function [qrs_amp_raw,qrs_i_raw,delay]=pan_tompkin(ecg,fs,gr)

%% function [qrs_amp_raw,qrs_i_raw,delay]=pan_tompkin(ecg,fs)

% Complete implementation of Pan-Tompkins algorithm

%% Inputs

% ecg : raw ecg vector signal 1d signal

% fs : sampling frequency e.g. 200Hz, 400Hz and etc

% gr : flag to plot or not plot (set it 1 to have a plot or set it zero not

% to see any plots

%% Outputs

% qrs_amp_raw : amplitude of R waves amplitudes

% qrs_i_raw : index of R waves

% delay : number of samples which the signal is delayed due to the

% filtering

%% Method :

%% PreProcessing

% 1) Signal is preprocessed , if the sampling frequency is higher then it is downsampled

% and if it is lower upsampled to make the sampling frequency 200 Hz

% with the same filtering setups introduced in Pan

% tompkins paper (a combination of low pass and high pass filter 5-15 Hz)

% to get rid of the baseline wander and muscle noise. 

% 2) The filtered signal

% is derivated using a derivating filter to high light the QRS complex.

% 3) Signal is squared.4)Signal is averaged with a moving window to get rid

% of noise (0.150 seconds length).

% 5) depending on the sampling frequency of your signal the filtering

% options are changed to best match the characteristics of your ecg signal

% 6) Unlike the other implementations in this implementation the desicion

% rule of the Pan tompkins is implemented completely.

%% Decision Rule 

% At this point in the algorithm, the preceding stages have produced a roughly pulse-shaped

% waveform at the output of the MWI . The determination as to whether this pulse

% corresponds to a QRS complex (as opposed to a high-sloped T-wave or a noise artefact) is

% performed with an adaptive thresholding operation and other decision

% rules outlined below;

% a) FIDUCIAL MARK - The waveform is first processed to produce a set of weighted unit

% samples at the location of the MWI maxima. This is done in order to localize the QRS

% complex to a single instant of time. The w[k] weighting is the maxima value.

% b) THRESHOLDING - When analyzing the amplitude of the MWI output, the algorithm uses

% two threshold values (THR_SIG and THR_NOISE, appropriately initialized during a brief

% 2 second training phase) that continuously adapt to changing ECG signal quality. The

% first pass through y[n] uses these thresholds to classify the each non-zero sample

% (CURRENTPEAK) as either signal or noise:

% If CURRENTPEAK > THR_SIG, that location is identified as a QRS complex

% candidate?and the signal level (SIG_LEV) is updated:

% SIG _ LEV = 0.125 CURRENTPEAK + 0.875?SIG _ LEV

% If THR_NOISE < CURRENTPEAK < THR_SIG, then that location is identified as a

% Noise peak?and the noise level (NOISE_LEV) is updated:

% NOISE _ LEV = 0.125CURRENTPEAK + 0.875?NOISE _ LEV

% Based on new estimates of the signal and noise levels (SIG_LEV and NOISE_LEV,

% respectively) at that point in the ECG, the thresholds are adjusted as follows:

% THR _ SIG = NOISE _ LEV + 0.25 ?(SIG _ LEV-NOISE _ LEV )

% THR _ NOISE = 0.5?(THR _ SIG)

% These adjustments lower the threshold gradually in signal segments that are deemed to

% be of poorer quality.

% c) SEARCHBACK FOR MISSED QRS COMPLEXES - In the thresholding step above, if

% CURRENTPEAK < THR_SIG, the peak is deemed not to have resulted from a QRS

% complex. If however, an unreasonably long period has expired without an abovethreshold

% peak, the algorithm will assume a QRS has been missed and perform a

% searchback. This limits the number of false negatives. The minimum time used to trigger

% a searchback is 1.66 times the current R peak to R peak time period (called the RR

% interval). This value has a physiological origin - the time value between adjacent

% heartbeats cannot change more quickly than this. The missed QRS complex is assumed

% to occur at the location of the highest peak in the interval that lies between THR_SIG and

% THR_NOISE. In this algorithm, two average RR intervals are stored,the first RR interval is 

% calculated as an average of the last eight QRS locations in order to adapt to changing heart 

% rate and the second RR interval mean is the mean 

% of the most regular RR intervals . The threshold is lowered if the heart rate is not regular 

% to improve detection.

