Dictionary:Hamming function

(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

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

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

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.

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