Python Data Analysis Cookbook

Estimating power spectral density with the Welch method

The Welch method is an improvement (it reduces noise) of the periodogram technique and is named after P.D. Welch. The noise of the power spectrum is reduced with the following steps:

1. We split the signal with a fixed number of overlapping points. If the overlap is 0, then we have Bartlett's method.
2. In the time domain, we apply window functions to each of the segments of step 1.
3. We compute the periodogram for each segment as explained in the Spectral analysis with periodograms recipe.
4. We average the periodograms, thus reducing noise. Averaging effectively smoothens the signal. However, we are now dealing with frequency bins (like in a histogram).

We will also explore the Fano factor, which is given ...