A fast digital method of estimating the autocorrelation of a Guassian stationary process
D. Hertz · IEEE Transactions on Acoustics Speech and Signal Processing · 1982
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})whereC_{N}=\frac{\pi}{2N^{2}} \sum\min{i=1}\max{N}|x_{i}|. This method is attractive sinceC_{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.