% d) ELIMINATION OF MULTIPLE DETECTIONS WITHIN REFRACTORY PERIOD - It is

% impossible for a legitimate QRS complex to occur if it lies within 200ms after a previously

% detected one. This constraint is a physiological one ?due to the refractory period during

% which ventricular depolarization cannot occur despite a stimulus[1]. As QRS complex

% candidates are generated, the algorithm eliminates such physically impossible events,

% thereby reducing false positives.

% e) T WAVE DISCRIMINATION - Finally, if a QRS candidate occurs after the 200ms

% refractory period but within 360ms of the previous QRS, the algorithm determines

% whether this is a genuine QRS complex of the next heartbeat or an abnormally prominent

% T wave. This decision is based on the mean slope of the waveform at that position. A slope of

% less than one half that of the previous QRS complex is consistent with the slower

% changing behaviour of a T wave ?otherwise, it becomes a QRS detection.

% Extra concept : beside the points mentioned in the paper, this code also

% checks if the occured peak which is less than 360 msec latency has also a

% latency less than 0,5*mean_RR if yes this is counted as noise

% f) In the final stage , the output of R waves detected in smoothed signal is analyzed and double

% checked with the help of the output of the bandpass signal to improve

% detection and find the original index of the real R waves on the raw ecg

% signal

%% References :

%[1]PAN.J, TOMPKINS. W.J,"A Real-Time QRS Detection Algorithm" IEEE

%TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-32, NO. 3, MARCH 1985.

%% Author : Hooman Sedghamiz

% Linkoping university 

% email : hoose792@student.liu.se

% hooman.sedghamiz@medel.com

% Any direct or indirect use of this code should be referenced 

% Copyright march 2014

%%

if ~isvector(ecg)

  error('ecg must be a row or column vector');

end

if nargin < 3

    gr = 1;   % on default the function always plots

end

ecg = ecg(:); % vectorize

%% Initialize

qrs_c =[]; %amplitude of R

qrs_i =[]; %index

SIG_LEV = 0; 

nois_c =[];

nois_i =[];

delay = 0;

skip = 0; % becomes one when a T wave is detected

not_nois = 0; % it is not noise when not_nois = 1

selected_RR =[]; % Selected RR intervals

m_selected_RR = 0;

mean_RR = 0;

qrs_i_raw =[];

qrs_amp_raw=[];

ser_back = 0; 

test_m = 0;

SIGL_buf = [];

NOISL_buf = [];

THRS_buf = [];

SIGL_buf1 = [];

NOISL_buf1 = [];

THRS_buf1 = [];

%% Plot differently based on filtering settings

if gr

 if fs == 200

  figure,  ax(1)=subplot(321);plot(ecg);axis tight;title('Raw ECG Signal');

 else

  figure,  ax(1)=subplot(3,2,[1 2]);plot(ecg);axis tight;title('Raw ECG Signal');

 end

end    

%% Noise cancelation(Filtering) % Filters (Filter in between 5-15 Hz)

if fs == 200

%% Low Pass Filter  H(z) = ((1 - z^(-6))^2)/(1 - z^(-1))^2

b = [1 0 0 0 0 0 -2 0 0 0 0 0 1];

a = [1 -2 1];

h_l = filter(b,a,[1 zeros(1,12)]); 

ecg_l = conv (ecg ,h_l);

ecg_l = ecg_l/ max( abs(ecg_l));

delay = 6; %based on the paper

if gr

ax(2)=subplot(322);plot(ecg_l);axis tight;title('Low pass filtered');

end

%% High Pass filter H(z) = (-1+32z^(-16)+z^(-32))/(1+z^(-1))

b = [-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1];

a = [1 -1];

h_h = filter(b,a,[1 zeros(1,32)]); 

ecg_h = conv (ecg_l ,h_h);

ecg_h = ecg_h/ max( abs(ecg_h));

