function P=findpeaksSL(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype) % Segmented peak finder, same syntax as findpeaksL except the 3rd to 6th % input arguments can be vectors with one entry for each segment. % function P=findpeaksSL(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype) % Locates and measures the positive peaks in a noisy x-y time series data. % Detects peaks by looking for downward zero-crossings in the first % derivative whose upward slopes 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 of each segment. Higher values will neglect % smaller features. "Smoothwidth" is a vector of the widths of the smooths % applied before peak detection; larger values ignore narrow peaks. If % smoothwidth=0, no smoothing is performed. "Peakgroup" is a vector of the % number points around the top part of the peak that are taken for % measurement. If Peakgroup=0 the local maximum is taken 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, 2016. Version 1, November, 2016 % % Example: Find, measure, and plot 2 noisy peaks with very different widths % x=1:.2:100; % y=lorentzian(x,20,1.5)+lorentzian(x,80,30)+.02.*randn(size(x)); % plot(x,y,'c.') % P=findpeaksSL(x,y,[0.001 .0001],[.2 .2],[5 10],[10 50],3) % text(P(:,2),P(:,3),num2str(P(:,1))) % disp(' ') % disp(' peak # Position Height Width Area') % disp(P) % % Related functions: % findpeaksG.m, 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) 2016 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 if isscalar(AmpThreshold),AmpThreshold=AmpThreshold.*ones(size(SlopeThreshold));end if isscalar(smoothwidth),smoothwidth=smoothwidth.*ones(size(SlopeThreshold));end if isscalar(peakgroup),peakgroup=peakgroup.*ones(size(SlopeThreshold));end smoothwidth=round(smoothwidth); peakgroup=round(peakgroup); if smoothwidth>1, d=SegmentedSmooth(deriv(y),smoothwidth,smoothtype); else d=deriv(y); end P=[0 0 0 0 0]; vectorlength=length(y); NumSegs=length(SlopeThreshold); peak=1; for j=2*round(smoothwidth/2)-1:length(y)-smoothwidth-1, Seg=fix(1+NumSegs./(vectorlength./j)); n=round(peakgroup(Seg)/2+1); % [j Seg] if sign(d(j)) > sign (d(j+1)), % Detects zero-crossing if d(j)-d(j+1) > SlopeThreshold(Seg), % if slope of derivative is larger than SlopeThreshold if y(j) > AmpThreshold(Seg), % if height of peak is larger than AmpThreshold xx=zeros(size(peakgroup(Seg)));yy=zeros(size(peakgroup(Seg))); for k=1:peakgroup(Seg), % Create sub-group of points near peak groupindex=j+k-n+2; if groupindex<1, groupindex=1;end if groupindex>vectorlength, groupindex=vectorlength;end % groupindex=groupindex xx(k)=x(groupindex); yy(k)=y(groupindex); end if peakgroup(Seg)>2, z=rmnan(ones(size(xx))./yy); coef=polyfit(xx,z,2); PeakY=4*coef(1)./((4*coef(1)*coef(3))-coef(2)^2); PeakX=-coef(2)/(2*coef(1)); MeasuredWidth=sqrt(abs(((4*coef(1)*coef(3))-coef(2)^2)./coef(1))./sqrt(abs(coef(1)))); % if the peak is too narrow for least-squares technique to work % 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) || PeakYly,endindix=ly;end indexrange=startindex:endindix; SmoothedSignal(indexrange)=SmoothSegment(indexrange,Segment); end function SmoothY=fastsmooth(Y,w,type,ends) % fastsmooth(Y,w,type,ends) smooths vector Y with smooth % of width w. Version 3.0, October 2016. % The argument "type" determines the smooth type: % If type=1, rectangular (sliding-average or boxcar) % If type=2, triangular (2 passes of sliding-average) % If type=3, pseudo-Gaussian (3 passes of sliding-average) % If type=4, pseudo-Gaussian (4 passes of same sliding-average) % If type=5, multiple-width (4 passes of different sliding-average) % The argument "ends" controls how the "ends" of the signal % (the first w/2 points and the last w/2 points) are handled. % If ends=0, the ends are zero. (In this mode the elapsed % time is independent of the smooth width). The fastest. % If ends=1, the ends are smoothed with progressively % smaller smooths the closer to the end. (In this mode the % elapsed time increases with increasing smooth widths). % fastsmooth(Y,w,type) smooths with ends=0. % fastsmooth(Y,w) smooths with type=1 and ends=0. % Examples: % fastsmooth([1 1 1 10 10 10 1 1 1 1],3)= [0 1 4 7 10 7 4 1 1 0] % % fastsmooth([1 1 1 10 10 10 1 1 1 1],3,1,1)= [1 1 4 7 10 7 4 1 1 1] % % x=1:100; % y=randn(size(x)); % plot(x,y,x,fastsmooth(y,5,3,1),'r') % xlabel('Blue: white noise. Red: smoothed white noise.') % % Copyright (c) 2012, Thomas C. O'Haver % switch type case 1 SmoothY=sa(Y,w,ends); case 2 SmoothY=sa(sa(Y,w,ends),w,ends); case 3 SmoothY=sa(sa(sa(Y,w,ends),w,ends),w,ends); case 4 SmoothY=sa(sa(sa(sa(Y,w,ends),w,ends),w,ends),w,ends); case 5 SmoothY=sa(sa(sa(sa(Y,round(1.6*w),ends),round(1.4*w),ends),round(1.2*w),ends),w,ends); end function SmoothY=sa(Y,smoothwidth,ends) w=round(smoothwidth); SumPoints=sum(Y(1:w)); s=zeros(size(Y)); halfw=round(w/2); L=length(Y); for k=1:L-w, s(k+halfw-1)=SumPoints; SumPoints=SumPoints-Y(k); SumPoints=SumPoints+Y(k+w); end s(k+halfw)=sum(Y(L-w+1:L)); SmoothY=s./w; % Taper the ends of the signal if ends=1. if ends==1, startpoint=(smoothwidth + 1)/2; SmoothY(1)=(Y(1)+Y(2))./2; for k=2:startpoint, SmoothY(k)=mean(Y(1:(2*k-1))); SmoothY(L-k+1)=mean(Y(L-2*k+2:L)); end SmoothY(L)=(Y(L)+Y(L-1))./2; end % ---------------------------------------------------------------------- function a=rmnan(a) % Removes NaNs and Infs from vectors, replacing with nearest real numbers. % Example: % >> 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