Best method to find maximum and minimum second derivatives of function

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Yuval Levental 2020-5-17

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评论： Yuval Levental 2020-5-20

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Hello,

I created this script to find the maximum and minimum second derivatives of a given array. I was wondering what possible improvements there could be. A sample image is attached for reference.

f = tracks_2(:,2);
windowWidth = 37;
polynomialOrder = 3;
f = sgolayfilt(f, polynomialOrder, windowWidth);
plot(f);
f1 = diff(f); %diff intstantly returns the derivative
plot(f1)
f1 = sgolayfilt(f1, polynomialOrder, 37);
f2 = diff(f1); %second derivative
plot(f2)
f2 = sgolayfilt(abs(f2), polynomialOrder, 15);
[pks,locs] = findpeaks(f2,'MinPeakProminence',0.05); %maximum peaks
plot(1:length(f),f,locs,f(locs),'*')

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John D'Errico 2020-5-17

编辑：John D'Errico 2020-5-17

IF you are going to smooth your data using a Savitsky-Golay filter, then you should arguably use a similar filter to give you the estimated first and second derivatives directly.

Note that I posted a function called movingslope on the file exchange. It does exactly that, at least for the first derivative.

Yuval Levental 2020-5-20