Abstract

This paper discusses the relationship between the zero crossings or zeros of band-limited signals and their nonlinear transformations. It is proved that the bandwidth of a signal can be compressed by a ratio of 1/n if and only if the signal has nth-order zero crossings or zeros (if complex). Also, a monotonic nonlinearity in the observation of a band-limited signal can be identified from the zero crossings (or zeros) of the derivative of the observed signal. (The results are for one-dimensional signals. Extensions to two-dimensional signals remain to be addressed.)

© 1986 Optical Society of America

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