Nonlinear Filtering of Signals Exhibiting Large Fluctuations in Strength

Abstract Considered in this paper is the following filtering problem: Given a signal which has a certain frequency spectrum (|ω| ≤ Ω) and a wide range of strength over that spectrum including such low levels which may not be distinguishable from noise and high levels that could distort the signal due to, say, inherent nonlinearities in the sensors over those ranges, (i) would it be possible to identify the signal correctly?, and (ii) how could it be done? Proposed is a scheme in which the original signal is first distorted by a mono-tonic function and is then passed through an ideal low-pass linear filter resulting in a filtered version of the distorted signal. It is shown that the original signal may be uniquely recovered from the ultimate filtered version of the distorted signal.