Hamming Window

In Time Series, the Hamming window is a weighted moving average transformation used to smooth the periodogram values. In the Hamming (named after R. W. Hamming) window or Tukey-Hamming window (Blackman and Tukey, 1958), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

wj = 0.54+0.46*cosine(p*j /p) (for j=0 to p)

w-j = wj (for j¹0)

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. Note also that the Time Series method of analysis will standardize the weights so that they sum to 1.

See also, Spectrum Analysis - Basic Notations and Principles.