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### Highlights from 1D Non-derivative Peak Finder

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# 1D Non-derivative Peak Finder

### Tristan Ursell (view profile)

21 Feb 2011 (Updated )

Up-sample and filter noisy data to find peaks without using derivatives.

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Description

PEAKFIND general 1D peak finding algorithm
Tristan Ursell, 2013.

peakfind(x_data,y_data)
peakfind(x_data,y_data,upsam)
peakfind(x_data,y_data,upsam,gsize,gstd)
peakfind(x_data,y_data,upsam,htcut,'cuttype')
peakfind(x_data,y_data,upsam,gsize,gstd,htcut,'cuttype')

[xpeaks]=peakfind()
[xout,yout,peakspos]=peakfind()

This function finds peaks without taking first or second derivatives, rather it uses local slope features in a given data set. The function has four basic modes.

Mode 1: peakfind(x_data,y_data) simply finds all peaks in the data
given by 'xdata' and 'ydata'.

Mode 2: peakfind(x_data,y_data,upsam) finds peaks after up-sampling
the data by the integer factor 'upsam' -- this allows for higher
resolution peak finding. The interpolation uses a cubic spline that
does not introduce fictitious peaks.

Mode 3: peakfind(x_data,y_data,upsam,gsize,gstd) up-samples and then
convolves the data with a Gaussian point spread vector of length
gsize (>=3) and standard deviation gstd (>0).

Mode 4: peakfind(x_data,y_data,upsam,htcut,'cuttype') up-samples the
data (upsam=1 analyzes the data unmodified). The string 'cuttype' can
either be 'abs' (absolute) or 'rel' (relative), which specifies a peak
height cutoff which is either:

'abs' - finds peaks that lie an absolute amount 'htcut' above the
lowest value in the data set.

for (htcut > 0) peaks are found if

peakheights > min(yout) + htcut

'rel' - finds peaks that are an amount 'htcut' above the lowest
value in the data set, relative to the full change in y-input
values.

for (0 < htcut < 1) peaks are found if

(peakheights-min(yout))/(max(yout)-min(yout)) > htcut

Upsampling and convolution allows one to find significant peaks in noisy data with sub-pixel resolution. The algorithm also finds peaks in data where the peak is surrounded by zero first derivatives, i.e. the peak is actually a large plateau.

The function outputs the x-position of the peaks in 'xpeaks' or the processed input data in 'xout' and 'yout' with 'peakspos' as the indices of the peaks, i.e. xpeaks = xout(peakspos).

If you want the algorithm to find the position of minima, simply input '-y_data'. Peaks within half the convolution box size of the boundary will be ignored (to avoid this, pad the data before processing).

Example 1:

x_data = -50:50;
y_data =(sin(x_data)+0.000001)./(x_data+0.000001)+1+0.025*(2*rand(1,length(x_data))-1);

[xout,yout,peakspos]=peakfind(x_data,y_data);
plot(x_data,y_data,'r','linewidth',2)
hold on
plot(xout,yout,'b','linewidth',2)
plot(xout(peakspos),yout(peakspos),'g.','Markersize',30)
xlabel('x')
ylabel('y')
title(['Found ' num2str(length(peakspos)) ' peaks.'])
box on

Example 2:

x_data = -50:50;
y_data =(sin(x_data)+0.000001)./(x_data+0.000001)+1+0.025*(2*rand(1,length(x_data))-1);

[xout,yout,peakspos]=peakfind(x_data,y_data,4,6,2,0.2,'rel');

plot(x_data,y_data,'r','linewidth',2)
hold on
plot(xout,yout,'b','linewidth',2)
plot(xout(peakspos),yout(peakspos),'g.','Markersize',30)
xlabel('x')
ylabel('y')
title(['Found ' num2str(length(peakspos)) ' peaks.'])
box on

MATLAB release MATLAB 7.9 (R2009b)
06 Dec 2011 Tristan Ursell

### Tristan Ursell (view profile)

No longer uses fspecial. Bug pointed out by Andrew has been fixed.

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06 Dec 2011 Tristan Ursell

### Tristan Ursell (view profile)

Hsueh-Hsin -- I will look into that, agreed it would be preferable to not call it.

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16 Nov 2011 Hsueh-Hsin

### Hsueh-Hsin (view profile)

'fspecial' from Image Processing Toolbox: could it be removed/replaced

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15 Nov 2011 Tristan Ursell

### Tristan Ursell (view profile)

Andrew -- thank you -- I will fix that!

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08 Nov 2011 Andrew Davis

### Andrew Davis (view profile)

Thanks for posting this, it works well, and the code is nicely laid out. One small bug, in order for the fourth method of calling the function to work, line 264 should be:
if and(npeaks>1,exist('cuttype'))

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08 Nov 2011 Andrew Davis

### Andrew Davis (view profile)

07 Sep 2011 Kiran

### Kiran (view profile)

15 Nov 2011

This update fixes two small bugs in the code.

06 Dec 2011

Replaced the use of 'fspecial', which requires the image processing toolbox, with a simple calculation.

09 Jul 2013

fixed small bug, expanded functionality