function [qrs_pos,sign,en_thres] = qrs_detect(ecg,varargin)
% QRS detector based on the P&T method. This is an offline implementation
% of the detector.
%
% inputs
% ecg: one ecg channel on which to run the detector (required)
% varargin
% THRES: energy threshold of the detector (default: 0.6)
% REF_PERIOD: refractory period in sec between two R-peaks (default: 0.250)
% fs: sampling frequency (default: 1KHz)
% fid_vec: if some subsegments should not be used for finding the
% optimal threshold of the P&Tthen input the indices of
% the corresponding points here
% SIGN_FORCE: force sign of peaks (positive value/negative value).
% Particularly usefull if we do window by window detection and want to
% unsure the sign of the peaks to be the same accross
% windows (which is necessary to build an FECG template)
% debug: 1: plot to bebug, 0: do not plot
%
% outputs
% qrs_pos: indexes of detected peak (in samples)
% sign: sign of the peaks (a pos or neg number)
% en_thres: energy threshold used
%
%
%
% FECG extraction toolbox, version 1.0, Sept 2013
% Released under the GNU General Public License
%
% Copyright (C) 2013 Joachim Behar
% Oxford university, Intelligent Patient Monitoring Group - Oxford 2013
% joachim.behar@eng.ox.ac.uk
%
% Last updated : 02-08-2013
%
% This program is free software; you can redistribute it and/or modify it
% under the terms of the GNU General Public License as published by the
% Free Software Foundation; either version 2 of the License, or (at your
% option) any later version.
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
% Public License for more details.
% == managing inputs
REF_PERIOD = 0.250;
THRES = 0.6;
fs = 1000;
fid_vec = [];
SIGN_FORCE = [];
debug = 0;
switch nargin
case 2
REF_PERIOD=varargin{1};
case 3
REF_PERIOD=varargin{1};
THRES=varargin{2};
case 4
REF_PERIOD=varargin{1};
THRES=varargin{2};
fs=varargin{3};
case 5
REF_PERIOD=varargin{1};
THRES=varargin{2};
fs=varargin{3};
fid_vec=varargin{4};
case 6
REF_PERIOD=varargin{1};
THRES=varargin{2};
fs=varargin{3};
fid_vec=varargin{4};
SIGN_FORCE=varargin{5};
case 7
REF_PERIOD=varargin{1};
THRES=varargin{2};
fs=varargin{3};
fid_vec=varargin{4};
SIGN_FORCE=varargin{5};
debug=varargin{6};
otherwise
error('qrs_detect: wrong number of input arguments \n');
end
[a b] = size(ecg);
if(a>b); NB_SAMP=a; elseif(b>a); NB_SAMP=b; ecg=ecg'; end;
tm = 1/fs:1/fs:ceil(NB_SAMP/fs);
% == constants
MED_SMOOTH_NB_COEFF = fs/100;
INT_NB_COEFF = round(7*fs/256); % length is 7 for fs=256Hz
LOW_CUT_FREQ = 5;
HIGH_CUT_FREQ = 45;
SEARCH_BACK = 1; % perform search back (FIXME: should be in function param)
MAX_FORCE = []; % if you want to force the energy threshold value (FIXME: should be in function param)
try
% == prefiltering
[b_lp,a_lp] = butter(5,HIGH_CUT_FREQ/(fs/2),'high');
[b_bas,a_bas] = butter(2,LOW_CUT_FREQ/(fs/2),'high'); % FIXME: use more coefficients?
ecg = ecg-mean(ecg); % (1) centre
bpfecg = ecg'-filtfilt(b_lp,a_lp,ecg'); % (2) remove higher freq (zero phase)
bpfecg = filtfilt(b_bas,a_bas,bpfecg); % (3) remove baseline (zero phase)
% == P&T operations
dffecg = diff(bpfecg'); % (4) differentiate (one datum shorter)
sqrecg = dffecg.*dffecg; % (5) square ecg
intecg = filter(ones(1,INT_NB_COEFF),1,sqrecg); % (6) integrate
mdfint = medfilt1(intecg,MED_SMOOTH_NB_COEFF); % (7) smooth
delay = ceil(INT_NB_COEFF/2);
mdfint = circshift(mdfint,-delay); % remove filter delay for scanning back through ECG
% look for some measure of signal quality with signal fid_vec? (FIXME)
if isempty(fid_vec); mdfintFidel = mdfint; else mdfintFidel(fid_vec>2) = 0; end;
% == P&T threshold
if NB_SAMP/fs>90; xs=sort(mdfintFidel(fs:fs*90)); else xs = sort(mdfintFidel(fs:end)); end;
if isempty(MAX_FORCE)
if NB_SAMP/fs>10
ind_xs = ceil(98/100*length(xs));
en_thres = xs(ind_xs); % if more than ten seconds of ecg then 98% CI
else
ind_xs = ceil(99/100*length(xs));
en_thres = xs(ind_xs); % else 99% CI
end
else
en_thres = MAX_FORCE;
end
% build an array of segments to look into
poss_reg = mdfint>(THRES*en_thres);
% in case empty because force threshold and crap in the signal
if isempty(poss_reg); poss_reg(10) = 1; end;
% == P&T QRS detection & search back
if SEARCH_BACK
indAboveThreshold = find(poss_reg); % ind of samples above threshold
RRv = diff(tm(indAboveThreshold)); % compute RRv
medRRv = median(RRv(RRv>0.01));
indMissedBeat = find(RRv>1.5*medRRv); % missed a peak?
