Std Graph Analysis Smooth Savitzky: Difference between revisions

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(Created page with "{{Docnav |Smooth |Std_Graph_Analysis_Smooth_Moving_window_average |Graph Analysis |IconL= |IconR= |IconC=Labrps.svg }} {{GuiCommand |Name=Std Graph Analysis Smooth Savitzky |MenuLocation=Analysis → Smooth → Savitzky Golay... |Phenomena=All |Version=0.001 |SeeAlso=Smooth, Std_Graph_Analysis_Smooth_Moving_window_average }} ==Description== The '''Std Graph Analysis Smooth Savitz...")
 
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This command performs a smoothing of the selected curve using the Savitzky-Golay method. The formula used to smooth the curve defined by the points yi=f(xi) is:
This command performs a smoothing of the selected curve using the Savitzky-Golay method. The formula used to smooth the curve defined by the points yi=f(xi) is:


The data consists of a set of points {''x''<sub>''j''</sub>, ''y''<sub>''j''</sub>}, ''j'' = 1, ..., ''n'', where ''x''<sub>''j''</sub> is an independent variable and ''y''<sub>''j''</sub> is an observed value. They are treated with a set of ''m'' convolution coefficients, ''C''<sub>i</sub>, according to the expression 
The data consists of a set of points {''x''<sub>''j''</sub>, ''y''<sub>''j''</sub>}, ''j'' = 1, ..., ''n'', where ''x''<sub>''j''</sub> is an independent  
:<math>Y_j= \sum _{i=\tfrac{1-m}2}^{\tfrac{m-1}2}C_i\, y_{j+i},\qquad  \frac{m+1}{2} \le j \le n-\frac{m-1}{2}</math>
Selected convolution coefficients are shown in the [[#Appendix|tables, below]]. For example, for smoothing by a 5-point quadratic polynomial, ''m'' = 5, ''i'' = −2, −1, 0, 1, 2 and the ''j''th smoothed data point, ''Y''<sub>j</sub>, is given by
 
:<math>Y_j = \frac{1}{35} (-3  y_{j - 2} + 12  y_{j - 1} + 17  y_j + 12  y_{j + 1} -3  y_{j + 2})</math>,
 
where, ''C''<sub>−2</sub> = −3/35, ''C''<sub>−1</sub> = 12 / 35, etc.


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Revision as of 08:53, 5 September 2022

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Std Graph Analysis Smooth Savitzky

Menu location
Analysis → Smooth → Savitzky Golay...
Phenomena
All
Default shortcut
None
Introduced in version
0.001
See also
Smooth, Std_Graph_Analysis_Smooth_Moving_window_average

Description

The Std Graph Analysis Smooth Savitzky command performs a smoothing of the selected curve using the Savitzky-Golay method.

Usage

  1. Select the Analysis → Smooth → Savitzky Golay... option from the menu.

Note

This command performs a smoothing of the selected curve using the Savitzky-Golay method. The formula used to smooth the curve defined by the points yi=f(xi) is:

The data consists of a set of points {xj, yj}, j = 1, ..., n, where xj is an independent

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