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Welch's Method
Welch's method [297] (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, zeropadded frame from the signal
by

(7.26) 
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

(7.27) 
In other words, it's just an average of periodograms across time.
When
is the rectangular window, the periodograms are formed
from nonoverlapping successive blocks of data. For other window
types, the analysis frames typically overlap, as discussed further in
§6.13 below.
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