Code covered by the BSD License

# 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.

findpeaksGSS(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
```function P=findpeaksGSS(x,y,SlopeThreshold,AmpThreshold,smoothwidth,peakgroup,smoothtype)
% function
% P=findpeaks(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, area, and start and stop position of
% each peak, assuming a Gaussian peak shape. 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)
% Skip peaks if peak measurement results in NaN values
% See http://terpconnect.umd.edu/~toh/spectrum/Smoothing.html and
% http://terpconnect.umd.edu/~toh/spectrum/PeakFindingandMeasurement.htm
% T. C. O'Haver, Version 1.1, Last revised December, 2013
%
% Example: Three noisy Gaussian peaks at x=20,50,80;
% all heights=1.0; all widths=10.
% x=1:.2:100;
% y=gaussian(x,20,10)+gaussian(x,50,10)+gaussian(x,80,10)+.1.*randn(size(x));
% findpeaksGSS(x,y,0.0004,0.3,17,21,3)
% Peak    Position    Height    Width     Area      Start     End
%  1       20.496     1.0033    9.2482    9.8784    8.5766   32.414
%  2       50.32      1.0235    7.7165    8.4077   40.375    60.265
%  3       79.691     1.0191   10.716    11.626    65.881    93.501
% Same signal without noise:
%  1         20         1       10       10.646     7.1122   32.888
%  2         50         1       10       10.646     37.112   62.888
%  3         80         1       10       10.646     67.112   92.888
%
% Related functions:
% findvalleys.m, findpeaksL.m, findpeaksb.m, findpeaksplot.m, peakstats.m,
% findpeaksnr.m, findpeaks.m, findpeaksLSS.m, findpeaksfit.m.

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),smoothwidth,smoothtype);
else
d=y;
end
n=round(peakgroup/2+1);
P=[0 0 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+1;
if groupindex<1, groupindex=1;end
if groupindex>vectorlength, groupindex=vectorlength;end
xx(k)=x(groupindex);yy(k)=y(groupindex);
end
if peakgroup>3,
[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 measurements fails and results in NaN, skip this
% peak
if isnan(PeakX) || isnan(PeakY) || PeakY<AmpThreshold,
% Skip this peak
else % Otherwiase count this as a valid peak
P(peak,:) = [round(peak) PeakX PeakY MeasuredWidth  1.0646.*PeakY*MeasuredWidth PeakX-1.288784*MeasuredWidth PeakX+1.288784*MeasuredWidth];
peak=peak+1; % Move on to next peak
end
end
end
end
end
% ----------------------------------------------------------------------
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 (toh@umd.edu) 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]
dif=abs(x-val);
index=find((dif-min(dif))==0);
closestval=x(index);

function d=deriv(a)
% First derivative of vector using 2-point central difference.
%  T. C. O'Haver, 1988.
n=length(a);
d(1)=a(2)-a(1);
d(n)=a(n)-a(n-1);
for j = 2:n-1;
d(j)=(a(j+1)-a(j-1)) ./ 2;
end

function SmoothY=fastsmooth(Y,w,type,ends)
% fastbsmooth(Y,w,type,ends) smooths vector Y with smooth
%  of width w. Version 2.0, May 2008.
% 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)
% 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.
% Example:
% 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]
%  T. C. O'Haver, May, 2008.
if nargin==2, ends=0; type=1; end
if nargin==3, ends=0; end
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);
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

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));```