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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Beamformers are spatial filters, therefore the terms beamformer and filter will be used interchangeably in this chapter.
- 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.
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.
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
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
Benesty, J., Chen, J., Habets, E.A.P.: Speech Enhancement in the STFT Domain. Springer Briefs in Electrical and Computer Engineering. Springer, Heidelberg (2011)
Benesty, J., Chen, J., Huang, Y.: Microphone Array Signal Processing. Springer, Berlin (2008)
Benesty, J., Makino, S., Chen, J. (eds.): Speech Enhancement. Springer, Heidelberg (2005)
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)
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)
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)
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)
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
Capon, J.: High resolution frequency-wavenumber spectrum analysis. Proc. IEEE 57, 1408–1418 (1969)
Cohen, I.: Analysis of two-channel generalized sidelobe canceller with post-filtering. IEEE Trans. Speech Audio Process. 11(6), 684–699 (2003)
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)
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)
Griffiths, L.J., Jim, C.W.: An alternative approach to linearly constrained adaptive beamforming. IEEE Trans. Antennas Propag. 30(1), 27–34 (1982)
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)
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)
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)
ITU-T: Objective Measurement of Active Speech Level (1993)
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)
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)
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)
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)
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)
Kuttruff, H.: Room Acoustics, 4th edn. Taylor and Francis, London (2000)
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)
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
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)
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)
Nordholm, S., Claesson, I., Eriksson, P.: The broadband Wiener solution for Griffiths-Jim beamformers. IEEE Trans. Signal Process. 40(2), 474–478 (1992)
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
Rafaely, B.: Plane-wave decomposition of the pressure on a sphere by spherical convolution. J. Acoust. Soc. Am. 116(4), 2149–2157 (2004)
Shalvi, O., Weinstein, E.: System identification using nonstationary signals. IEEE Trans. Signal Process. 44(5), 2055–2063 (1996)
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
Teutsch, H.: Wavefield decomposition using microphone arrays and its application to acoustic scene analysis. Ph.D. thesis, Friedrich-Alexander Universität Erlangen-Nürnberg (2005)
van Trees, H.L.: Detection, Estimation, and Modulation Theory Optimum Array Processing, vol. IV. Wiley, New York (2002)
van Trees, H.L.: Optimum Array Processing. Detection, Estimation and Modulation Theory. Wiley, New York (2002)
van Veen, B.D., Buckley, K.M.: Beamforming: a versatile approach to spatial filtering. IEEE Acoust. Speech Signal Mag. 5(2), 4–24 (1988)
Wiener, N.: The Extrapolation, Interpolation and Smoothing of Stationary Time Series. Wiley Inc., New York (1949)
Williams, E.G.: Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, 1st edn. Academic Press, London (1999)
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-42211-4_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42209-1
Online ISBN: 978-3-319-42211-4
eBook Packages: EngineeringEngineering (R0)