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Peaks search.

A special case of the general task of the curve fitting is a peaks revealing . A fitting curve with peaks is a task that is often aroused for evaluation of  various types of spectrograms (mass, Raman or X-ray spectrometry) analysis.

To do peaks search in LeoStatistic:

Go to "Statistics" tab of control panel

and press "Peaks revealing" button. The panel for "Peaks revealing" scheme will appear:

Note that the task of the peaks search is in some way subjective as soon the same curve could be considered by one as having peaks and completely random noisy by other. As for software program the answer depend on specific values of criteria for recognizing a peak.

The fitting of the curve that is presumed to get peaks will be done with the following procedure:

At first a base line can be extracted from the fitting curve to eliminate an influence of systematic variance of instrumental signal or for analyzing peaks of a second order. To do this chose one of the options in "Correction of base line" control. The program will in best of its ability find such best line (linear, square, exponent) and corrects all curve considering the base line as a null signal.

The curve above base (null) line will be fitted by equation:

              (1)

where x_oi and σ_i - are position of maximum and standard deviation of the peak. A_i - is a volume (integral) of the peak.

As soon an algorithm of the peaks fitting in LeoStatistic is our state of art proprietary we will not described it here in full details. Interesting parties should contact us directly for request of acquaint of the codes and/or full description of the procedure. Here we will present very general description to provide a meaning of the search parameters setting by users in control panel.

• The approximate values of the noise as a maximum value of distribution in intensities of the signals are calculated.
• Standard deviation of the noise are calculated too taking into consideration only points around defined average noise value I_noise.
• In a loop until value I_max/I_noise finding for largest signal more then filter criteria set by user.
• If width at the half of maximum intensity of largest peak less then given by user N_spike - maximum width for noise like instrumental effect. Points of spike peak will be smoothed into curve and new largest peak will be looking for.
• In both criteria I_max/I_noise and N_spike for found peak give positive result - the top part of the curve are approximated by equation for  normal distribution  to find best  x_oi and σ_i position and standard deviation (width of the peak).
• A fitting curve is corrected by extracting part related to found peak.
• Next largest peak is evaluated until noise criteria gives negative result.
• Final approximation procedure finding average noise and all volumes for all peaks produces final result.

In additional a special case of the chromatogram additional criteria for recognizing a peak can be activated in LeoStatistic by checking up a control "chromatograms peaks". In this case a most intense peaks is used to calculate effective number of plates in the chromatographic column:

N_plates = 5.545*(x_o/σ)²             (2)

All other peaks will be considered as a valid chromatogram peaks if the number of plates calculated by formula (2) is in range for the value taken from largest and as is most reliable peak.

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