Zero crossings, bandwidth compression, and restoration of nonlinearly distorted band-limited signals
Farokh Marvasti, Anil Kumar Jain · Journal of the Optical Society of America A · 1986
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.)