Std Graph Analysis Smooth Savitzky - Revision history

LabRPS at 16:33, 5 September 2022

2022-09-05T16:33:59Z

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	\|[[Std_Graph_Analysis_Smooth_Moving_window_average]]		\|[[Std_Graph_Analysis_Smooth_Moving_window_average\|Moving Window Average]]
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	\|[[Std_Analysis_Menu\|Graph Analysis]]		\|[[Std_Analysis_Menu\|Graph Analysis]]
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LabRPS at 16:33, 5 September 2022

2022-09-05T16:33:13Z

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	\|Phenomena=All		\|Phenomena=All
	\|Version=0.001		\|Version=0.001
	\|SeeAlso=[[Std_Graph_Analysis_Smooth\|Smooth]], [[Std_Graph_Analysis_Smooth_Moving_window_average]]		\|SeeAlso=[[Std_Graph_Analysis_Smooth\|Smooth]], [[Std_Graph_Analysis_Smooth_Moving_window_average\|Moving Window Average]]
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LabRPS at 16:28, 5 September 2022

2022-09-05T16:28:30Z

← Older revision		Revision as of 09:28, 5 September 2022
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	==Note==		==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:~~		This command performs a smoothing of the selected curve using the Savitzky-Golay method.

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LabRPS: /* Note */

2022-09-05T16:28:09Z

Note

← Older revision		Revision as of 09:28, 5 September 2022
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	==Note==		==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:		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~~
	~~<math>Y_j= x^{2}</math>~~

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LabRPS: /* Note */

2022-09-05T16:20:34Z

Note

← Older revision		Revision as of 09:20, 5 September 2022
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	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		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>		<math>Y_j= x^{2}</math>

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LabRPS: /* Note */

2022-09-05T16:15:09Z

Note

← Older revision		Revision as of 09:15, 5 September 2022
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	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		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>		<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>

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LabRPS: /* Note */

2022-09-05T15:54:56Z

Note

← Older revision		Revision as of 08:54, 5 September 2022
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	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		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>

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LabRPS at 15:53, 5 September 2022

2022-09-05T15:53:33Z

← Older revision		Revision as of 08:53, 5 September 2022
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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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LabRPS: 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..."

2022-09-05T15:50:22Z

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..."

New page

{{Docnav
|[[Std_Graph_Analysis_Smooth|Smooth]]
|[[Std_Graph_Analysis_Smooth_Moving_window_average]]
|[[Std_Analysis_Menu|Graph Analysis]]
|IconL=
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}}

{{GuiCommand
|Name=Std Graph Analysis Smooth Savitzky
|MenuLocation=Analysis → Smooth → Savitzky Golay...
|Phenomena=All
|Version=0.001
|SeeAlso=[[Std_Graph_Analysis_Smooth|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==
# Select the {{MenuCommand|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 variable and ''y''''j'' is an observed value. They are treated with a set of ''m'' convolution coefficients, ''C''i, according to the expression
:<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''j, 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''−2 = −3/35, ''C''−1 = 12 / 35, etc.

{{Docnav
|[[Std_Graph_Analysis_Smooth|Smooth]]
|[[Std_Graph_Analysis_Smooth_Moving_window_average]]
|[[Std_Analysis_Menu|Graph Analysis]]
|IconL=
|IconR=
|IconC=Labrps.svg
}}

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