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Peak finding and measurement

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Peak finding and measurement


Tom O'Haver (view profile)


20 Jul 2006 (Updated )

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

function ipeakdemo2
% 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 set of peaks. 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

% For each simulated peak, compute the amplitude, position, and width
amp=round(5.*randn(1,38));  % Amplitudes of the peaks  (Change if desired)
pos=[200:100:3900];   % Positions of the peaks (Change if desired)
wid=60.*ones(size(pos));   % Widths of the peaks (Change if desired)
Noise=0.05; % 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];
for k=1:length(pos)
  if amp(k)>.2,  % Keep only those peaks above a certain amplitude
      % Create a series of peaks of different x-positions
      A(k,:)=exp(-((x-pos(k))./(0.6005615.*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)]; 
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+5.*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
SmoothWidth=round(WidthPoints/2);  % SmoothWidth should be roughly equal to 1/2 the peak width (in points)
FitWidth=round(WidthPoints/2); % FitWidth should be roughly equal to 1/2 the peak widths(in points)

% Now call iPeak, with specified values of AmpT, SlopeT, SmoothW, and FitW.
% (You can change theses values if desired).

% Compare MeasuredPeaks to ActualPeaks
disp(['Signal to noise ratio of smallest peak = ' num2str(min(ActualPeaks(:,3))./Noise)])
disp('         Peak #    Position      Height       Width        Area')

for n=1:SizeResults(1),
    % MeasuredPeaks(n,1)=indexn;

disp('Demonstration of error caused by overlapping peaks on a large offset')
disp('baseline. Hint: Use the B key and click on the baseline points,')
disp('then press the P key to display the peak table. Or turn on the Autozero mode ')
disp('(T key) and use the Normal curve fit (N key) or Multiple curve fit (M key).') 
disp('Jump to the next/previous peaks using the Spacebar/Tab keys.')
disp('End of demo.')
% ----------------------------------------------------------------------
function g = gaussian(x,pos,wid)
%  gaussian(X,pos,wid) = gaussian peak centered on pos, half-width=wid
%  X may be scalar, vector, or matrix, pos and wid both scalar
% Examples: gaussian([0 1 2],1,2) gives result [0.5000    1.0000    0.5000]
% plot(gaussian([1:100],50,20)) displays gaussian band centered at 50 with width 20.
g = exp(-((x-pos)./(0.6005615.*wid)).^2);

function [index,closestval]=val2ind(x,val)
% Returns the index and the value of the element of vector x that is closest to val
% If more than one element is equally close, returns vectors of indicies and values
% Tom O'Haver ( October 2006
% Examples: If x=[1 2 4 3 5 9 6 4 5 3 1], then val2ind(x,6)=7 and val2ind(x,5.1)=[5 9]
% [indices values]=val2ind(x,3.3) returns indices = [4 10] and values = [3 3]

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