"A Kramer Type Sampling Theorem for a Class of Random Processes".

JUAN MANUEL MEDINA; BRUNO CERNUSCHI FRÍAS

San Miguel de Tucumán

Congreso; Reunión Anual de la Unión Matemática Argentina; 2011

Universidad Nacional de Tucumán

The classical Kramer sampling theorem is a universal method to obtain orthogonalsampling formulas [1] [2]. Kramer’s result proves a sampling formula which holdsin the range space of a linear integral transformation defined in a suitable Lebesgue space L2(R, μ). This contains the classical Shannon sampling theorem for bandlimited functions. Sampling formulas are very useful in the context of signal pro-cessing theory.In this work we prove an analogous result for finite variance random signals definedover a probability space with an orthogonal random measure, and an appropriate measurable function. A converse of this result is also discussed,that is: under suitable conditions on the sampling scheme we obtain a Riesz basisof the closed linear span of the whole process. This containsas particular cases some classical related results for stationary random processes .References[1] H.P. Kramer, “A generalized Sampling theorem”, J. Math Phys. , 63, 68-72,1957.[2] M.Z. Nashed and G.G. Walter, “Reproducing kernel Hilber spaces from sam-pling expansions”, Contemp. Math., 190, 221-226, 1995.