Std Graph Analysis Smooth Savitzky: Difference between revisions

Revision as of 07:53, 5 September 2022

Previous: Smooth

Next: Std_Graph_Analysis_Smooth_Moving_window_average

Menu location
Std Graph Analysis Smooth Savitzky
Analysis → Smooth → Savitzky Golay...
Phenomena
All
Default shortcut
None
Introduced in version
0.001
See also
Smooth, Std_Graph_Analysis_Smooth_Moving_window_average
Contents 1 Description 2 Usage 3 Note

Description

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

Usage

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 {x_j, y_j}, j = 1, ..., n, where x_j is an independent

Previous: Smooth

Next: Std_Graph_Analysis_Smooth_Moving_window_average

Graph Analysis

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@@ Line 26: / Line 26: @@
 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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Std Graph Analysis Smooth Savitzky: Difference between revisions

Revision as of 07:53, 5 September 2022

Description

Usage

Note

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