The Fit
Local Maxima Peaks option fits peaks with local maxima, where all peaks are sufficiently resolved
to evidence an apex or mode.PeakLab v1 Documentation Contents AIST Software Home AIST Software Support
Fitting Peaks Overview
PeakLab offers three AutoFit (automated fitting) options for identifying and fitting peaks, two of which are capable of finding hidden peaks. PeakLab defines hidden peaks as those which do not evidence a local maximum within the data stream.
Peak AutoPlacement and Fitting Options
The Fit
Local Maxima Peaks option fits peaks with local maxima, where all peaks are sufficiently resolved
to evidence an apex or mode.
The Fit
Hidden Peaks -Residuals option uncovers hidden peaks by looking at residuals, the difference between
the peaks identified by local maxima and smoothed data.
The Fit
Hidden Peaks - Second Derivative reveals hidden peaks by looking for local minima in smoothed second
derivative data.
Peak Functions
Automated, Graphical, and Numerical Peak Placement
The primary peak placement is fully automatic. Peaks are placed by one of the aforementioned autoplacement criteria. Only a single peak model can be automatically placed for all peaks. Whether all peak widths and shapes are constant or varying is a simple matter of whether the Vary options are checked or unchecked. When the width or shape is allowed to vary, a peak refinement algorithm is used to characterize each peak as exactly as possible from the raw data. Most data sets require no more than adjusting the few controls which affect the automated detection.
The secondary placement operation is fully graphical. Peaks are added by left clicking the mouse at the desired center and amplitude. Each peak will have a primary anchor defining its amplitude and center. Additional anchors will be present if widths or shapes are allowed to vary. By clicking and holding down the left mouse button when on an anchor, a peak is easily moved to a new X position, increased or decreased in amplitude, changed in width, or modified in asymmetry or shape. By left clicking on a peak's primary anchor, a peak is toggled on and off. A right click on the primary anchor opens a numeric adjust popup dialog where that specific peak can be changed to a different function or deleted. Here you can also access supplemental functions, such as transition equations, which can also be graphically placed and adjusted. This secondary level of placement requires no numerical knowledge of functions or function parameters.
The tertiary peak placement is for special cases that cannot be graphically placed and adjusted, such as user-defined models. Here placement is by numerically adjusting the parameter values. A right click on the primary peak anchor opens the peak popup dialog. In addition to offering every model available in PeakLab, this dialog offers the means to adjust the numerical parameters of the model, and also to lock a given parameter (its value will not change during fitting), or to share a given parameter (its value is shared with all others at this parameter position also marked as shared). PeakLab also offers a common parameters dialog which allows a given parameter to be simultaneously set for all peaks, and when possible, for all data sets.
Recommendations
If each peak in the data is readily identified as having a local maximum in the data stream (there are no hidden peaks), you should use the Fit Local Maxima Peaks option. The algorithm adjusts the widths of peaks so that the overall area of the placed peaks is equal to that of the raw data.
When hidden peaks are present, it is difficult to say whether the Fit Hidden Peaks - Residuals option or the Fit Hidden Peaks - Second Derivative algorithm will be most successful in automatically identifying them. Each of these algorithms have their own strengths and weaknesses.
The AutoFit Peaks I Residuals option is the only procedure that is unaffected by data lacking uniformly spaced X-values, provided the Loess procedure is used for smoothing. It is also quite forgiving in terms of smoothing levels. When hidden peaks are present, this tends to produce negative residuals where peaks have been found, and positive residuals where hidden peaks exist. Residuals peaks that exceed a simple user-adjustable amplitude threshold are automatically added when the Add Residuals is checked.
The AutoFit Peaks II Second Derivative option uses the Savitzky-Golay algorithm to produce a smooth second derivative. As such, a constant X spacing is required. If data lacks this uniform X-spacing, this option can still be used, provided the data is first processed with PeakLab's Interpolate/Upsample option. This procedure is more demanding of smoothing levels, since second derivative peaks (local minima) can be "washed out" by excessive smoothing, and since an ideally smoothed second derivative will require a greater smoothing power than the raw data. This algorithm locates peaks exclusively from local minima in the smoothed second derivative data.
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