function?P=findpeaks（xySlopeThresholdAmpThresholdsmoothwidthpeakgroupsmoothtype）
%?function?P=findpeaks（xySlopeThresholdAmpThresholdsmoothwidthpeakgroupsmoothtype）
%?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
%?T.?C.?O‘Haver?1995.??Version?5.1?Last?revised?December?2012
%?Skip?peaks?if?peak?measurement?results?in?NaN?values
%?Examples:
%?findpeaks（0:.01:2humps（0:.01:2）0-155）
%?x=[0:.01:50];findpeaks（xcos（x）0-155）
%?x=[0:.01:5]‘;findpeaks（xx.*sin（x.^2）.^20-155）
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）;
if?smoothwidth>1
????d=fastsmooth（deriv（y）smoothwidthsmoothtype）;
else
????d=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
????if?sign（d（j））?>?sign?（d（j+1））?%?Detects?zero-crossing
????????if?d（j）-d（j+1）?>?SlopeThreshold*y（j）?%?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+2;
????????????????????if?groupindex<1?groupindex=1;end
????????????????????if?groupindex>vectorlength?groupindex=vectorlength;end
????????????????????xx（k）=x（groupindex）;yy（k）=y（groupindex）;
????????????????end
????????????????if?peakgroup>3
????????????????????[coefSMU]=polyfit（xxlog（abs（yy））2）;??%?Fit?parabola?to?log10?of?sub-group?with?centering?and?scaling
????????????????????c1=coef（3）;c2=coef（2）;c3=coef（1）;
????????????????????PeakX=-（（MU（2）.*c2/（2*c3））-MU（1））;???%?Compute?