Open AccessMixed Spectra for Stable Signals from Discrete Observations
Author(s) -
Rachid Sabre
Publication year - 2021
Publication title -
signal and image processing : an international journal
Language(s) - English
Resource type - Journals
eISSN - 2229-3922
pISSN - 0976-710X
DOI - 10.5121/sipij.2021.12502
Subject(s) - aliasing , spectral density estimation , mathematics , spectral density , discrete time and continuous time , sampling (signal processing) , discrete time signal , variance (accounting) , continuous spectrum , signal (programming language) , polynomial , kernel density estimation , zero (linguistics) , algorithm , mathematical analysis , computer science , fourier transform , statistics , physics , filter (signal processing) , telecommunications , analog signal , philosophy , signal transfer function , business , linguistics , accounting , quantum mechanics , transmission (telecommunications) , computer vision , programming language , estimator
This paper concerns the continuous-time stable alpha symmetric processes which are inivitable in the modeling of certain signals with indefinitely increasing variance. Particularly the case where the spectral measurement is mixed: sum of a continuous measurement and a discrete measurement. Our goal is to estimate the spectral density of the continuous part by observing the signal in a discrete way. For that, we propose a method which consists in sampling the signal at periodic instants. We use Jackson's polynomial kernel to build a periodogram which we then smooth by two spectral windows taking into account the width of the interval where the spectral density is non-zero. Thus, we bypass the phenomenon of aliasing often encountered in the case of estimation from discrete observations of a continuous time process.