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Spatial Sampling and Signal Transformation

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Theory and Applications of Spherical Microphone Array Processing

Part of the book series: Springer Topics in Signal Processing ((STSP,volume 9))

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Abstract

This chapter examines issues relating to spatial signal acquisition and transformation. Many publications that propose algorithms for parameter estimation or signal enhancement purposes begin from the outset using signals in either or both of the time-frequency and spherical harmonic domains. One aim of the current chapter is to provide some of the algorithmic details necessary to process signals directly from the microphones, which will then enable subsequent spherical harmonic domain processing to be applied. In addition, we present a number of spatial sampling schemes, which determine the placement of microphones on the sphere such that spatial aliasing is minimized, and we discuss the advantages and disadvantages of two common array types: the open and rigid arrays with omnidirectional microphones.

Portions of Sect. 3.4 were first published in [8], and are reproduced here with the author’s permission.

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Notes

  1. 1.

    This equation assumes the sign convention used in engineering. If the acoustics convention is used, this equation is given by \(b_l(k) = (-i)^l j_l(kr)\). For more information on the effects of the choice of sign convention, see Sect. 2.3.

  2. 2.

    This equation assumes the sign convention used in engineering. If the acoustics convention is used, this equation is given by \(b_l(kr_{\text {a}},kr) = (-i)^l \left( j_l(kr) - \frac{j'_l(kr_{\text {a}})}{h^{(1)'}_l(kr_{\text {a}})} h_l^{(1)}(kr) \right) \), where \(h_l^{(1)}= \left( h_l^{(2)}\right) ^{*}\) denotes the spherical Hankel function of the first kind. For more information on the effects of the choice of sign convention, see Sect. 2.3.

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Correspondence to Daniel P. Jarrett .

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Jarrett, D.P., Habets, E.A.P., Naylor, P.A. (2017). Spatial Sampling and Signal Transformation. In: Theory and Applications of Spherical Microphone Array Processing. Springer Topics in Signal Processing, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-42211-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-42211-4_3

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