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Signal-Dependent Array Processing

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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))

Abstract

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.

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Notes

  1. 1.

    Beamformers are spatial filters, therefore the terms beamformer and filter will be used interchangeably in this chapter.

  2. 2.

    The dependency on time is omitted for brevity. In practice, the signals acquired using a spherical microphone array are usually processed in the short-time Fourier transform domain, as explained in Sect. 3.1, where the discrete frequency index is denoted by \(\nu \).

  3. 3.

    If the real SHT is applied instead of the complex SHT, the complex spherical harmonics \(Y_{lm}\) used throughout this chapter should be replaced with the real spherical harmonics \(R_{lm}\), as defined in Sect. 3.3.

  4. 4.

    We use the complex conjugate weights \(\mathbf {w}^{\text {H}}\) rather than the weights \(\mathbf {w}^{\text {T}}\); this notational convention originates in the spatial domain [37].

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Authors and Affiliations

  1. Kilburn & Strode LLP, London, UK

    Daniel P. Jarrett

  2. International Audio Laboratories Erlangen, Erlangen, Germany

    Emanuël A. P. Habets

  3. Department of Electrical and Electronic Engineering, Imperial College London, London, UK

    Patrick A. Naylor

Authors
  1. Daniel P. Jarrett
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  2. Emanuël A. P. Habets
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  3. Patrick A. Naylor
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Correspondence to Daniel P. Jarrett .

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Jarrett, D.P., Habets, E.A.P., Naylor, P.A. (2017). Signal-Dependent Array Processing. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-42211-4_7

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