Computationally efficient estimation of the mean frequency for real-valued signals

It can be shown that the mean frequency of a real-valued stochastic signal can be expressed as an integral of the normalized autocorrelation function r(τ) weighted by a function equal to 1/τ². The fast decline of the weighting function implies that the behavior of the autocorrelation function for small values of τ is the most important portion for estimation of the mean frequency of a signal. It is demonstrated in a simulation study that estimates of the mean frequency with mean squared error equal to the error in estimates obtained via a FFT derived mean frequency estimate can be obtained by using just a few lags of the normalized autocorrelation function with a computational effort substantially less than that required for estimation via FFT. Upper bounds, that can be used as guidelines when implementing the estimator, are given for the bias error introduced by using just a few lag values of the autocorrelation function.