Tukey Window

In Time Series , the Tukey window is a weighted moving average transformation used to smooth the periodogram values. In the Tukey (Blackman and Tukey, 1958) or Tukey-Hanning window (named after Julius Von Hann), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:
wj = 0.5 + 0.5*cos( *j/p) (for j=0 to p)
w-j = wj (for j 0)

where p = (m-1)/2x.
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, Spectrum Analysis - Basic Notations and Principles .