The Hann Window, sometimes called the Hanning Window (not to be confused with the Hamming Window) or the raised cosine window, is an apodization function used to taper non-periodic signals before they're fed through a Fourier Transform in order to minimise spectral leakage.

A Hann Window from -1 to 1 with an amplitude of 1.0 is:

y = cos2(πx/2) = 0.5 + 0.5 cos(πx)
It was named after the Austrian meteorologist Julius von Hann.