Reconstruction of Bandlimited Signals in Linear Canonical Transform Domain From Finite Nonuniformly Spaced Samples

We investigate the reconstruction of bandlimited signals in the linear canonical transform (LCT) domain from a finite set of nonuniformly spaced samples. Based on the reproducing property of the reproducing kernel belonging to the class of bandlimited signals in LCT domain, we derive an interpolating formula with minimum mean-squared error that interpolates the finite set of nonuniformly spaced samples, and show that it is identical to the minimum energy bandlimited in LCT domain interpolator. Singular value decomposition is also used to set up a reconstruction algorithm which guarantees that the reconstruction result also achieves the minimum energy reconstruction.