Approximate Signal Reconstruction Using Nonuniform Samples in Fractional Fourier and Linear Canonical Transform Domains

Approximate signal reconstruction formulas for the class of L(2)(R) signals in the fractional Fourier and linear canonical transform (LCT) domains are presented. The results make use of the finite number of nonuniform samples of the signal in fractional Fourier or LCT domains taken at the positions determined by the zeros of the Hermite polynomials. The results provide exact representation for the class of signals that can be expressed in the form of polynomials of some finite order. The truncation error bounds in the presented results are also discussed. Simulation results for some of the proposed theorems are also presented.