## How to take the fourth derivative of a reflectance graph

Asked by Erin Browne

### Erin Browne (view profile)

on 21 Mar 2019
Latest activity Commented on by Torsten

### Torsten (view profile)

on 27 Mar 2019
Accepted Answer by Torsten

### Torsten (view profile)

Hi I am looking to calculate and plot the fourth derivtative of a reflectance plot for coral spectra - commonly done in papers by the savistky and golay, 1964 method.
I have used the smoothing function on my coral mean spectra (x3) (1st image)
S2 = smooth(S1);
plot(wv1, S2);
xlim([400 750])
Then went to take my 1st derivative (2nd image)
This turned out ok using this coding:
dy = diff(S2)/diff(wv1);
plot(wv1(2:end),dy)
xlim([400 750])
But I believe this is the wrong method for taking the derivative of the reflectance spectra as I loose data going fromm 1446x1 to 1445x1 each time i derive i.e.
taking the second derivative like so:
d2ydx2 = diff(dy)./diff(wv1);
plot(wv1(1:1444),d2ydx2)
xlim([400 750])
producing a graph like image 3 - which when it comes to the 4th i have lost nearly all the data (image 4)
Does anyone know where I am going wrong, as this must be much more straight forward given it has been used so frequently.
Thanks

### Torsten (view profile)

on 21 Mar 2019

If you have the signal processing toolbox licenced, use "sgolay" and "sgolayfilt".
https://de.mathworks.com/matlabcentral/fileexchange/30299-savitzky-golay-smooth-differentiation-filters-and-filter-application

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Torsten

### Torsten (view profile)

on 22 Mar 2019
These are the tools I was referring to. They do not only smooth the data, but also return approximations for derivatives, if requested.
Erin Browne

### Erin Browne (view profile)

on 26 Mar 2019
thanks for the help!
I've found that this method isn't working as my data is in 1nm and due to the fact it is going up and down so close together when taking any avergaing method it loses the quite obvious peaks, if you understand what im trying to say.
I believe binning into coarser resolutions may help?
Torsten

### Torsten (view profile)

on 27 Mar 2019
I think trying to determine the 4th derivative of such data is quite a challenge, not to say quite impossible in my opinion.