Welch's Method

Welch's method [275] (also called the periodogram method) for estimating power spectra is carried out by dividing the time signal into successive blocks, forming the periodogram for each block, and averaging.

Denote the th windowed, zero-padded frame from the signal by

where is defined as the window hop size, and let denote the number of available frames. Then the periodogram of the th block is given by

as before, and the Welch estimate of the power spectral density is given by

In other words, it's just an average of periodograms across time. When is the rectangular window, the periodograms are formed from non-overlapping successive blocks of data. For other window types, the analysis frames typically overlap, as discussed further in §5.13 below.

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Subsections

• Welch Autocorrelation Estimate
• Resolution versus Stability

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.