Abstract
This paper analyzes applications of cumulant analysis in speech processing. The main focus is made on an integral representation for cumulants using integrals involving cyclic products of kernels. These integrals serve as a tool for statistical analysis of different statistics appearing in speech processing and speech recognition. As an example, we consider statistics based on the sample correlogram. A representation for the cumulants of these statistics using integrals involving cyclic products of kernels is obtained.
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References
Avram, F.: Generalized Szego Theorems and Asymptotics of Cumulants by Graphical Methods. Trans. Amer. Math. Soc. 330, 637–649 (1992)
Avram, F., Taqqu, M.: On the Generalized Brascamp-Lieb-Barthe Inequality, a Szegő Type Limit Theorem, and the Asymptotic Theory of Random Sums, Integrals and Quadratic Forms (2005) (manuscript), http://www.univ-pau.fr/~avram/papers/avramtaqqu.pdf
Buldygin, V., Utzet, F., Zaiats, V.: Asymptotic Normality of Cross-Correlogram Estimators of the Response Function. Statist. Inf. Stoch. Process. 7, 1–34 (2004)
Chi, C.-Y., Hwang, J.-L., Rau, C.-F.: A New Cumulant Based Parameter Estimation Method for Noncausal Autoregressive Systems. IEEE Trans. Signal Process. 42, 2524–2527 (1994)
Grenander, U., Szegő, G.: Toeplitz Forms and Their Applications. University of California Press, San Francisco (1958)
Ihm, B.-C., Park, D.-J.: Blind Separation of Sources Using Higher-Order Cumulants. Signal Process. 73, 267–276 (1999)
Makhoul, J.: Linear Prediction: A Tutorial Review. Proc. IEEE 63, 561–580 (1975)
Nemer, E., Goubran, R., Mahmoud, S.: Speech Enhancement Using Fourth-Order Cumulants and Optimum Filters in the Subband Domain. Speech Comm. 36, 219–246 (2002)
Paliwal, K.K., Sondhi, M.M.: Recognition of Noisy Speech Using Cumulant-Based Linear Prediction Analysis. In: International Conference on Acoustics, Speech and Signal Processing, ICASSP 1991, April 14–17, pp. 429–432 (1991)
Salavedra, J.M., Hernando, H.: Third-Order Cumulant-Based Wiener Filtering Algorithm Applied to Robust Speech Recognition. In: Ramponi, G., Sicuranza, G.L., Carrato, S., Marsi, S. (eds.) 8th European Signal Processing Conference, EUSIPCO 1996, Trieste, Italy, September 10-13 (1996)
Sugrailis, D.: On Multiple Poisson Stochastic Integrals and Associated Markov Semigroups. Probab. Math. Statist. 3, 217–239 (1984)
Swami, A., Mendel, J.M.: Adaptive System Identification Using Cumulants. In: International Conference on Acoustics, Speech and Signal Processing, ICASSP 1988, New York, NY, USA, vol. 4, pp. 2248–2251 (1988)
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Zaiats, V., Solé-Casals, J., Martí-Puig, P., Reig-Bolaño, R. (2010). Applications of Cumulants in Speech Processing. In: Solé-Casals, J., Zaiats, V. (eds) Advances in Nonlinear Speech Processing. NOLISP 2009. Lecture Notes in Computer Science(), vol 5933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11509-7_23
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DOI: https://doi.org/10.1007/978-3-642-11509-7_23
Publisher Name: Springer, Berlin, Heidelberg
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