or, in terms of the haversine function,
Thanks to the basic properties of the Fourier transform, its spectrum is
with the spectrum of the rectangular window
(the modulation factor vanished 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.
i.e. (using continuous version to illustrate)
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.
- Harris, F. J. (1978). "On the use of windows for harmonic analysis with the discrete Fourier transform". Proceedings of the IEEE 66: 51. doi:10.1109/PROC.1978.10837.
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