The recovery of distorted band-limited stochastic processes

This paper deals with the problem of recovering a bandlimited process after it has been distorted by an instantaneous nonf(t) uniquely. More precisely, if fi(t) and fi(t) are two linearity and subsequently band-limited. Several uniqueness theorems for functions band-limited to (W,W), and if A[f,(t)] and the input-output relationships are derived. In contrast with the deterA[fi(t)] have spectra which are equal in the band (W, W), ministic case, no requirement that the nonlinearity be monotonic is made then,f,(t) = fi(t) for almost all t. Beurling’s theorem is not here. An iterative procedure for the recovery of the input is presented. constructive, however. An explicit procedure for the recovApplications to two-level quantizers are considered, and a new result on the determination of a band-limited Gaussian process from its zero ery of f(t) was derived by Landau [l], [2] for a class of crossings is obtained. companding functions A(x). It has long been conjectured that a result similar to