% find interval onto which a beat might have been missed
indStart = indAboveThreshold(indMissedBeat);
indEnd = indAboveThreshold(indMissedBeat+1);
for i=1:length(indStart)
% look for a peak on this interval by lowering the energy threshold
poss_reg(indStart(i):indEnd(i)) = mdfint(indStart(i):indEnd(i))>(0.5*THRES*en_thres);
end
end
% find indices into boudaries of each segment
left = find(diff([0 poss_reg'])==1); % remember to zero pad at start
right = find(diff([poss_reg' 0])==-1); % remember to zero pad at end
% looking for max/min?
if SIGN_FORCE
sign = SIGN_FORCE;
else
nb_s = length(left<30*fs);
loc = zeros(1,nb_s);
for j=1:nb_s
[~,loc(j)] = max(abs(bpfecg(left(j):right(j))));
loc(j) = loc(j)-1+left(j);
end
sign = mean(ecg(loc)); % FIXME: change to median?
end
% loop through all possibilities
compt=1;
NB_PEAKS = length(left);
maxval = zeros(1,NB_PEAKS);
maxloc = zeros(1,NB_PEAKS);
for i=1:NB_PEAKS
if sign>0
% if sign is positive then look for positive peaks
[maxval(compt) maxloc(compt)] = max(ecg(left(i):right(i)));
else
% if sign is negative then look for negative peaks
[maxval(compt) maxloc(compt)] = min(ecg(left(i):right(i)));
end
maxloc(compt) = maxloc(compt)-1+left(i); % add offset of present location
% refractory period - has proved to improve results
if compt>1
if maxloc(compt)-maxloc(compt-1)<fs*REF_PERIOD && abs(maxval(compt))<abs(maxval(compt-1))
maxloc(compt)=[]; maxval(compt)=[];
elseif maxloc(compt)-maxloc(compt-1)<fs*REF_PERIOD && abs(maxval(compt))>abs(maxval(compt-1))
maxloc(compt-1)=[]; maxval(compt-1)=[];
else
compt=compt+1;
end
else
% if first peak then increment
compt=compt+1;
end
end
qrs_pos = maxloc; % datapoints QRS positions
R_t = tm(maxloc); % timestamps QRS positions
R_amp = maxval; % amplitude at QRS positions
hrv = 60./diff(R_t); % heart rate
catch ME
for enb=1:length(ME.stack); disp(ME.stack(enb)); end;
qrs_pos = [1 10 20]; sign = 1; en_thres = 0.5;
end
% == plots
if debug
figure(1);
ax(1) = subplot(4,1,1); plot(tm,ecg); hold on;plot(tm,bpfecg,'r')
title('raw ECG (blue) and zero-pahse FIR filtered ECG (red)'); ylabel('ECG');
xlim([0 tm(end)]); hold off;
ax(2) = subplot(4,1,2); plot(tm(1:length(mdfint)),mdfint);hold on;
plot(tm,max(mdfint)*bpfecg/(2*max(bpfecg)),'r',tm(left),mdfint(left),'og',tm(right),mdfint(right),'om');
title('Integrated ecg with scan boundaries over scaled ECG');
ylabel('Int ECG'); xlim([0 tm(end)]); hold off;
ax(3) = subplot(4,1,3); plot(tm,bpfecg,'r');hold on;
plot(R_t,R_amp,'+k');
title('ECG with R-peaks (black) and S-points (green) over ECG')
ylabel('ECG+R+S'); xlim([0 tm(end)]); hold off;
ax(4) = subplot(4,1,4); hold off; plot(R_t(1:length(hrv)),hrv,'r+')
hold on, title('HR')
ylabel('RR (s)'); xlim([0 tm(end)]);
linkaxes(ax,'x');
set(findall(gcf,'type','text'),'fontSize',14,'fontWeight','bold');
end
% NOTES
% Finding the P&T energy threshold: in order to avoid crash due to local
% huge bumps, threshold is choosen at 98-99% of amplitude distribution.
% first sec removed for choosing the thres because of filter init lag.
%
% Search back: look for missed peaks by lowering the threshold in area where the
% RR interval variability (RRv) is higher than 1.5*medianRRv
%
% Sign of the QRS (signForce): look for the mean sign of the R-peak over the
% first 30sec when looking for max of abs value. Then look for the
% R-peaks over the whole record that have this given sign. This allows to
% not alternate between positive and negative detections which might
% happen in some occasion depending on the ECG morphology. It is also
% better than forcing to look for a max or min systematically.