Polynomial Expansion Of The Probability Density Function About Gaussian Mixtures

Abstract

A polynomial expansion to probability density function (pdf ) approximation about Gaussian mixture densities is proposed in this paper. Using known polynomial series expansions we apply the Parzen estimator to derive an orthonormal basis that is able to represent the characteristics of probability distributions that are not concentrated in the vicinity of the mean point such as the Gaussian pdf. The blind source separation problem is used to illustrate the applicability of the proposal in practical analysis of the dynamics of the recovered data pdf estimation. Simulations are carried out to illustrate the analysis. © 2004 IEEE.163172Cavalcante, C.C., (2004) On Blind Source Separation: Proposals and Analysis of Multi-user Processing Strategies, , Ph.D. thesis, State University of Campinas (UNICAMP) - DECOM, Campinas, SP - Brazil, AprilCavalcante, C.C., Cavalcanti, F.R.P., Mota, J.C.M., Romano, J.M.T., A Constrained version of fitting PDF algorithm for blind source separation (2003) Proceeding of IEEE Signal Processing Advances for Wireless Communications (SPAWC 2003), , Rome, Italy, June, 15-18Haykin, S., (1998) Neural Networks: A Comprehensive Foundation, , Prentice Hall, 2nd ednHyvärinen, A., Oja, E., Karhunen, J., (2001) Independent Component Analysis, , John Wiley & SonsLacoume, J.-L., Amblard, P.-O., Comon, P., (1997) Statistiques D'Ordre Supérieur Pour le Traitement du Signal, , (Traitement du Signal), Paris: MassonLaster, J.D., (1997) Robust GMSK Demodulation Using Demodulator Diversity and BER Estimation, , Ph.D. thesis, Faculty of the Virginia Polytechnic Institute and State University, Blacksburg, Virginia, MarchNikias, C.L., Petropulu, A.P., (1993) Higher-order Spectra Analysis, , Prentice HallPapadias, C.B., (2000) Blind Separation of Independent Sources Based on Multiuser Kurtosis Optimization Criteria, 2, pp. 147-179. , John-Wiley & Sons, chap. 4Papoulis, A., (1991) Probability, Random Variables and Stochastic Processes, , (Electrical & Electronic Engineering Series), McGraw-Hill International, 3rd ednParzen, E., On estimation of a probability density function and mode (1962) The Annals of Mathematical Statistics, 33 (3), pp. 1066-1076. , SeptemberSilverman, B.W., (1986) Density Estimation for Statistics and Data Analysis, , (Monographs on Statistics and Applied Probability), Bristol, Great Britain: Chapman and HallTherrien, C.W., (1992) Discrete Random Signals and Statistical Signal Processing, , (Prentice-Hall Signal Processing Series), Prentice-Hall InternationalWegman, E.J., Nonparametric probability density estimation: I. A summary of available methods (1972) Technometrics, 14 (3), pp. 533-546. , Augus