Alpha Stable Random Fields and Additive Error

This work studies the estimation of spectral density for random field (two-dimensional signal) when the spectral measure have certain mixture and the process is observed with a constant error. The objective of this paper is to give an estimator of the constant error by using the Jackson polynomial kernel. We show that the rate of convergence depends of size of sample and the behaviours of the spectral density at origin. Indeed the estimator converges rapidly when the spectral density is null at origin. Few long memory signals are taken here as example.