Hann function
The Hann function, named after the Austrian meteorologist Julius von Hann, is a discrete window function given by
or
or, in terms of the haversine function,
The Hann window is a linear combination of modulated rectangular windows . From Euler's formula
![w_{r}={\mathbf {1}}_{{[0,N-1]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60686048227000343f225f8767f485d2db3d054f)
Due to the basic properties of the Fourier transform, its spectrum is
with the spectrum of the rectangular window
(the modulation factor vanishes if windows are time-shifted around 0).
Hann function is the original name, in honour of von Hann; however, the erroneous "Hanning" function is also heard of on occasion, derived from the paper in which it was named, where the term "hanning a signal" was used to mean applying the Hann window to it. The confusion arose from the similar Hamming function, named after Richard Hamming.
The Hann function is typically used as a window function in digital signal processing to select a subset of a series of samples in order to perform a Fourier transform or other calculations.
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