Hann function

The Hann function, named after the Austrian meteorologist Julius von Hann, is a discrete probability mass function given by

w(n)= 0.5\; \left(1 - \cos \left ( \frac{2 \pi n}{N-1} \right) \right)

or

w(n)= \sin^2 \left ( \frac{ \pi n}{N-1} \right)

Or, in terms of the haversine function, w(n) = haversin[2πn/(N-1)].

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Name

Hann function is the original name, in honour of von Hann; however, the erroneous 'Hanning' function is also heard of on occasion. The confusion arose from the similar Hamming function, named after Richard Hamming.

Use

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.

i.e. (using continuous version to illustrate)

S(\tau)= \int w(t%2B\tau)f(t) \, dt

The advantage of the Hann window is very low aliasing, and the tradeoff is slightly decreased resolution (widening of the main lobe). If the Hann window is used to sample a signal in order to convert to frequency domain, it is complex to reconvert to the time domain without adding distortions.

See also

External links