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In this paper, sampling Theorems for perfect signal reconstruction using samples of a signal taken below the Nyquist rate involving nonlinear signal reconstruction technique are presented. The presented results are in contrast with the linear time-invariant filtering based signal reconstruction in the celebrated Shannon sampling theory. It is shown that using  k th order nonlinearity in the signal reconstruction system, the required sampling rate for perfect signal reconstruction can be reduced by the same factor  k  for positive odd values of it. The extensions of the proposed sampling expansion to the fractional Fourier transform and linear canonical transform domains are also derived. Simulation results of the proposed technique are given to validate the proposed approach.

Sampling Theorems with Nonlinear Signal Reconstruction Scheme