beamforming", IEEE Trans. Signal Processing, vol. 46, no. 5, pp. 1463-1469, May 1998.
Abstract BibTeX
Official: Link DOI: 10.1109/78.668812 PDF: 00668812.pdf Google-Scholar: [40]
Abstract: A new method of direction-of-arrival (DOA) estimation for multiple broadband farfield signals is presented. The technique uses a beamspace preprocessing structure based on frequency invariant beamforming. Specifically, a set of beam-shaping filters focus the received array data in the time domain, thereby avoiding the need for frequency decomposition. Hence, the proposed method is conceptually different from most other broadband DOA estimators, which require frequency decomposition. Numerical results are presented to demonstrate the use of the new method and compare it with conventional coherent signal subspace methods.
@article{KennedyJ1998c,
    title = {Broadband {DOA} Estimation Using Frequency Invariant Beamforming},
    author = {Ward, D. B. and Ding, Z. and Kennedy, R. A.},
    journal = {IEEE Trans. Signal Processing},
    volume = {46},
    pages = {1463-1469},
    month = {May},
    year = {1998}}
R. A. Kennedy, T. D. Abhayapala, D. B. Ward, and R. C. Williamson, "Nearfield Broadband Frequency Invariant Beamforming", Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'96, vol. 2, pp. 909-912, May 1996.
Abstract BibTeX
Official: Link DOI: 10.1109/ICASSP.1996.543268 PDF: 00543268.pdf Google-Scholar: [13]
Abstract: This paper presents a method for nearfield frequency invariant broadband array beamforming. This means that we can design an array with associated signal processing to achieve a desired frequency invariant beam pattern (as a function of direction) at any nominal finite distance over an arbitrarily wide range of frequencies. The challenge here is to compensate accurately for the nearfield distortions (both magnitude and phase) which are more acute at the lower frequencies of the operating bandwidth than the higher frequencies. The methodology uses spherical harmonics to transform the nearfield broadband frequency invariant beampattern specification to an equivalent farfield frequency varying beampattern specification. A simulation example is presented to demonstrate the effectiveness of this method in producing a nearfield beam pattern which is frequency invariant over an octave bandwidth.
@inproceedings{KennedyC1996a,
    title = {Nearfield Broadband Frequency Invariant Beamforming},
    author = {Kennedy, R. A. and Abhayapala, T. D. and Ward, D. B. and Williamson, R. C.},
    booktitle = {Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'96},
    volume = {2},
    pages = {909-912},
    month = {May},
    year = {1996}}
D. B. Ward, R. A. Kennedy, and R. C. Williamson, "FIR Filter Design for Frequency Invariant Beamformers", IEEE Signal Processing Lett., vol. 3, no. 3, pp. 69-71, March 1996.
Abstract BibTeX
Official: Link DOI: 10.1109/97.481158 PDF: 00481158.pdf Google-Scholar: [41]
Abstract: Two methods of implementing FIR filters for a frequency invariant beamformer are presented. Each of these methods uses a single underlying set of filter coefficients obtained directly from the desired beamformer response. One method uses multirate processing, and the other is based on a single sampling rate.
@article{KennedyJ1996b,
    title = {{FIR} Filter Design for Frequency Invariant Beamformers},
    author = {Ward, D. B. and Kennedy, R. A. and Williamson, R. C.},
    journal = {IEEE Signal Processing Lett.},
    volume = {3},
    pages = {69-71},
    month = {March},
    year = {1996}}
D. B. Ward, R. A. Kennedy, and R. C. Williamson, "Theory and design of broadband sensor arrays with frequency invariant far-field beam patterns", J. Acoust. Soc. Am., vol. 97, no. 2, pp. 1023-1034, February 1995.
Abstract BibTeX
Official: Link DOI: 10.1121/1.412215 PDF: KennedyJ1995b.pdf Google-Scholar: [105]
Abstract: The theory and design of a broadband array of sensors with a frequency invariant far-field beam pattern over an arbitrarily wide design bandwidth is presented. The frequency invariant beam pattern property is defined in terms of a continuously distributed sensor, and the problem of designing a practical sensor array is then treated as an approximation to this continuous sensor using a discrete set of filtered broadband omnidirectional array elements. The design methodology is suitable for one-, two-, and three-dimensional sensor arrays; it imposes no restrictions on the desired aperture distribution (beam shape), and can cope with arbitrarily wide bandwidths. An important consequence of the results is that the frequency response of the filter applied to the output of each sensor can be factored into two components: One component is related to a slice of the desired aperture distribution, and the other is sensor independent. The results also indicate that the locations of the sensors are not a crucial design consideration, although it is shown that nonuniform spacings simultaneously avoid spatial aliasing and minimize the number of sensors. An example design which covers a 10:1 frequency range (which is suitable for speech acquisition using a microphone array) illustrates the utility of the method. Finally, the theory is generalized to cover a parameterized class of arrays in which the frequency dependence of the beam pattern can be controlled in a continuous manner from a classical single-frequency design to a frequency invariant design.
@article{KennedyJ1995b,
    title = {Theory and design of broadband sensor arrays with frequency invariant far-field beam patterns},
    author = {Ward, D. B. and Kennedy, R. A. and Williamson, R. C.},
    journal = {J. Acoust. Soc. Am.},
    volume = {97},
    pages = {1023-1034},
    month = {February},
    year = {1995}}