Nonuniform reconstruction of periodic bandlimited signals without sampling points’ number restriction

Abstract

Since the periodic bandlimited signal space is a reproducing kernel Hilbert space, a closed-form interpolating formula with minimum mean-squared error that interpolates finite nonuniform samples without number restriction is proposed by using the representer theorem and the Hilbert projection theorem, and it turns out to be the minimum energy periodic bandlimited interpolator. The influence of the number of sampling points on the reconstruction performance is then presented. Simulations are also performed to verify the correctness of the derived results.