Abstract
It is well known that stereophonic acoustic echo, due to the coupling between two loudspeakers and two microphones, can be modelled by a two-input/twooutput system with real random variables. In this chapter, we recast this problem as a single-input/single-output system with complex random variables by using the widely linear model. As a consequence, the four real-valued acoustic impulse responses are converted to one complex-valued impulse response. Also, all important conventional measures are reformulated in this new context. The main advantage of this approach is that instead of handling two (real) output signals separately, we only handle one (complex) output signal. This makes it convenient to handle the main three challenges of SAEC, i.e., system identification, double-talk detection, and echo suppression.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sondhi, M.M., Morgan, D.R., Hall, J.L.: Stereophonic acoustic echo cancellation–An overview of the fundamental problem. IEEE Signal Process. Lett. 2, 148–151 (1995)
Benesty, J., Morgan, D.R., Sondhi, M.M.: A better understanding and an improved solution to the specific problems of stereophonic acoustic echo cancellation. IEEE Trans. Speech, Audio Process. 6, 156–165 (1998)
Picinbono, B., Chevalier, P.: Widely linear estimation with complex data. IEEE Trans. Signal Process. 43, 2030–2033 (1995)
Mandic, D.P., Still, S., Douglas, S.C.: Duality between widely linear and dual channel adaptive filtering. In: Proc. IEEE ICASSP, pp. 1729–1732 (2009)
Ollila, E.: On the circularity of a complex random variable. IEEE Signal Process. Lett. 15, 841–844 (2008)
Mandic, D.P., Goh, S.L.: Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. Wiley, Chichester (2009)
Amblard, P.O., Gaeta, M., Lacoume, J.L.: Statistics for complex variables and signals–Part I: variables. Signal Process. 53, 1–13 (1996)
Amblard, P.O., Gaeta, M., Lacoume, J.L.: Statistics for complex variables and signals–Part II: signals. Signal Process. 53, 15–25 (1996)
Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. J. Machine Learning Res. 49, 1208–1215 (2001)
Huang, Y., Benesty, J., Chen, J.: Acoustic MIMO Signal Processing. Springer, Berlin (2006)
Paleologu, C., Benesty, J., Ciochină, S.: Sparse Adaptive Filters for Echo Cancellation. Morgan & Claypool, San Rafael (2010)
Hänsler, E., Schmidt, G.: Acoustic Echo and Noise Control–A Practical Approach. Wiley, Hoboken (2004)
Benesty, J., Gänsler, T., Morgan, D.R., Sondhi, M.M., Gay, S.L.: Advances in Network and Acoustic Echo Cancellation. Springer, Berlin (2001)
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Benesty, J., Paleologu, C., Gänsler, T., Ciochină, S. (2011). Problem Formulation. In: A Perspective on Stereophonic Acoustic Echo Cancellation. Springer Topics in Signal Processing, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22574-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-22574-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22573-4
Online ISBN: 978-3-642-22574-1
eBook Packages: EngineeringEngineering (R0)