findpeaks

FINDPEAKS finds peaks with optional quadratic interpolation [K,V]=(X,M,W)

  Inputs:  X        is the input signal (does not work with UInt datatype)
           M        is mode:
                       'q' performs quadratic interpolation
                       'v' finds valleys instead of peaks
           W        is the width tolerance; a peak will be eliminated if there is
                    a higher peak within +-W samples

 Outputs:  K        are the peak locations in X (fractional if M='q')
           V        are the peak amplitudes: if M='q' the amplitudes will be interpolated
                    whereas if M~='q' then V=X(K).

0001 function [k,v]=findpeaks(x,m,w)
0002 %FINDPEAKS finds peaks with optional quadratic interpolation [K,V]=(X,M,W)
0003 %
0004 %  Inputs:  X        is the input signal (does not work with UInt datatype)
0005 %           M        is mode:
0006 %                       'q' performs quadratic interpolation
0007 %                       'v' finds valleys instead of peaks
0008 %           W        is the width tolerance; a peak will be eliminated if there is
0009 %                    a higher peak within +-W samples
0010 %
0011 % Outputs:  K        are the peak locations in X (fractional if M='q')
0012 %           V        are the peak amplitudes: if M='q' the amplitudes will be interpolated
0013 %                    whereas if M~='q' then V=X(K).
0014 
0015 % Outputs are column vectors regardless of whether X is row or column.
0016 % If there is a plateau rather than a sharp peak, the routine will place the
0017 % peak in the centre of the plateau. When the W input argument is specified,
0018 % the routine will eliminate the lower of any pair of peaks whose separation
0019 % is <=W; if the peaks have exactly the same height, the second one will be eliminated.
0020 % All peak locations satisfy 1<K<length(X).
0021 %
0022 % If no output arguments are specified, the results will be plotted.
0023 %
0024 
0025 %       Copyright (C) Mike Brookes 2005
0026 %      Version: $Id: findpeaks.m 713 2011-10-16 14:45:43Z dmb $
0027 %
0028 %   VOICEBOX is a MATLAB toolbox for speech processing.
0029 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
0030 %
0031 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0032 %   This program is free software; you can redistribute it and/or modify
0033 %   it under the terms of the GNU General Public License as published by
0034 %   the Free Software Foundation; either version 2 of the License, or
0035 %   (at your option) any later version.
0036 %
0037 %   This program is distributed in the hope that it will be useful,
0038 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0039 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0040 %   GNU General Public License for more details.
0041 %
0042 %   You can obtain a copy of the GNU General Public License from
0043 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0044 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0045 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0046 
0047 if nargin<2
0048     m=' ';
0049 end
0050 nx=length(x);
0051 if any(m=='v')
0052     x=-x(:);        % invert x if searching for valleys
0053 else
0054     x=x(:);        % force to be a column vector
0055 end
0056 dx=x(2:end)-x(1:end-1);
0057 r=find(dx>0);
0058 f=find(dx<0);
0059 
0060 if length(r)>0 & length(f)>0    % we must have at least one rise and one fall
0061     dr=r;
0062     dr(2:end)=r(2:end)-r(1:end-1);
0063     rc=repmat(1,nx,1);
0064     rc(r+1)=1-dr;
0065     rc(1)=0;
0066     rs=cumsum(rc); % = time since the last rise
0067     
0068     df=f;
0069     df(2:end)=f(2:end)-f(1:end-1);
0070     fc=repmat(1,nx,1);
0071     fc(f+1)=1-df;
0072     fc(1)=0;
0073     fs=cumsum(fc); % = time since the last fall
0074     
0075     rp=repmat(-1,nx,1);
0076     rp([1; r+1])=[dr-1; nx-r(end)-1];
0077     rq=cumsum(rp);  % = time to the next rise
0078     
0079     fp=repmat(-1,nx,1);
0080     fp([1; f+1])=[df-1; nx-f(end)-1];
0081     fq=cumsum(fp); % = time to the next fall
0082     
0083     k=find((rs<fs) & (fq<rq) & (floor((fq-rs)/2)==0));   % the final term centres peaks within a plateau
0084     v=x(k);
0085     
0086     if any(m=='q')         % do quadratic interpolation
0087         b=0.5*(x(k+1)-x(k-1));
0088         a=x(k)-b-x(k-1);
0089         j=(a>0);            % j=0 on a plateau
0090         v(j)=x(k(j))+0.25*b(j).^2./a(j);
0091         k(j)=k(j)+0.5*b(j)./a(j);
0092         k(~j)=k(~j)+(fq(k(~j))-rs(k(~j)))/2;    % add 0.5 to k if plateau has an even width
0093     end
0094     
0095     % now purge nearby peaks
0096     
0097     if nargin>2
0098         j=find(k(2:end)-k(1:end-1)<=w);
0099         while any(j)
0100             j=j+(v(j)>=v(j+1));
0101             k(j)=[];
0102             v(j)=[];
0103             j=find(k(2:end)-k(1:end-1)<=w);
0104         end
0105     end
0106 else
0107     k=[];
0108     v=[];
0109 end
0110 if any(m=='v')
0111     v=-v;    % invert peaks if searching for valleys
0112 end
0113 if ~nargout
0114     if any(m=='v')
0115         x=-x;    % re-invert x if searching for valleys
0116         ch='v';
0117     else
0118         ch='^';
0119     end
0120     plot(1:nx,x,'-',k,v,ch);
0121 end