A Theoretical Investigation of a Method for Analyzing Random Signals.

摘要

The zero crossings of random noise can be divided into two types,corresponding to the forward and backward rotation of a complex vector whose real and imaginary parts are the noise signal and its Hilbert transform. The statistics of the two kinds of crossing are being investigated to see how well a detection system,based upon measurements of the two kinds of crossings,can determine the presence of a non random signal in a Gaussian noise environment. A formula for the probability that the vector is rotating backwards at any fixed line had previously been used. A rigorous derivation of a more general version of this formula has now been obtained.