ECG signal filtering problem

clc clearvars

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % load signal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% dummy data Fs = 10000; samples = 20000; t = (0:samples-1)'*1/Fs; signal = sin(2*pi*50*t)+2*sin(2*pi*440*t)+1e-2*randn(samples,1); % two sine + some noise

%% decimate (if needed) % NB : decim = 1 will do nothing (output = input) decim = 5; if decim>1 signal = decimate(signal,decim); Fs = Fs/decim; end samples = length(signal); t = (0:samples-1)*1/Fs;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FFT parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NFFT = Fs; % so delta f = 1 Hz Overlap = 0.75; w = hanning(NFFT); % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.

%% notch filter section %%%%%% % H(s) = (s^2 + 1) / (s^2 + s/Q + 1)

fc = 50; % notch freq wc = 2*pi*fc; Q = 5; % adjust Q factor for wider (low Q) / narrower (high Q) notch % at f = fc the filter has gain = 0

w0 = 2*pi*fc/Fs; alpha = sin(w0)/(2*Q);

            b0 =   1;
            b1 =  -2*cos(w0);
            b2 =   1;
            a0 =   1 + alpha;
            a1 =  -2*cos(w0);
            a2 =   1 - alpha;

% analog notch (for info) num1=[1/wc^2 0 1]; den1=[1/wc^2 1/(wc*Q) 1];

% digital notch (for info) num1z=[b0 b1 b2]; den1z=[a0 a1 a2];

freq = (fc-1:0.01:fc+1); [g1,p1] = bode(num1,den1,2*pi*freq); g1db = 20*log10(g1+1e-6);

[gd1,pd1] = dbode(num1z,den1z,1/Fs,2*pi*freq); gd1db = 20*log10(gd1+1e-6);

figure(1); plot(freq,g1db,'b',freq,gd1db,'+r'); title(' Notch: H(s) = (s^2 + 1) / (s^2 + s/Q + 1)'); legend('analog','digital'); xlabel('Fréquence (Hz)'); ylabel(' dB')

% now let's filter the signal signal_filtered = filtfilt(num1z,den1z,signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % display : averaged FFT spectrum before / after notch filter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq,fft_spectrum] = myfft_peak(signal, Fs, NFFT, Overlap); % sensor_spectrum_dB = 20*log10(fft_spectrum);% convert to dB scale (ref = 1)

% demo findpeaks [pks,locs]= findpeaks(sensor_spectrum_dB,'SortStr','descend','NPeaks',2);

[freq,fft_spectrum_filtered] = myfft_peak(signal_filtered, Fs, NFFT, Overlap); sensor_spectrum_filtered_dB = 20*log10(fft_spectrum_filtered);% convert to dB scale (ref = 1)

figure(2),plot(freq,sensor_spectrum_dB,'b',freq,sensor_spectrum_filtered_dB,'r');grid title(['Averaged FFT Spectrum / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']); legend('before notch filter','after notch filter'); xlabel('Frequency (Hz)');ylabel(' dB') text(freq(locs)+1,pks,num2str(freq(locs)))

function [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap) % FFT peak spectrum of signal (example sinus amplitude 1 = 0 dB after fft). % Linear averaging % signal - input signal, % Fs - Sampling frequency (Hz). % nfft - FFT window size % Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft if samples<nfft s_tmp = zeros(nfft,channels); s_tmp((1:samples)) = signal; signal = s_tmp; samples = nfft; end

% window : hanning window = hanning(nfft); window = window(:);

% compute fft with overlap offset = fix((1-Overlap)*nfft); spectnum = 1+ fix((samples-nfft)/offset); % Number of windows % % for info is equivalent to : % noverlap = Overlap*nfft; % spectnum = fix((samples-noverlap)/(nfft-noverlap)); % Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum % Select first half if rem(nfft,2) % nfft odd select = (1:(nfft+1)/2)'; else select = (1:nfft/2+1)'; end fft_spectrum = fft_spectrum(select,:); freq_vector = (select - 1)*Fs/nfft; end