Abstract

Aliased signals due to undersampling or nonbandlimited signals can be reconstructed exactly if the original signal is redundant. The necessary and sufficient conditions are found for a class of nonlinear operators ( )^1/n for bandwidth compression. We have shown that the necessary and sufficient condition for such a compression is that the signal has nth ord. zeros. There are other nonlinear operators such as 1n(y), e^y, y^a, 1/y that are potentially capable of bandwidth reduction (making a nonbandlimited signal bandlimited). It is shown that any nonlinear distortion can be compensated provided that the nonlinear operation is analytic and monotonic. This fact has a potential application wherever nonlinear distortion is a problem. The signal recovery is due to the fact that the zeros of a bandlimited signal are somehow preserved in the derivative of the distorted signal. From the zeros of a bandlimited signal, one can always find the original signal within a scale factor.

© 1985 Optical Society of America