Std Graph Analysis Smooth Savitzky

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Next: Std_Graph_Analysis_Smooth_Moving_window_average

Graph Analysis

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 {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]\displaystyle{ 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 tables, below. For example, for smoothing by a 5-point quadratic polynomial, m = 5, i = −2, −1, 0, 1, 2 and the jth smoothed data point, Y_j, is given by

[math]\displaystyle{ 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.

Previous: Smooth

Next: Std_Graph_Analysis_Smooth_Moving_window_average

Graph Analysis

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