Rational characteristic functions and Markov chains: application to modeling probability density functions

  • Authors:

  • Josep Vidal;Antonio Bonafonte;Natalia Fernández

  • Affiliations:

  • Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, Campus Nord UPC, Modul D-5 c/Gran Capita s/n, 08034 Barcelona, Spain;Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, Campus Nord UPC, Modul D-5 c/Gran Capita s/n, 08034 Barcelona, Spain;Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, Campus Nord UPC, Modul D-5 c/Gran Capita s/n, 08034 Barcelona, Spain

  • Venue:
  • Signal Processing
  • Year:
  • 2004

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Abstract

We investigate in this paper how to estimate the probability density function (PDF) of a random variable using a rational parametric model for its characteristic function (CF). The choice of the model is motivated by the problem of better modeling the duration of the speech states within a hidden Markov model (HMM). While in the conventional case, the duration of each state is modeled by an exponentially decreasing PDF, we propose the use of a multiple-state Markov chain. The PDF of the time spent within this Markov chain turns out to fit an ARMA model for the CF. Linear estimates are derived based on the method of moments and the theoretical performance is derived and compared to the maximum likelihood (ML) estimates. Identifiability and consistency issues are also addressed. Application on real data of duration of units in speech show good fitting.