I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
Answer
As far as I can see this is just going to be the uncertainty of the mean of your dataset. To determine this you must know the uncertainty in the individual data points.
For the simple case where you can consider the uncertainty in the data to be constant for all points then the the uncertainty of the mean is
$$ u_c=\frac{u}{\sqrt n}$$
for the case where the errors are different then
$$ u_c=\frac{\sqrt{\sum u_i^2}}{n} $$ the general formula for combining uncertainties is
$$ u_c^2 = \sum \left(\frac{\partial f}{\partial x_i}\right)^2 u_i^2 $$
However, I would also point out there are several flaws with your approach. Firstly, if the peak is asymmetric the centroid will not be aligned with the peak position. Similarly, the method treats all points with equal weighting when determining peak position. Therefore, the result can be effected by noise far from the peak which likely has no relevance to the actual uncertainty of the peak position.
See this http://terpconnect.umd.edu/~toh/spectrum/PeakFindingandMeasurement.htm for a better approach to peak finding.
No comments:
Post a Comment