# How do I find the (x,y) coordinates of the peaks and valleys of a graph?

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Dave Phillips on 1 Nov 2015
I am new to Matlab and I am not sure how to find the coordinates of the peaks or valleys of my graph. After looking online, I tried using findpeaks() which did give me the y-values of the local maxima of my function ((e^(−at))*cos(2πft), where t is time and a and f are constants). However, I have not been able to find the corresponding x-values (and findpeaks() omits a local max at the y-intercept). I am also not at all sure how to find the coordinates for the valleys (minima or "troughs").

Image Analyst on 1 Nov 2015
The x values are the second return argument of findpeaks(). It's the index number. Your formula does not have an x by name so you have to go with the index number. If you have a second array for t, then to get the t values you'd do
[peakValues, indexes] = findpeaks(y);
tValues = t(indexes);
To get valleys, you invert the signal, so that now what used to be valleys are now peaks, and use findpeaks() again
invertedY = max(y) - y;
[peakValues, indexes] = findpeaks(invertedY);
tValues = t(indexes);
Markus Wahl on 24 Nov 2018
An alternative could be to take the absolute value of your vector to find only the indexes of both peaks and values.. Would need to go back and evaluate the original function to get the y-values, though.

### More Answers (1)

Sergio Yanez-Pagans on 28 Mar 2021
You can use my MATLAB file exchange function, it's really easy to implement and use:
Hope you find this useful!

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