Difference between revisions of "Dictionary:Hamming function"

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{{#category_index:H|Hamming function}}
 
{{#category_index:H|Hamming function}}
 
(ham&#x2019; &#x2202;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&#x2019; &#x2202;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==
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Latest revision as of 21:07, 19 July 2016

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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

,
,

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

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.

External links

find literature about
Hamming function
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