Estimation of Spectra After Hard Clipping of Gaussian Processes”?

Abstract

Certain types of non-linear transformations of stochastic signal processes have proven useful in engineering applications. A form of processing called hard clipping (or hard limiting) has frequently been used in electronic systems which work in “real time” in order to reduce the number of information bits which the system has to process. With hard clipping only one binary digit is used per sample value of an input signal X(t). However, information is lost about X(t) and the spectrum which is calculated from the clipped signal is a distorted form of the original signal spectrum. By a sine transformation of the sample covariance of the clipped process, a consistent estimator is derived for the spectral density of X(t). The asymptotic variance-covariance function is calculated for this estimator.