How to get rid of ringing/overshoot in an ecg signal while using notch filter?

Hallo all,

i have an ecg signal which contains 50 Hz noise. I want to get rid off the noise.

First of all i do a pre processing step with a highpass and lowpass and. After this i use the notch filter.

Notch filter code:

f_noise = 50; %noise to filter
fs = 500;

f_notch = f_noise/fs; %normalized noise
N =[exp(j*2*pi*f_notch);exp(-j*2*pi*f_notch)]; %place zeros
P = 0.5*N; %place additional poles with same angular as zeros 
b = poly(N); a = poly(P); %get filter coeff.

Problem here i got an "overshoot" in the QRS complex (see Picture).

A other member suggested this notch filter to implement:

%Notchfilter by Daniel. M
Fs = 500;
Fn = fs/2; % Nyquist frequency
numHarmonics = 0; % Let's do 50, 100, 150, 200, 250; 0 -> filter only 50 Hz
lineFreq = 50; % Hz
for fq = ((0:numHarmonics)+1) * lineFreq
    Fl = fq + [-1, 1]; % notch around Fl. Could try [-2, 2] if too tight
    [z,p,k] = butter(1, Fl/Fn, 'stop');
    sos = zp2sos(z,p,k);
    ecg_signal_005_150_notch = filtfilt(sos, 1, ecg_signal_005_150); % assumes data is [time x ... dimensions]
    % overwrites data, and filters sequentially for each notch
end

This solution removes the "overshoot" perfectly but it adds "ringing" (see picture).

Does somebody know a good trade-off between ringing and overshoot?

Best regards

[Daniel M]

I took another crack at this and couldn't come up with anything satisfactory (within my available time). Can you not just do a band pass filter from 0.5 to 40?

Answer 1

[Daniel M]

clearvars
clc
close all

fs = 500;
ecg = xlsread('Noisy_50HZ_ECG.xlsx');

ecg = detrend(ecg.');
ecg = sgolayfilt(ecg,0,5);

T = 1/fs;
L = length(ecg);
t = (0:L-1)*T;

filtfreq = [0.5 40];
xlim = [49 51];

%%%% Apply my own filters
[B,A] = butter(4, filtfreq./(fs/2));
f_ecg = filtfilt(B,A,ecg);

%%% Notch filter
data = f_ecg;

Fn = fs/2; % Nyquist frequency
numHarmonics = 3; % Let's do 50, 100, 150, 200
lineFreq = 50; % Hz

for fq = ((0:numHarmonics)+1) * lineFreq
    Fl = fq + [-1, 1];
    [z,p,k] = butter(6, Fl/Fn, 'stop');
    sos = zp2sos(z,p,k);
    
    data = filtfilt(sos, 1, data); 
end

figure
plot(t,ecg,'b.-',t,data,'r-')
set(gca,'XLim',[48 52])

figure
plot(t,data)
set(gca,'XLim',[49 51])

I also tried an FIR notch, using the fieldtrip toolbox, different bandpasses, etc. But this is what I think worked best.

(Reading the data from https://www.mathworks.com/matlabcentral/answers/487640-ecg-spectrum-wrong#comment_762871)

[Stephan Lallinger]

Daniel first of all thank you so much for your time and work.

Thats incredible how much you helped and discussed with me the last days.

I read a lot of papers about this topic and most researchers and doctors came to the conclusion you should use a frequency witdh of 0.05 - 150 Hz (up to 250 Hz for children).

I still learned a lot from your techniques so i will try to find a solution for the notch problem.

I will try your code and "play around" with parameters.

Thank you and best regards!

[Daniel M]

It seems that the problem is that the noise at 50 isn't "just" at 50, there are smaller peaks at 40, 41.3, 43.8, 46.2, 48.7, 51.2, 53.8 etc. I don't know if a broad notch around 50 will be effective, or if you could do many invididual narrow notches (for example, using findpeaks on the frequency spectrum and performing notches on them).

By the way, here are two FIR filters for you to explore as well.

% Broad FIR notch
fs = 500;
Fn = fs/2;                                       
b=fir1(48, [49.8 50.2]/Fn, 'stop');
figure
freqz(b, 1, 2^16, fs)

% Narrow FIR notch
sb_frq = [47 49 51 53]; % Define Passband / Stopband Frequencies
mags = [1 0 1]; % Design Lowpass Filter
devs = [0.05  0.01  0.05]; % Allowed Deviations
[n,Wn,beta,ftype] = kaiserord(sb_frq,mags,devs,fs); % Use Kaiser Window
n = n + rem(n,2); % Define Filter Order
b = fir1(n,Wn,ftype,kaiser(n+1,beta),'scale'); % Design Filter
figure
freqz(b, 1, 2^16, fs)

[Stephan Lallinger]

Maybe a notch filter is not the best solution for an ecg with the bandwidth of 0.05 - 150 Hz.

I tried the "broad FIR" solution before the notch and it wasn't that good.

I tried also serverals windows like Gaussian, Kaiser and Hann but maybe i could improve here.

Iam also working on adaptive filter solutions with reference noise and without.

Best solutions i got is with your code and this settings:

for fq = ((0:numHarmonics)+1) * lineFreq
    Fl = fq + [-0.1, 0.1]; % notch around Fl. Could try [-2, 2] if too tight
    [a,b] = butter(1, Fl/Fn, 'stop');
    %sos = zp2sos(z,p,k);
    ecg_bandpassed = filtfilt(a,b, ecg_bandpassed); % assumes data is [time x ... dimensions]
    % overwrites data, and filters sequentially for each notch
end

I needs roughly 5 seconds to settle down but then it is quite good.

To be honest i was suprised because the corners are very sharp and the order is just 1.

It also seems zero phase filtering is much better then using just "filter" or convolution.

Normally i use convolution for filtering i have no experience with "filtfilt" function.

For clearifaction i used not the 50 Hz noisy signal. Instead i used a clear ecg and added the noise via Matlab.

[Daniel M]

It makes sense that it would work well with a "perfect" 50 Hz noise signal. But real world applications are not so ideal, as you have learned.

If you eventually find a solution that works well for you, please post here for myself and others to learn from. Good luck!