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Extract 'Specifying Custom Fit Curve (Fit Formula) (Pro edition only)' Create subsection 'Nonlinear Curve Fitting' in contents
MagicPlot can approximately locate peaks in spectrum. To locate peaks click on Guess
button in Fit Curves
tab of Fit Plot. Peak guessing is performed by looking for local minimums of second derivative of data-baseline.
While Guess Peaks
window is open you can see the preview of guessed peaks on Fit Plot. This preview is updated every time you change the parameters in the window.
Smoothing is used in order to filter narrow peaks which can be guessed from noise. MagicPlot peak guess tool is capable of smoothing both data and second derivative before finding local minimums. Smoothing is used only to find peaks and does not affect the data on Fit Plot.
Savitzky–Golay method is used for smoothing. This algorithm performs a local polynomial regression of specified degree on specified number of points. Bigger points number leads to better smoothing.
MagicPlot sorts found peaks by amplitude and suggests only a specified number of greatest peaks. You can change the number of guessed peaks with slider or by entering value in the text field with spinner.
You can use cubic spline to fit and subtract baseline on Fit Plot. To create spline curve click on Add
button in Fit Curves
tab of Fit Plot.
Don't use splines to subtract baselines which can be fit well enough with line curve (line or constant baseline). You can subtract wide peaks by mistake using spline.
Created spline has 3 anchor points by default. You can move, add and remove anchor points:
Spline anchor point (x, y) coordinates are treated as fit parameters so you can perform fitting with spline. Note that the anchor point coordinates will be varied but the number of point will remain. You also can lock some parameters (usually x coordinates) by setting Lock
check boxes in parameters table.
It is recommended to set appropriate fit intervals which contain only baseline without peaks. In such case Fit One Curve
button is more acceptable than Fit by Sum
button, because the individual interval for current curve will be used and the interval from Fit Interval
tab (which is used to fit by sum of curves) is ignored. Select spline curve and check Set Interval
check box in the bottom of the panel to edit spline interval, then click on Fit One Curve
button.
Set Baseline
check box in spline row in curves table to subtract spline from data.
Setting intervals in Fit interval
tab of Fit Plot is initially intended for setting data range which is used for fitting by sum of fit curves. However, this tab can also be used to calculate integrals and statistics on these intervals (Statistics is only available in Pro edition). Data-Baseline is used to calculate the results.
MagicPlot can integrate data on selected intervals and calculate peak moments (x mean, variance, skewness, kurtosis). Spectrum line is treated as probability distribution curve: x values are treated as 'independent variable' and y values are treated as 'probability'. Standard statistical formulas are used to calculate moments.
Statistical data and integrals are automatically updated if x or y data is changed or intervals are changed.
All statistical data is summarized in the intervals table:
Move interval borders with mouse. Double click on interval to split it at desired position. Right click opens context menu from which new intervals can be created on free space and existing intervals can be deleted or split.
MagicPlot can calculate relative integrals to compare the relative intensity of spectrum lines. To compute relative integrals set Relative integrals
check box. MagicPlot designate the smallest integral as 1 but you can enter a custom value. If you want to set not the smallest integral as reference point, enter 1 first and then enter the value of desired integral relative to 1 to this field, so that other integrals will be calculated relative to this new value.
Property | Formula |
---|---|
Integral | Calculated using Trapezoidal rule |
X Mean (expected value) | |
Variance | |
Standard deviation | |
Skewness | |
Kurtosis | |
Y Sum |
Intermediate values are calculated as follows:
Property | Formula |
---|---|
Raw moments | ,~ n = 1…4 |
Normalization coefficient | |
Central moments | |
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MagicPlot indicates columns for which formulas or other evaluators (FFT, integral, etc.) are set with blue header color. You can see the formula in column header tool tip.
On the screenshot above:
To fit the width of one column, double click on right separator line in table header. To fit selected columns widths, double click one of column separators in table header.
You can quickly transform X or Y data on Fit Plot by using Transform X/Y
items in Processing
menu. These menu items open set column formula dialog for table column which is used as X or Y. Note that this transformation affects the table with plot data.
Make Waterfall
menu item opens waterfall window in which you can specify shift increment. MagicPlot tries to guess handsome shift values on basis of the number of curves and current scale.
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This is the table of predefined fit curves.
Name | Formula | Additional Properties |
---|---|---|
Line | ||
Parabola | Vertex: |
|
Gaussian | Area: Standard deviation: |
|
Gaussian-A (normalized) | Amplitude: Standard deviation: |
|
Lorentzian | Area: |
|
Lorentzian-A (normalized) | Amplitude: |
|
Gauss Derivative | Area (second integral): Standard deviation: Peak-to-peak horizontal: Peak-to-peak vertical: |
|
Lorentz Derivative | Area (second integral): Peak-to-peak horizontal: Peak-to-peak vertical: |