Code covered by the BSD License

# Peak finding and measurement

20 Jul 2006 (Updated 14 Nov 2013)

Function to locate and measure the positive peaks and valleys in noisy data sets.

ipeakdemo4.m
```% Demonstration script for iPeak function. It generates a test signal
% consisting of several peaks, adds random noise, runs ipeak, then prints out
% the actual and the measured peak positions, heights, widths and areas.
% Each time you run it you get a different sample of noise. You can easily
% evaluate the accuracy of the measurements because the actual peak
% parameter values in this simulation are always integers.
%   T. C. O'Haver, September 2011
increment=1;
x=[1:increment:500];

% For each simulated peak, compute the amplitude, position, and width
amp=[1 2 3 4];  % Amplitudes of the peaks  (Change if desired)
pos=[100 200 300 400];   % Positions of the peaks (Change if desired)
wid=[30 30 30 30];   % Widths of the peaks (Change if desired)
Noise=0.5; % Amount of random noise added to the signal. (Change if desired)

% A = matrix containing one of the unit-amplidude peak in each of its rows
A = zeros(length(pos),length(x));
ActualPeaks=[0 0 0 0 0];
p=1;
for k=1:length(pos)
% Create a series of peaks of different x-positio ns
A(k,:)=exp(-((x-pos(k))./(0.6005612.*wid(k))).^2); % Gaussian peaks
% A(k,:)=ones(size(x))./(1+((x-pos(k))./(0.5.*wid(k))).^2);  % Lorentzian peaks
% Assembles actual parameters into ActualPeaks matrix: each row = 1
% peak; columns are Peak #, Position, Height, Width, Area
ActualPeaks(p,:) = [p pos(k) amp(k) wid(k) 1.0646.*amp(k).*wid(k)];
p=p+1;
end
z=amp*A;  % Multiplies each row by the corresponding amplitude and adds them up
y=z+Noise.*randn(size(z));  % Optionally adds random noise
% y=y+gaussian(x,0,4000); % Optionally adds a broad background signal
demodata=[x' y']; % Assembles x and y vectors into data matrix

% Initial values of variable peak detection parameters
WidthPoints=mean(wid)/increment; % Average number of points in half-width of peaks
SlopeThreshold=0.7*WidthPoints^-2; % Formula for estimating value of SlopeThreshold
AmpThreshold=0.05*max(y);
SmoothWidth=31;  % Larger-than-usual values of SmoothWidth and FitWidth
FitWidth=40; % will help deal with the very poor signal-to-noise ratio.

% Now call iPeak, with specified values of AmpT, SlopeT, SmoothW, and FitW.
% (You can change theses values if desired).
MeasuredPeaks=ipeak(demodata,0,AmpThreshold,SlopeThreshold,SmoothWidth,FitWidth,ActualPeaks(1,2),200);

% Compare MeasuredPeaks to ActualPeaks
disp('-----------------------------------------------------------------')
disp('Detection and measurement of 4 peaks in a very noisy signal')
disp(['Signal-to-noise ratio of first peak = ' num2str(amp(1)/Noise) ] )
disp('         Peak #    Position      Height       Width        Area')
ActualPeaks
MeasuredPeaks

if size(ActualPeaks)==size(MeasuredPeaks),
PercentErrors=100.*(ActualPeaks-MeasuredPeaks)./ActualPeaks
AveragePercentErrors=mean(abs(100.*(ActualPeaks-MeasuredPeaks)./ActualPeaks))
end
disp('The peak at x=100 is usually detected, but the accuracy of peak ')
disp('parameter measurement is poor because of the low signal-to-noise ratio.')
disp('Jump to the next/previous peaks using the Spacebar/Tab keys.')
disp(' ')
disp('An even better way to measure this signal is to use the peakfit')
disp('function, now that we know the number of peaks and their approximate')
disp('positions and widths. Zoom out until all 4 peaks are shown, press')
disp('the N key and press enter the peak shape (1) and number ot trials. ')
disp('Compare to the the iPeak results obtained by pressing the P key. ')
disp(' ')
disp('End of script.')```

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