[Scilab-users] Peaks and valleys [was: Forum dedicated to Scilab developments -> practical concern]

[Dang Ngoc Chan, Christophe]

Hello,

> De : paul.carrico at free.fr
> Envoyé : mercredi 5 octobre 2016 21:56
>
> In attachment is typically a project I'm working on :
> determination of peaks and valley on a noisy signal;
> Trying to  avoid reinventing the wheel,
> I had a look on information's and algorithms on internet ....
> not so easy topics I was thinking at the first time.

I used to work in the X-ray diffraction and fluorescence field,
where the detection of peaks is a main concern.
All this depends on the signal-to-noise ratio, but we used the following algorithms,
Applied one after the other:

— cutting the signal that is below the background noise:
in the X-ray field, the noise follows a Poisson statistics,
so if you know the background level (determined "manually"),
you can eliminate bands where the signal is below bkg + 3*sigma

— Savitzky-Golay algorithm for smoothing and determining the first and second derivative:
the peak summit is a local minimum of the 2nd derivative,
and the inflection points (i.e. its zeroes) can be used to estimate the peak width and also possibly its location
(chord middle)
https://commons.wikimedia.org/wiki/File:Savitzky-golay_pic_gaussien_bruite.svg

— eliminating the parasites:
in this field, the peaks have a minimum width,
so you can remove any detected peak if the first derivative is unexpectedly high.

We also used "de-summation",
i.e. from a set of peak position
(determined automatically or manually),
we generate a curve as a sum of "perfect peaks"
(Gaussian, Lorentzian, pseudo-Voigt, Pearson-VII etc.)
and we adjust the peaks parameters (position, width, shape)
to minimise the quadratic difference with the signal
(i.e. non-linear regression).

I don't know if this is useful in your field,
but the Savitzky-Golay algorithm is something widely used
and easy to implement (especially if the points are uniformly spaced in x)
and if the peak position and width have a physical meaning,
de-summation can be powerful.

--
Christophe Dang Ngoc Chan
Mechanical calculation engineer
This e-mail may contain confidential and/or privileged information. If you are not the intended recipient (or have received this e-mail in error), please notify the sender immediately and destroy this e-mail. Any unauthorized copying, disclosure or distribution of the material in this e-mail is strictly forbidden.