Blackman-Tukey method

Now, we mentioned that the PSD is defined as the Fourier transform of the autocorrelation function. Although our periodgram method does not use the autocorrelation function directly, it is equivalent to it. The problem is that we only have a finite record length so for small lags, we have lots of samples to compute the autocorrelation from, but at large lags we only have a few samples to compute the autocorrelation from . Thus, the autocorrelation estimates will have more variance at large lags and will likely be less accurate. The Blackman-Tukey method takes this into account by weighting the autocorrelation estimate by a window function (typically the triangular window). See [6].

P_xx^BT(f )= $\overset{N-1}{\underset{m=-(N-1)}{\sum}}$w(m)$\hat{{r}}_{{xx}}^{}$(m)e^-i2$\pi$fm

And of course we can average multiple overlapping segments for this method.

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