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Hann function
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Hann function : ウィキペディア英語版
Hann function

The Hann function, named after the Austrian meteorologist Julius von Hann, is a discrete window function given by
:w(n)= 0.5\; \left(1 - \cos \left ( \frac \right) \right)
or
:w(n)= \sin^2 \left ( \frac \right)
or, in terms of the haversine function,
:w(n)=\operatorname\left(\frac \right).
== Spectrum ==

The Hann window is a linear combination of modulated rectangular windows w_r = \mathbf_. From Euler's formula
:w(n)= \frac \,w_r(n) -\frac e^} w_r(n) - \frace^} w_r(n)
Due to the basic properties of the Fourier transform, its spectrum is
:\hat (\omega) = \frac \hat_r (\omega) - \frac \hat_r \left(\omega + \frac\right) - \frac \hat_r \left(\omega - \frac\right)
with the spectrum of the rectangular window
:\hat_r (\omega) = e^} \frac
(the modulation factor vanishes if windows are time-shifted around 0)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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