Generalized Cosine Windows
Blackman, flat top, Hamming, Hann, and rectangular windows are all special cases of the generalized cosine window. These windows are combinations of sinusoidal sequences with frequencies that are multiples of 2π/(N – 1), where N is the window length. One special case is the Blackman window:
N = 128; A = 0.42; B = 0.5; C = 0.08; ind = (0:N-1)'*2*pi/(N-1); w = A - B*cos(ind) + C*cos(2*ind);
Changing the values of the constants
C in the previous expression generates different
generalized cosine windows like the Hamming and Hann windows. Adding
additional cosine terms of higher frequency generates the flat top
window. The concept behind these windows is that by summing the individual
terms to form the window, the low frequency peaks in the frequency
domain combine in such a way as to decrease sidelobe height. This
has the side effect of increasing the mainlobe width.
The Hamming and Hann windows are two-term generalized cosine
windows, given by
0.46 for the Hamming
0.5 for the Hann.
Note that the definition of the generalized cosine window shown
in the earlier MATLAB® code yields zeros at samples 1 and
This Window Designer screen shot compares Blackman, Hamming, Hann, and Flat Top windows.