delay = delay + 16; % 16 samples for highpass filtering

if gr

ax(3)=subplot(323);plot(ecg_h);axis tight;title('High Pass Filtered');

end

else

%% bandpass filter for Noise cancelation of other sampling frequencies(Filtering)

f1=5; %cuttoff low frequency to get rid of baseline wander

f2=15; %cuttoff frequency to discard high frequency noise

Wn=[f1 f2]*2/fs; % cutt off based on fs

N = 3; % order of 3 less processing

[a,b] = butter(N,Wn); %bandpass filtering

ecg_h = filtfilt(a,b,ecg);

ecg_h = ecg_h/ max( abs(ecg_h));

if gr

ax(3)=subplot(323);plot(ecg_h);axis tight;title('Band Pass Filtered');

end

end

%% derivative filter H(z) = (1/8T)(-z^(-2) - 2z^(-1) + 2z + z^(2))

h_d = [-1 -2 0 2 1]*(1/8);%1/8*fs

ecg_d = conv (ecg_h ,h_d);

ecg_d = ecg_d/max(ecg_d);

delay = delay + 2; % delay of derivative filter 2 samples

if gr

ax(4)=subplot(324);plot(ecg_d);axis tight;title('Filtered with the derivative filter');

end

%% Squaring nonlinearly enhance the dominant peaks

ecg_s = ecg_d.^2;

if gr

ax(5)=subplot(325);plot(ecg_s);axis tight;title('Squared');

end

%% Moving average Y(nt) = (1/N)[x(nT-(N - 1)T)+ x(nT - (N - 2)T)+...+x(nT)]

ecg_m = conv(ecg_s ,ones(1 ,round(0.150*fs))/round(0.150*fs));

delay = delay + 15;

if gr

ax(6)=subplot(326);plot(ecg_m);axis tight;title('Averaged with 30 samples length,Black noise,Green Adaptive Threshold,RED Sig Level,Red circles QRS adaptive threshold');

axis tight;

end

%% Fiducial Mark 

% Note : a minimum distance of 40 samples is considered between each R wave

% since in physiological point of view no RR wave can occur in less than

% 200 msec distance

[pks,locs] = findpeaks(ecg_m,'MINPEAKDISTANCE',round(0.2*fs));

%% initialize the training phase (2 seconds of the signal) to determine the THR_SIG and THR_NOISE

THR_SIG = max(ecg_m(1:2*fs))*1/3; % 0.25 of the max amplitude 

THR_NOISE = mean(ecg_m(1:2*fs))*1/2; % 0.5 of the mean signal is considered to be noise

SIG_LEV= THR_SIG;

NOISE_LEV = THR_NOISE;

%% Initialize bandpath filter threshold(2 seconds of the bandpass signal)

THR_SIG1 = max(ecg_h(1:2*fs))*1/3; % 0.25 of the max amplitude 

THR_NOISE1 = mean(ecg_h(1:2*fs))*1/2; %

SIG_LEV1 = THR_SIG1; % Signal level in Bandpassed filter

NOISE_LEV1 = THR_NOISE1; % Noise level in Bandpassed filter

%% Thresholding and online desicion rule

for i = 1 : length(pks)

   %% locate the corresponding peak in the filtered signal 

    if locs(i)-round(0.150*fs)>= 1 && locs(i)<= length(ecg_h)

          [y_i x_i] = max(ecg_h(locs(i)-round(0.150*fs):locs(i)));

       else

          if i == 1

            [y_i x_i] = max(ecg_h(1:locs(i)));

            ser_back = 1;

          elseif locs(i)>= length(ecg_h)

            [y_i x_i] = max(ecg_h(locs(i)-round(0.150*fs):end));

          end

     end

  %% update the heart_rate (Two heart rate means one the moste recent and the other selected)

    if length(qrs_c) >= 9 

        diffRR = diff(qrs_i(end-8:end)); %calculate RR interval

        mean_RR = mean(diffRR); % calculate the mean of 8 previous R waves interval

        comp =qrs_i(end)-qrs_i(end-1); %latest RR

        if comp <= 0.92*mean_RR || comp >= 1.16*mean_RR

            % lower down thresholds to detect better in MVI

                THR_SIG = 0.5*(THR_SIG);

