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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].

References

  1. Avargel, Y., Cohen, I.: On multiplicative transfer function approximation in the short-time Fourier transform domain. IEEE Signal Process. Lett. 14(5), 337–340 (2007). doi:10.1109/LSP.2006.888292

    Article  Google Scholar 

  2. Benesty, J., Chen, J., Habets, E.A.P.: Speech Enhancement in the STFT Domain. Springer Briefs in Electrical and Computer Engineering. Springer, Heidelberg (2011)

    Google Scholar 

  3. Benesty, J., Chen, J., Huang, Y.: Microphone Array Signal Processing. Springer, Berlin (2008)

    Google Scholar 

  4. Benesty, J., Makino, S., Chen, J. (eds.): Speech Enhancement. Springer, Heidelberg (2005)

    Google Scholar 

  5. Bitzer, J., Kammeyer, K.D., Simmer, K.U.: An alternative implementation of the superdirective beamformer. In: Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics. New Paltz, New York (1999)

    Google Scholar 

  6. Bitzer, J., Simmer, K., Kammeyer, K.D.: Theoretical noise reduction limits of the generalized sidelobe canceller for speech enhancement. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 5, pp. 2965–2968 (1999)

    Google Scholar 

  7. Brandwood, D.H.: A complex gradient operator and its application in adaptive array theory. In: Proceedings of the IEEE 130(1, Parts F and H), 11–16 (1983)

    Google Scholar 

  8. Braun, S., Jarrett, D.P., Fischer, J., Habets, E.A.P.: An informed spatial filter for dereverberation in the spherical harmonic domain. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 669–673. Vancouver, Canada (2013)

    Google Scholar 

  9. Breed, B.R., Strauss, J.: A short proof of the equivalence of LCMV and GSC beamforming. IEEE Signal Process. Lett. 9(6), 168–169 (2002). doi:10.1109/LSP.2002.800506

    Article  Google Scholar 

  10. Capon, J.: High resolution frequency-wavenumber spectrum analysis. Proc. IEEE 57, 1408–1418 (1969)

    Article  Google Scholar 

  11. Cohen, I.: Analysis of two-channel generalized sidelobe canceller with post-filtering. IEEE Trans. Speech Audio Process. 11(6), 684–699 (2003)

    Article  Google Scholar 

  12. Gannot, S., Burshtein, D., Weinstein, E.: Signal enhancement using beamforming and nonstationarity with applications to speech. IEEE Trans. Signal Process. 49(8), 1614–1626 (2001)

    Article  Google Scholar 

  13. Gannot, S., Cohen, I.: Adaptive beamforming and postfiltering. In: Benesty, J., Sondhi, M.M., Huang, Y. (eds.) Springer Handbook of Speech Processing, Chap. 47. Springer, Heidelberg (2008)

    Google Scholar 

  14. Griffiths, L.J., Jim, C.W.: An alternative approach to linearly constrained adaptive beamforming. IEEE Trans. Antennas Propag. 30(1), 27–34 (1982)

    Article  Google Scholar 

  15. Habets, E.A.P., Benesty, J., Cohen, I., Gannot, S., Dmochowski, J.: New insights into the MVDR beamformer in room acoustics. IEEE Trans. Audio, Speech, Lang. Process. 18, 158–170 (2010)

    Google Scholar 

  16. Habets, E.A.P., Benesty, J., Gannot, S., Cohen, I.: The MVDR beamformer for speech enhancement. In: Cohen, I., Benesty, J., Gannot, S. (eds.) Speech Processing in Modern Communication: Challenges and Perspectives, Chap. 9. Springer, Heidelberg (2010)

    Google Scholar 

  17. Habets, E.A.P., Benesty, J., Naylor, P.A.: A speech distortion and interference rejection constraint beamformer. IEEE Trans. Audio, Speech, Lang. Process. 20(3), 854–867 (2012)

    Google Scholar 

  18. ITU-T: Objective Measurement of Active Speech Level (1993)

    Google Scholar 

  19. Chen, J., Benesty, Y.H., Doclo, S.: New insights into the noise reduction Wiener filter. IEEE Trans. Audio, Speech, Lang. Process. 14, 1218–1234 (2006)

    Google Scholar 

  20. Jarrett, D.P., Habets, E.A.P.: On the noise reduction performance of a spherical harmonic domain tradeoff beamformer. IEEE Signal Process. Lett. 19(11), 773–776 (2012)

