function P=findpeaksE(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype) % function % P=findpeaksE(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smootht % ype) Function to locate the positive peaks in a noisy x-y time series % data set. Detects peaks by looking for downward zero-crossings in the % first derivative that exceed SlopeThreshold. Returns matrix (P) containing % peak number and position, height, width, area, and percent fitting error % of each peak. Arguments "slopeThreshold", "ampThreshold" and % "smoothwidth" control peak sensitivity. Higher values will neglect % smaller features. "Smoothwidth" is the width of the smooth applied before % peak detection; larger values ignore narrow peaks. "Peakgroup" is the % number points around the top part of the peak that are taken for % measurement. The argument "smoothtype" determines the smooth algorithm: % If smoothtype=1, rectangular (sliding-average or boxcar) If % smoothtype=2, triangular (2 passes of sliding-average) If smoothtype=3, % pseudo-Gaussian (3 passes of sliding-average) % See http://terpconnect.umd.edu/~toh/spectrum/Smoothing.html and % http://terpconnect.umd.edu/~toh/spectrum/PeakFindingandMeasurement.htm T. % C. O'Haver, 1995. Version 5.3, Last revised December, 2014 % Example 1: x=[0:.01:50];y=cos(x);P=findpeaksE(x,y,0,-1,5,5) % Example 2: x=[0:.01:2];y=humps(x);P=findpeaksE(x,y,0,-.01,5,5) % Example 3: % x=[0:.01:5];y=x.*sin(x.^2).^2+.1*whitenoise(x); % P=findpeaksE(x,y,.0001,1,15,10) if nargin~=7;smoothtype=1;end % smoothtype=1 if not specified in argument if smoothtype>3;smoothtype=3;end if smoothtype<1;smoothtype=1;end smoothwidth=round(smoothwidth); peakgroup=round(peakgroup); d=fastsmooth(deriv(y),smoothwidth,smoothtype); n=round(peakgroup/2+1); P=[0 0 0 0 0 0]; vectorlength=length(y); peak=1; AmpTest=AmpThreshold; for j=smoothwidth:length(y)-smoothwidth, if sign(d(j)) > sign (d(j+1)), % Detects zero-crossing if d(j)-d(j+1) > SlopeThreshold, % if slope of derivative is larger than SlopeThreshold if y(j) > AmpTest, % if height of peak is larger than AmpThreshold xx=zeros(size(peakgroup));yy=zeros(size(peakgroup)); for k=1:peakgroup, % Create sub-group of points near peak groupindex=j+k-n+1; if groupindex<1, groupindex=1;end if groupindex>vectorlength, groupindex=vectorlength;end xx(k)=rmnan(x(groupindex));yy(k)=rmnan(y(groupindex)); end [Height, Position, Width]=gaussfit(xx,yy); PeakX=real(Position); % Compute peak position and height of fitted parabola PeakY=real(Height); MeasuredWidth=real(Width); residual=yy-PeakY*gaussian(xx,PeakX,MeasuredWidth); Error=100.*abs(stdev(residual)./PeakY); % if the peak is too narrow for least-squares technique to work % well, just use the max value of y in the sub-group of points near peak. if peakgroup<3, PeakY=max(yy); pindex=val2ind(yy,PeakY); PeakX=xx(pindex(1)); end % Construct matrix P. One row for each peak % detected, containing the peak number, peak % position (x-value) and peak height (y-value). if isnan(PeakX) || isnan(PeakY) || PeakY> v=[1 2 3 4 Inf 6 7 Inf 9]; % >> rmnan(v) % ans = % 1 2 3 4 4 6 7 7 9 la=length(a); if isnan(a(1)) || isinf(a(1)),a(1)=0;end for point=1:la, if isnan(a(point)) || isinf(a(point)), a(point)=a(point-1); end end % ---------------------------------------------------------------------- function y=smoothnegs(y) % Replaces zeros and negative points with 2 passes of 3-point average ly=length(y); if min(y)<=0, if y(1)<=0,y(1)=y(1)+y(2)+y(3)./3;end for pnt=2:ly-1, if y(pnt)<=0,y(pnt)=y(pnt-1)+y(pnt)+y(pnt+1)./3;end end if y(ly)<=0,y(ly)=y(ly-2)+y(ly-1)+y(ly)./3;end end if min(y)<=0, if y(1)<=0,y(1)=y(1)+y(2)+y(3)./3;end for pnt=2:ly-1, if y(pnt)<=0,y(pnt)=y(pnt-1)+y(pnt)+y(pnt+1)./3;end end if y(ly)<=0,y(ly)=y(ly-2)+y(ly-1)+y(ly)./3;end end % ---------------------------------------------------------------------- function [Height, Position, Width]=gaussfit(x,y) % Converts y-axis to a log scale, fits a parabola % (quadratic) to the (x,ln(y)) data, then calculates % the position, width, and height of the % Gaussian from the three coefficients of the % quadratic fit. This is accurate only if the data have % no baseline offset (that is, trends to zero far off the % peak) and if there are no zeros or negative values in y. % % Example 1: Simplest Gaussian data set % [Height, Position, Width]=gaussfit([1 2 3],[1 2 1]) % returns Height = 2, Position = 2, Width = 2 % % Example 2: best fit to synthetic noisy Gaussian % x=50:150;y=100.*gaussian(x,100,100)+10.*randn(size(x)); % [Height,Position,Width]=gaussfit(x,y) % returns [Height,Position,Width] clustered around 100,100,100. % % Example 3: plots data set as points and best-fit Gaussian as line % x=[1 2 3 4 5];y=[1 2 2.5 2 1]; % [Height,Position,Width]=gaussfit(x,y); % plot(x,y,'o',linspace(0,8),Height.*gaussian(linspace(0,8),Position,Width)) % Copyright (c) 2012, Thomas C. O'Haver maxy=max(y); for p=1:length(y), if y(p)<(maxy/100),y(p)=maxy/100;end end % for p=1:length(y), z=log(y); coef=polyfit(x,z,2); a=coef(3); b=coef(2); c=coef(1); Height=exp(a-c*(b/(2*c))^2); Position=-b/(2*c); Width=2.35482/(sqrt(2)*sqrt(-c)); function stddev=stdev(a) % Octave and Matlab compatible standard deviation function sa=size(a); reshape(a,1,length(a)); if sa(1)>sa(2), stddev=std(a); else stddev=(std(a')); end;