                %THR_NOISE = 0.5*(THR_SIG);  

               % lower down thresholds to detect better in Bandpass filtered 

                THR_SIG1 = 0.5*(THR_SIG1);

                %THR_NOISE1 = 0.5*(THR_SIG1); 

        else

            m_selected_RR = mean_RR; %the latest regular beats mean

        end 

    end

      %% calculate the mean of the last 8 R waves to make sure that QRS is not

       % missing(If no R detected , trigger a search back) 1.66*mean

       if m_selected_RR

           test_m = m_selected_RR; %if the regular RR availabe use it   

       elseif mean_RR && m_selected_RR == 0

           test_m = mean_RR;   

       else

           test_m = 0;

       end

    if test_m

          if (locs(i) - qrs_i(end)) >= round(1.66*test_m)% it shows a QRS is missed 

              [pks_temp,locs_temp] = max(ecg_m(qrs_i(end)+ round(0.200*fs):locs(i)-round(0.200*fs))); % search back and locate the max in this interval

              locs_temp = qrs_i(end)+ round(0.200*fs) + locs_temp -1; %location 

              if pks_temp > THR_NOISE

               qrs_c = [qrs_c pks_temp];

               qrs_i = [qrs_i locs_temp];

               % find the location in filtered sig

               if locs_temp <= length(ecg_h)

                [y_i_t x_i_t] = max(ecg_h(locs_temp-round(0.150*fs):locs_temp));

               else

                [y_i_t x_i_t] = max(ecg_h(locs_temp-round(0.150*fs):end));

               end

               % take care of bandpass signal threshold

               if y_i_t > THR_NOISE1 

                      qrs_i_raw = [qrs_i_raw locs_temp-round(0.150*fs)+ (x_i_t - 1)];% save index of bandpass 

                      qrs_amp_raw =[qrs_amp_raw y_i_t]; %save amplitude of bandpass 

                      SIG_LEV1 = 0.25*y_i_t + 0.75*SIG_LEV1; %when found with the second thres 

               end

               not_nois = 1;

               SIG_LEV = 0.25*pks_temp + 0.75*SIG_LEV ;  %when found with the second threshold             

             end 

          else

              not_nois = 0;

          end

    end

    %%  find noise and QRS peaks

    if pks(i) >= THR_SIG

                 % if a QRS candidate occurs within 360ms of the previous QRS

                 % ,the algorithm determines if its T wave or QRS

                 if length(qrs_c) >= 3

                      if (locs(i)-qrs_i(end)) <= round(0.3600*fs)

                        Slope1 = mean(diff(ecg_m(locs(i)-round(0.075*fs):locs(i)))); %mean slope of the waveform at that position

                        Slope2 = mean(diff(ecg_m(qrs_i(end)-round(0.075*fs):qrs_i(end)))); %mean slope of previous R wave

                             if abs(Slope1) <= abs(0.5*(Slope2))  % slope less then 0.5 of previous R

                                 nois_c = [nois_c pks(i)];

                                 nois_i = [nois_i locs(i)];

                                 skip = 1; % T wave identification

                                 % adjust noise level in both filtered and

                                 % MVI

                                 NOISE_LEV1 = 0.125*y_i + 0.875*NOISE_LEV1;

                                 NOISE_LEV = 0.125*pks(i) + 0.875*NOISE_LEV; 

                             else

                                 skip = 0;

                             end

                      end

                 end

        if skip == 0  % skip is 1 when a T wave is detected       

        qrs_c = [qrs_c pks(i)];

        qrs_i = [qrs_i locs(i)];

        % bandpass filter check threshold

         if y_i >= THR_SIG1

                        if ser_back 

                           qrs_i_raw = [qrs_i_raw x_i];  % save index of bandpass 

                        else

                           qrs_i_raw = [qrs_i_raw locs(i)-round(0.150*fs)+ (x_i - 1)];% save index of bandpass 

