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The periodogram is not a consistent estimator of the true power

spectral density of a wide-sense stationary process. Welch’s technique to reduce the

variance of the periodogram breaks the time series into segments, usually

overlapping.

Welch’s method computes a modified periodogram for each segment and then averages

these estimates to produce the estimate of the power spectral density. Because the

process is wide-sense stationary and Welch’s method uses PSD estimates of different

segments of the time series, the modified periodograms represent approximately

uncorrelated estimates of the true PSD and averaging reduces the variability.

The segments are typically multiplied by a window function, such as a Hamming

window, so that Welch’s method amounts to averaging modified periodograms. Because

the segments usually overlap, data values at the beginning and end of the segment

tapered by the window in one segment, occur away from the ends of adjacent segments.

This guards against the loss of information caused by windowing.

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