ARMA signals with specified symmetric marginal probability distribution

Bernard Picinbono (1, 2)

1 Ecole Supérieure d'Electricité - SUPELEC (FRANCE)
2 L2S - Laboratoire des signaux et systèmes

Except in the case of normal (i.e., Gaussian) distribution, it is very difficult to calculate the marginal probability distribution of ARMA signals. By using a particular form of modeling such signals with random coefficients we show that the problem can be solved and we present an algorithm allowing the numerical generation of ARMA signals with arbitrary specified marginal distribution function. Their properties are analyzed in computer experiments. The experimental results show in general a very good agreement with theoretical calculations.

Mots clés: statistical signal analysis; ARMA signals; autoregressive signals; Bernoulli signals; innovation; linear prediction; moving average signals; non-Gaussian signals and noise; probability distribution; random coefficients; signal and noise modeling; statistical signal analysis.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Bernard Picinbono. ARMA signals with specified symmetric marginal probability distribution. IEEE Transactions on Signal Processing, 2010, 58 (3), pp.1542-1552. ⟨hal-00547042⟩