# Difference between revisions of "Dictionary:Hamming function"

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{{#category_index:H|Hamming function}} | {{#category_index:H|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. | (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. | ||

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The Hamming function (different from the [[Dictionary:Hanning_function|''Hanning function'']] ) is | The Hamming function (different from the [[Dictionary:Hanning_function|''Hanning function'']] ) is | ||

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<center><math>0.54+0.46 \cos{\phi, \quad -\pi < \phi < \phi}</math>,</center> | <center><math>0.54+0.46 \cos{\phi, \quad -\pi < \phi < \phi}</math>,</center> | ||

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<center><math>0,\quad \phi<-\pi\text{ or }\phi > \pi </math>,</center> | <center><math>0,\quad \phi<-\pi\text{ or }\phi > \pi </math>,</center> | ||

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where <math>\phi</math> increases linearly from <math>-\pi</math> to <math>\pi</math> across the window. For the ''k''th element out of ''n'' elements within the window, <math>\phi=2\pi k/(n+1) + \pi</math>. | where <math>\phi</math> increases linearly from <math>-\pi</math> to <math>\pi</math> across the window. For the ''k''th element out of ''n'' elements within the window, <math>\phi=2\pi k/(n+1) + \pi</math>. | ||

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[[File:Segw12.jpg|center|thumb|600px|FIG. W-12. <b>Windows</b> in the time and frequency domains. (<b>a</b>) Window shapes in time-domain. (<b>b</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.]] | [[File:Segw12.jpg|center|thumb|600px|FIG. W-12. <b>Windows</b> in the time and frequency domains. (<b>a</b>) Window shapes in time-domain. (<b>b</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.]] | ||

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Named after R. W. Hamming. | Named after R. W. Hamming. | ||

− | ==External links== | + | ==External links== <!--T:8--> |

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## Latest revision as of 21:07, 19 July 2016

(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

where increases linearly from to across the window. For the *k*th element out of *n* elements within the window, .

Named after R. W. Hamming.