# Positivité d'une covariance de type MA(2) ou MA(3)

Abstract : The covariance function $\gamma _k$ of a real discrete-time moving average of order $q$ random signal is zero for $k > \vert q \vert$ but its other values must satisfy some conditions ensuring that $\gamma _k$ is a non-negative-definite function, which means that its Fourier transform, or its power spectrum, is non-negative. There are some general conditions ensuring this property but they cannot be used in order to determine the domain $D_+$ such that when the vector ${\bf c}$ of components $\gamma _k$ belongs to this domain then $\gamma _k$ has the required non-negative property. The boundaries of the domain are determined for $q = 2$ and $q = 3$ theoretically and computer simulations exhibit an excellent agreement between theoretical and simulated results.
Mots-clés :
Document type :
Journal articles
Domain :

Cited literature [4 references]

https://hal-centralesupelec.archives-ouvertes.fr/hal-01656610
Contributor : Bernard Picinbono <>
Submitted on : Tuesday, December 5, 2017 - 6:35:45 PM
Last modification on : Wednesday, October 14, 2020 - 3:56:58 AM

### File

MA(2) BON.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01656610, version 1

### Citation

Bernard Picinbono. Positivité d'une covariance de type MA(2) ou MA(3). Traitement du Signal, Lavoisier, 2016, 22 (4), pp. 403-414. ⟨hal-01656610⟩

Record views