# Dictionary:Hamming function

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(ham’ ∂ng) A function used to shape the cutoff of a window or gate in data processing to avoid the undesirable effects of sharp truncation.

The Hamming function (different from the Hanning function ) is

${\displaystyle 0.54+0.46\cos {\phi ,\quad -\pi <\phi <\phi }}$,
${\displaystyle 0,\quad \phi <-\pi {\text{ or }}\phi >\pi }$,

where ${\displaystyle \phi }$ increases linearly from ${\displaystyle -\pi }$ to ${\displaystyle \pi }$ across the window. For the kth element out of n elements within the window, ${\displaystyle \phi =2\pi k/(n+1)+\pi }$.

FIG. W-12. Windows in the time and frequency domains. (a) Window shapes in time-domain. (b) Spectral shapes. The effective width of the boxcar is greater than that for the other window shapes and hence the central lobe is sharper.

Named after R. W. Hamming.