Finding the full width half maximum of a peak

I have been trying to figure out the full width half maximum (FWHM) of the the blue peak (see image). The green peak and the magenta peak combined make up the blue peak. I have been using the following equation to find the FWHM of the green and magenta peaks: fwhm = 2*np.sqrt(2*(math.log(2)))*sd where sd = standard deviation. I created the green and magenta peaks and I know the standard deviation which is why I can use that equation.

I created the green and magenta peaks using the following code:

def make_norm_dist(self, x, mean, sd):
    import numpy as np

    norm = []
    for i in range(x.size):
        norm += [1.0/(sd*np.sqrt(2*np.pi))*np.exp(-(x[i] - mean)**2/(2*sd**2))]
    return np.array(norm)

If I did not know the blue peak was made up of two peaks and I only had the blue peak in my data, how would I find the FWHM?

I have been using this code to find the peak top:

peak_top = 0.0e-1000
for i in x_axis:
    if i > peak_top:
        peak_top = i

I could divide the peak_top by 2 to find the half height and then try and find y-values corresponding to the half height, but then I would run into trouble if there are no x-values exactly matching the half height.

I am pretty sure there is a more elegant solution to the one I am trying.

python matplotlib

Edit Report

Here is a nice little function using the spline approach.

from scipy.interpolate import splrep, sproot, splev

class MultiplePeaks(Exception): pass
class NoPeaksFound(Exception): pass

def fwhm(x, y, k=10):
    """
    Determine full-with-half-maximum of a peaked set of points, x and y.

    Assumes that there is only one peak present in the datasset.  The function
    uses a spline interpolation of order k.
    """

    half_max = amax(y)/2.0
    s = splrep(x, y - half_max, k=k)
    roots = sproot(s)

    if len(roots) > 2:
        raise MultiplePeaks("The dataset appears to have multiple peaks, and "
                "thus the FWHM can't be determined.")
    elif len(roots) < 2:
        raise NoPeaksFound("No proper peaks were found in the data set; likely "
                "the dataset is flat (e.g. all zeros).")
    else:
        return abs(roots[1] - roots[0])

answered 2013-01-14T22:16:38.607

Finding the full width half maximum of a peak

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