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.