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

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Abstract

The concept of informed array processing is introduced in this chapter. The conceptual aim of informed array processing is to incorporate relevant spatial information about the problem to be solved into the design of spatial filters and into the estimation of the second-order statistics that are required to implement the beamformers of Chap. 7. Informed array processing techniques are developed for two important signal enhancement problems: noise reduction and dereverberation.

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Notes

  1. 1.

    For brevity, the dependency of all quantities on \(\ell \) is omitted throughout Sects. 9.1.1 and 9.1.2.

  2. 2.

    For brevity, the dependency of all quantities on the discrete time and frequency indices \(\ell \) and \(\nu \) is omitted where possible in the rest of Sect. 9.1.

  3. 3.

    When the sphere is a 2-sphere (i.e., an ordinary sphere), as it is here, the von Mises–Fisher distribution is sometimes referred to simply as a Fisher distribution.

  4. 4.

    A number of audio examples are also available at http://www.ee.ic.ac.uk/sap/sphdoa/.

  5. 5.

    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 \(\nu \).

  6. 6.

    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.

  7. 7.

    It should be noted that this simplified expression is only valid if the filter is applied to mode strength compensated eigenbeams. As a result, it is different to the expression given in Chap. 6.

  8. 8.

    A number of audio examples can be accessed from https://www.audiolabs-erlangen.de/resources/2013-ICASSP-RR.

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Jarrett, D.P., Habets, E.A.P., Naylor, P.A. (2017). Informed 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_9

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