function P=findpeaksTplot(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype) % A variant of findpeaksT that measures the peak parameters by constructing % a triangle around each peak with sides tangent to the sides of the peak, % the plot the peaks. % Example: % x=[-10:.2:10]; % y=sin(x).^2; % P=findpeaksTplot(x,y,0.003,0.5,7,9,3); P=findpeaksG(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype); sP=size(P); NumPeaks=sP(1); for peak=1:NumPeaks, center=P(peak,2); wid=P(peak,4); n0=val2ind(x,center); x1=center-wid/1.44; x2=center-wid/5.57; range1=val2ind(x,x1):val2ind(x,x2); coeff1=polyfit(x(range1),y(range1),1); x4=center+wid/1.44; x3=center+wid/5.57; range2=val2ind(x,x3):val2ind(x,x4); coeff2=polyfit(x(range2),y(range2),1); x0=(coeff2(2)-coeff1(2))/(coeff1(1)-coeff2(1)); y0=coeff1(2)+x0*coeff1(1); base1=-coeff1(2)/coeff1(1); base2=-coeff2(2)/coeff2(1); basewidth=base2-base1; b=sqrt((center-base1)^2+y0^2); a=sqrt((base2-center)^2+y0^2); c=basewidth; area(peak)=sqrt((a+b-c)*(a-b+c)*(-a+b+c)*(a+b+c))/4; drange1=val2ind(x,base1):val2ind(x,center); drange2=val2ind(x,center):val2ind(x,base2); P(peak,2)=x0; P(peak,3)=y0; P(peak,4)=basewidth/2; P(peak,5)=area(peak); plot(x,y,'.') hold on plot(x(drange1),polyval(coeff1,x(drange1)),'r') plot(x(drange2),polyval(coeff2,x(drange2)),'r') end hold off % ---------------------------------------------------------------------- function P=findpeaksG(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype) % function P=findpeaksG(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype) % 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 list (P) containing peak number and position, % height, width, and area 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. If smoothwidth=0, no smoothing % is performed. "Peakgroup" is the number points around the top % part of the peak that are taken for measurement. If Peakgroup=0 % the local maximum is takes as the peak height and position. % 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 % (c) T.C. O'Haver, 1995, 2014. Version 6, Last revised March, 2016 % Simplified code: Replaced line 91 with call to gaussfit.m function % % Examples: % findpeaksG(0:.01:2,humps(0:.01:2),0,-1,5,5) % x=[0:.01:50];findpeaks(x,cos(x),0,-1,5,5) % x=[0:.01:5]';findpeaks(x,x.*sin(x.^2).^2,0,-1,5,5) % x=[-10:.1:10];y=exp(-(x).^2);findpeaks(x,y,0.005,0.3,3,5,3); % Find, measure, and plot noisy peak with unknown position % x=[-10:.2:10]; % y=exp(-(x+5*randn()).^2)+.1.*randn(size(x)); % P=findpeaksG(x,y,0.003,0.5,7,9,3); % xx=linspace(min(x),max(x)); % yy=P(3).*gaussian(xx,P(2),P(4)); % plot(x,y,'.',xx,yy) % % Related functions: % findvalleys.m, findpeaksL.m, findpeaksb.m, findpeaksb3.m, % findpeaksplot.m, peakstats.m, findpeaksnr.m, findpeaksGSS.m, % findpeaksLSS.m, findpeaksfit.m, findsteps.m, findsquarepulse.m, idpeaks.m % Copyright (c) 2013, 2014 Thomas C. O'Haver % % Permission is hereby granted, free of charge, to any person obtaining a copy % of this software and associated documentation files (the "Software"), to deal % in the Software without restriction, including without limitation the rights % to use, copy, modify, merge, publish, distribute, sublicense, and/or sell % copies of the Software, and to permit persons to whom the Software is % furnished to do so, subject to the following conditions: % % The above copyright notice and this permission notice shall be included in % all copies or substantial portions of the Software. % % THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR % IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, % FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE % AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER % LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, % OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN % THE SOFTWARE. % 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 if smoothwidth<1;smoothwidth=1;end smoothwidth=round(smoothwidth); peakgroup=round(peakgroup); if smoothwidth>1, d=fastsmooth(deriv(y),smoothwidth,smoothtype); else d=deriv(y); end n=round(peakgroup/2+1); P=[0 0 0 0 0]; vectorlength=length(y); peak=1; AmpTest=AmpThreshold; for j=2*round(smoothwidth/2)-1:length(y)-smoothwidth-1, 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 or(y(j) > AmpTest, y(j+1) > AmpTest), % if height of peak is larger than AmpThreshold (new version by Anthony Willey) % if y(j) > AmpTest, % if height of peak is larger than AmpThreshold (old version) xx=zeros(size(peakgroup));yy=zeros(size(peakgroup)); for k=1:peakgroup, % Create sub-group of points near peak groupindex=j+k-n+2; if groupindex<1, groupindex=1;end if groupindex>vectorlength, groupindex=vectorlength;end xx(k)=x(groupindex);yy(k)=y(groupindex); end if peakgroup>2, [Height, Position, Width]=gaussfit(xx,yy); PeakX=real(Position); % Compute peak position and height of fitted parabola PeakY=real(Height); MeasuredWidth=real(Width); % 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. else PeakY=max(yy); pindex=val2ind(yy,PeakY); PeakX=xx(pindex(1)); MeasuredWidth=0; end % Construct matrix P. One row for each peak detected, % containing the peak number, peak position (x-value) and % peak height (y-value). If peak measurement fails and % results in NaN, or if the measured peak height is less % than AmpThreshold, skip this peak if isnan(PeakX) || isnan(PeakY) || PeakY