The Hanning window has a shape similar to that of half a cycle of a cosine wave. The following equation defines the Hanning window.
for n = 0, 1, 2, …, N - 1
where N is the length of the window and w is the window value.
The following figure shows a Hanning window with N = 32.
The Hanning window is useful for analyzing transients longer than the time duration of the window and for general-purpose applications.