Name
Abstract | ||
|---|---|---|
Microphone arrays sample the sound field in both space and time with the major objective being the extraction of the signal propagating from a desired direction-of-arrival (DOA). In order to reconstruct a spatial sinusoid from a set of discrete samples, the spatial sampling must occur at a rate greater than a half of the wavelength of the sinusoid. This principle has long been adapted to the microphone array context: in order to form an unambiguous beampattern, the spacing between elements in a microphone array needs to conform to this spatial Nyquist criterion. The implicit assumption behind the narrowband beam-pattern is that one may use linearity and Fourier analysis to describe the response of the array to an arbitrary wideband plane wave. In this paper, this assumption is analyzed. A formula for the broadband beampattern is derived. It is shown that in order to quantify the spatial filtering abilities of a broadband array, the incoming signal's bifrequency spectrum must be taken into account, particularly for nonstationary signals such as speech. Multi-dimensional Fourier analysis is then employed to derive the broadband spatial transform, which is shown to be the limiting case of the broadband beampattern as the number of sensors tends to infinity. The conditions for aliasing in broadband arrays are then determined by analyzing the effect of computing the broadband spatial transform with a discrete spatial aperture. It is revealed that the spatial Nyquist criterion has little importance for microphone arrays. Finally, simulation results show that the well-known steered response power (SRP) method is formulated with respect to stationary signals, and that modifications are necessary to properly form steered beams in nonstationary signal environments. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/TSP.2008.2010596 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
microphone array context,discrete spatial aperture,spatial sampling,microphone array,broadband beampattern,incoming signal,index terms—beamforming,spatial aliasing,micro- phone arrays,microphone arrays sample,spatial nyquist criterion,broadband array,wavenumber-fre- quency spectrum.,spatial sinusoid,spatial filtering,sampling methods,speech,indexing terms,spectrum,direction of arrival,linearity,plane waves,beamforming,fourier analysis,filtering | Beamforming,Telecommunications,Control theory,Sensor array,Antenna array,Nyquist stability criterion,Microphone array,Aliasing,Acoustics,Microphone,Mathematics,Spatial filter | Journal |
Volume | Issue | ISSN |
57 | 4 | 1053-587X |
Citations | PageRank | References |
19 | 1.33 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jacek Dmochowski | 1 | 74 | 6.52 |
| Jacob Benesty | 2 | 1386 | 136.42 |
| Sofiène Affes | 3 | 962 | 97.26 |