In
signal processing, a window function (or apodization function) is a
function that is zero-valued outside of some chosen
interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation. When another function or a signal (data) is multiplied by a window function, the product is also zero-valued outside the interval: all that is left is the "view" through the window. Applications of window functions include spectral analysis,
filter design and
beamforming.
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In
Time Series , the Bartlett window is a weighted moving average transformation used to smooth the periodogram values. In the Bartlett window (Bartlett, 1950) the weights are computed as:
wj = 1-(j/p) (for j = 0 to p)
w-j = wj (for j 0)
where p = (m-1)/2
This weight function will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center.
See also,
Basic Notations and Principles .
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