Title :
Equivalence Between Representations for Samplable Stochastic Processes and its Relationship With Riesz Bases
Author :
Medina, Juan Miguel ; Cernuschi-Frias, Bruno
Author_Institution :
Dept. Mat., Univ. de Buenos Aires, Buenos Aires, Argentina
Abstract :
We characterize random signals which can be linearly determined by their samples. This problem is related to the question of the representation of random variables by means of a countable Riesz basis. We study different representations for processes which are linearly determined by a countable Riesz basis. This concerns the representation of continuous time processes by means of discrete samples.
Keywords :
signal processing; stochastic processes; continuous time processes; countable Riesz basis; random signals; samplable stochastic processes; Convergence; Extraterrestrial measurements; Hilbert space; Indexes; Kernel; Random processes; Stochastic processes; Finite variance random processes; KL-expansions; Riesz bases; reproducing kernel Hilbert space; sampling;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2272874