                        end

                           qrs_amp_raw =[qrs_amp_raw y_i];% save amplitude of bandpass 

          SIG_LEV1 = 0.125*y_i + 0.875*SIG_LEV1;% adjust threshold for bandpass filtered sig

         end

        % adjust Signal level

        SIG_LEV = 0.125*pks(i) + 0.875*SIG_LEV ;

        end

    elseif THR_NOISE <= pks(i) && pks(i)<THR_SIG

         %adjust Noise level in filtered sig

         NOISE_LEV1 = 0.125*y_i + 0.875*NOISE_LEV1;

         %adjust Noise level in MVI

         NOISE_LEV = 0.125*pks(i) + 0.875*NOISE_LEV; 

    elseif pks(i) < THR_NOISE

        nois_c = [nois_c pks(i)];

        nois_i = [nois_i locs(i)];

        % noise level in filtered signal

        NOISE_LEV1 = 0.125*y_i + 0.875*NOISE_LEV1;

        %end

         %adjust Noise level in MVI

        NOISE_LEV = 0.125*pks(i) + 0.875*NOISE_LEV;  

    end

    %% adjust the threshold with SNR

    if NOISE_LEV ~= 0 || SIG_LEV ~= 0

        THR_SIG = NOISE_LEV + 0.25*(abs(SIG_LEV - NOISE_LEV));

        THR_NOISE = 0.5*(THR_SIG);

    end

    % adjust the threshold with SNR for bandpassed signal

    if NOISE_LEV1 ~= 0 || SIG_LEV1 ~= 0

        THR_SIG1 = NOISE_LEV1 + 0.25*(abs(SIG_LEV1 - NOISE_LEV1));

        THR_NOISE1 = 0.5*(THR_SIG1);

    end

% take a track of thresholds of smoothed signal

SIGL_buf = [SIGL_buf SIG_LEV];

NOISL_buf = [NOISL_buf NOISE_LEV];

THRS_buf = [THRS_buf THR_SIG];

% take a track of thresholds of filtered signal

SIGL_buf1 = [SIGL_buf1 SIG_LEV1];

NOISL_buf1 = [NOISL_buf1 NOISE_LEV1];

THRS_buf1 = [THRS_buf1 THR_SIG1];

 skip = 0; %reset parameters

 not_nois = 0; %reset parameters

 ser_back = 0;  %reset bandpass param   

end

if gr

hold on,scatter(qrs_i,qrs_c,'m');

hold on,plot(locs,NOISL_buf,'--k','LineWidth',2);

hold on,plot(locs,SIGL_buf,'--r','LineWidth',2);

hold on,plot(locs,THRS_buf,'--g','LineWidth',2);

if ax(:)

linkaxes(ax,'x');

zoom on;

end

end

%% overlay on the signals

if gr

figure,az(1)=subplot(311);plot(ecg_h);title('QRS on Filtered Signal');axis tight;

hold on,scatter(qrs_i_raw,qrs_amp_raw,'m');

hold on,plot(locs,NOISL_buf1,'LineWidth',2,'Linestyle','--','color','k');

hold on,plot(locs,SIGL_buf1,'LineWidth',2,'Linestyle','-.','color','r');

hold on,plot(locs,THRS_buf1,'LineWidth',2,'Linestyle','-.','color','g');

az(2)=subplot(312);plot(ecg_m);title('QRS on MVI signal and Noise level(black),Signal Level (red) and Adaptive Threshold(green)');axis tight;

hold on,scatter(qrs_i,qrs_c,'m');

hold on,plot(locs,NOISL_buf,'LineWidth',2,'Linestyle','--','color','k');

hold on,plot(locs,SIGL_buf,'LineWidth',2,'Linestyle','-.','color','r');

hold on,plot(locs,THRS_buf,'LineWidth',2,'Linestyle','-.','color','g');

az(3)=subplot(313);plot(ecg-mean(ecg));title('Pulse train of the found QRS on ECG signal');axis tight;

line(repmat(qrs_i_raw,[2 1]),repmat([min(ecg-mean(ecg))/2; max(ecg-mean(ecg))/2],size(qrs_i_raw)),'LineWidth',2.5,'LineStyle','-.','Color','r');

linkaxes(az,'x');

zoom on;

end

end