Peak Search Algorithm

Our peak search program adopts a method that does not require any kind of prior processing such as smoothing and background subtraction.
The following are parameters of a peak:
x0 : peak position,
h : peak height,
FWHM : full width at half maximum.

The following 1--4 explain all the steps of the algorithm:
1. Computes the second derivative of the input x-y plot data, by using a cubic polynomial that approximates the x-y plot locally.
2. Obtain all the local minimum points of the second derivative with a negative y-value. Approximate the area between the x-axis and the graph of the second derivative (A in the following figure):

Figure 1 : Example of the second derivative of a 1-dimensional Guaussian-like peak.

3. Using the following formula, estimate the peak height h at every local minimum point x0 ("peak height" means the "y-value of the peaktop" minus "estimated background value"):

where x1 and x2 are the x-coordinates at which the second derivative equals zero (Figure 1).
4. If the above h is larger than the threshold determined from the input parameters, a peak with the height h exists at x0. Estimate the FWHM using the following formula:

Eq. 1 and Eq. 2 are the equations any 1-dimensional Gaussian function satisfies.

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