A fast digital method of estimating the autocorrelation of a Guassian stationary process

Given a zero mean stationary Gaussian process
{x_{n}}
, it is shown that the autocorrelation can be estimated by
\hat{R}_{xx}(j) = C_{N} \sum\min{i=1}\max{N} x_{i} sign(x_{i+j})
where
C_{N}=\frac{\pi}{2N^{2}} \sum\min{i=1}\max{N}|x_{i}|
. This method is attractive since
C_{N}
needs to he Computed only once, and
\sum\min{i=1}\max{N} x_{i} sign (x_{i+j})
can be computed by additions only. Moreover, the shape of the autocorrelation given by
\hat{R}_{xx}(j)/C_{N}
can be computed by additions only.