where is unit-variance white noise.
for nonnegative lags ( ). More completely, we can write
Thus, the autocorrelation of is a triangular pulse centered on lag 0. The true (unbiased) autocorrelation is given by
The true power spectral density (PSD) is then
Figure 6.3 shows a collection of measured autocorrelations together with their associated smoothed-PSD estimates.
Example: Synthesis of 1/F Noise (Pink Noise)
Matlab for Welch's Method