Abstract
There are different ways to perform noise reduction in the time domain. The simplest way, perhaps, is to estimate a sample of the desired signal at a time by applying a filtering vector to the observation signal vector. This approach is investigated in this chapter and many well-known optimal filtering vectors are derived. We start by explaining the single-channel signal model for noise reduction in the time domain.
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Notes
- 1.
In this work, we consider the uncorrelated interference as part of the noise in the definitions of the performance measures.
- 2.
Very often in the literature, authors use \(1/\upsilon_{{\rm sd}}\left({\mathbf{h}} \right)\) as a measure of the SNR improvement. This is wrong! Obviously, we can define whatever we want, but in this is case we need to be careful to compare “apples with apples.” For example, it is not appropriate to compare \(1/\upsilon_{{\rm sd}} \left({\mathbf{h}} \right) \hbox{ to } \hbox{iSNR}\) and only \(\hbox{oSNR} \left({\mathbf{h}} \right)\) makes sense to compare to iSNR.
References
J. Benesty, J. Chen, Y. Huang, I. Cohen, Noise Reduction in Speech Processing (Springer, Berlin, 2009)
P. Vary, R. Martin, Digital Speech Transmission: Enhancement, Coding and Error Concealment (Wiley, Chichester, 2006)
P. Loizou, Speech Enhancement: Theory and Practice (CRC Press, Boca Raton, 2007)
J. Benesty, J. Chen, Y. Huang, S. Doclo, Study of the Wiener filter for noise reduction, in Speech Enhancement, Chap. 2, ed. by J. Benesty, S. Makino, J. Chen (Springer, Berlin, 2005)
J. Chen, J. Benesty, Y. Huang, S. Doclo, New insights into the noise reduction Wiener filter. IEEE Trans. Audio Speech Language Process. 14, 1218–1234 (2006)
S. Haykin, Adaptive Filter Theory, 4th edn. (Prentice-Hall, Upper Saddle River, 2002)
J.N. Franklin, Matrix Theory (Prentice-Hall, Englewood Cliffs, 1968)
J. Capon, High resolution frequency-wavenumber spectrum analysis. Proc. IEEE 57, 1408–1418 (1969)
R.T. Lacoss, Data adaptive spectral analysis methods. Geophysics 36, 661–675 (1971)
O. Frost, An algorithm for linearly constrained adaptive array processing. Proc. IEEE 60, 926–935 (1972)
M. Er, A. Cantoni, Derivative constraints for broad-band element space antenna array processors. IEEE Trans. Acoust. Speech Signal Process. 31, 1378–1393 (1983)
I. Cohen, Noise spectrum estimation in adverse environments: improved minima controlled recursive averaging. IEEE Trans. Speech Audio Process. 11, 466–475 (2003)
I. Cohen, J. Benesty, S. Gannot (eds.), Speech Processing in Modern Communication—Challenges and Perspectives (Springer, Berlin, 2010)
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Benesty, J., Chen, J. (2011). Single-Channel Noise Reduction with a Filtering Vector. In: Optimal Time-Domain Noise Reduction Filters. SpringerBriefs in Electrical and Computer Engineering(), vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19601-0_2
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DOI: https://doi.org/10.1007/978-3-642-19601-0_2
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