    Article  Google Scholar 

  21. Jarrett, D.P., Habets, E.A.P., Benesty, J., Naylor, P.A.: A tradeoff beamformer for noise reduction in the spherical harmonic domain. In: Proceedings of the International Workshop Acoustics, Signal Enhancement (IWAENC). Aachen, Germany (2012)

    Google Scholar 

  22. Jarrett, D.P., Habets, E.A.P., Naylor, P.A.: Spherical harmonic domain noise reduction using an MVDR beamformer and DOA-based second-order statistics estimation. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 654–658. Vancouver, Canada (2013)

    Google Scholar 

  23. Jarrett, D.P., Thiergart, O., Habets, E.A.P., Naylor, P.A.: Coherence-based diffuseness estimation in the spherical harmonic domain. In: Proceedings of the IEEE Convention of Electrical and Electronics Engineers in Israel (IEEEI). Eilat, Israel (2012)

    Google Scholar 

  24. Kuttruff, H.: Room Acoustics, 4th edn. Taylor and Francis, London (2000)

    Google Scholar 

  25. Markovich, S., Gannot, S., Cohen, I.: Multichannel eigenspace beamforming in a reverberant noisy environment with multiple interfering speech signals. IEEE Trans. Audio, Speech, Lang. Process. 17(6), 1071–1086 (2009)

    Google Scholar 

  26. Markovich-Golan, S., Gannot, S.: Performance analysis of the covariance subtraction method for relative transfer function estimation and comparison to the covariance whitening method. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 544–548 (2015). doi:10.1109/ICASSP.2015.7178028

  27. Markovich-Golan, S., Gannot, S., Cohen, I.: A sparse blocking matrix for multiple constraints GSC beamformer. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 197–200 (2012)

    Google Scholar 

  28. Meyer, J., Elko, G.: A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 2, pp. 1781–1784 (2002)

    Google Scholar 

  29. Nordholm, S., Claesson, I., Eriksson, P.: The broadband Wiener solution for Griffiths-Jim beamformers. IEEE Trans. Signal Process. 40(2), 474–478 (1992)

    Article  Google Scholar 

  30. Peled, Y., Rafaely, B.: Linearly constrained minimum variance method for spherical microphone arrays in a coherent environment. In: Proceedings of the Hands-Free Speech Communication and Microphone Arrays (HSCMA), pp. 86–91 (2011). doi:10.1109/HSCMA.2011.5942416

  31. Rafaely, B.: Plane-wave decomposition of the pressure on a sphere by spherical convolution. J. Acoust. Soc. Am. 116(4), 2149–2157 (2004)

    Article  Google Scholar 

  32. Shalvi, O., Weinstein, E.: System identification using nonstationary signals. IEEE Trans. Signal Process. 44(5), 2055–2063 (1996)

    Article  Google Scholar 

  33. Souden, M., Benesty, J., Affes, S.: On optimal frequency-domain multichannel linear filtering for noise reduction. IEEE Trans. Audio, Speech, Lang. Process. 18(2), 260–276 (2010). http://dx.doi.org/10.1109/TASL.2009.2025790

  34. Teutsch, H.: Wavefield decomposition using microphone arrays and its application to acoustic scene analysis. Ph.D. thesis, Friedrich-Alexander Universität Erlangen-Nürnberg (2005)

    Google Scholar 

  35. van Trees, H.L.: Detection, Estimation, and Modulation Theory Optimum Array Processing, vol. IV. Wiley, New York (2002)

    Google Scholar 

  36. van Trees, H.L.: Optimum Array Processing. Detection, Estimation and Modulation Theory. Wiley, New York (2002)

    Google Scholar 

  37. van Veen, B.D., Buckley, K.M.: Beamforming: a versatile approach to spatial filtering. IEEE Acoust. Speech Signal Mag. 5(2), 4–24 (1988)

    Google Scholar 

  38. Wiener, N.: The Extrapolation, Interpolation and Smoothing of Stationary Time Series. Wiley Inc., New York (1949)

    Google Scholar 

  39. Williams, E.G.: Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, 1st edn. Academic Press, London (1999)

    Google Scholar 

  40. Yan, S., Sun, H., Svensson, U.P., Ma, X., Hovem, J.M.: Optimal modal beamforming for spherical microphone arrays. IEEE Trans. Audio, Speech, Lang. Process. 19(2), 361–371 (2011). doi:10.1109/TASL.2010.2047815

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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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