Correlation function estimation by a polarity method using stochastic reference signals

Instead of estimating correlation functions by conventional means, a specific polarity scheme may be used on bounded processes. The method is based on a rather simple relationship between the correlation functions before and after infinite clipping, provided that stochastic reference signals of uniform distribution are added to the process. This correlation technique has been known for some time. Because of the apparent computational advantages, its application to the estimation of correlation functions from discrete or sampled data is being examined. A general derivation of the appropriate moment relationship is given and a complete mean-square error analysis of estimates is provided under the assumption of white-noise-type reference signals. It is shown that correlation function estimates obtained by this polarity method possess a mean-square error that differs from the error of conventional estimates only by a term proportional to
1/N
, where
N
is the sample size. This term may be made arbitrarily small. Thus, only small degradations in the accuracy of estimates have to be expected when using the polarity approach.