MATLAB: Change in frequency domain with resampling

ecgfrequency domaininterpolationresample

I have resampled my ECG data from 62 Hz to 500 Hz. But there seems to be a lot of difference before and after resampling in the frequency amplitude diagram (please see attached figures). The frequency content should be preserved in resampling. I presume the issue is with the time vector. I donot have the original time vector. I only have the number of samples and sampling frequency. I am creating a new time vector using following method:

samT=length(sr)/500; %length of the signal divided by new resampled frequency

tl = linspace(0,samT,500);

sf = 1/(tl(2)-tl(1));

t = (0:length(tl)-1)/sf;

Also out of interp1 and resample which one would be better in this situation?

Any lead would be appreciated.

Best Answer

interp1 have different options to choose from but resample has anti-aliasing filter.

Frequency vector will be different for both the ffts and can be calculated by

F=(0:L/2)*fs/L where L is the length of fft output and fs is the sampling frequency of the signal.

Check the MATLAB script for reference.

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MATLAB: Which filter to use to remove baseline wander on ECG

Your signal is unfortunately sampled at a relatively low rate, so signal processing is difficult. Your signal also has harmonics of what appear to be a 1.5 Hz signal that are propagated through the entire signal. This noise may give the appearance of baseline wander that actually does not exist, since it is simply the summation of these harmonics. Those are essentially impossible to eliminate without also eliminating parts of your signal.

This analysis and filter appear to work acceptably well:

F = openfig('Normal ECG Signal2.fig');
f = gca;
EKG = findobj(f, 'Type','line');
t = EKG.XData;                                              % Recover Data
s = EKG.YData;
L = numel(t);                                               % Signal Length
Ts = mean(diff(t));
St = std(diff(t));                                          % Test For Uniform Sampling
tr = linspace(min(t), max(t), L);                           % New, Regularly-Sampled Time Vector
Tsr = mean(diff(tr)) * 1E-3;                                % Convert To Seconds
sr = resample(s, tr);                                       % Resample To Regularly-Sampled Signal
Fsr = 1/Tsr;                                                % Sampling Frequency (Hz)

Fnr = Fsr/2;
figure
plot(tr, sr)
grid
FTsr = fft(sr-mean(sr))/L;                                  % Fourier Transform Of Mean-Corrected Signal
Fv = linspace(0, 1, fix(L/2)+1)*Fnr;
Iv = 1:numel(Fv);
figure
plot(Fv, abs(FTsr(Iv))*2)
grid
Fs = Fsr;                                                   % Sampling Frequency (Hz)
Fn = Fs/2;                                                  % Nyquist Frequency (Hz)
Ws = 0.5/Fn;                                                % Passband Frequency Vector (Normalised)
Wp = 1.5/Fn;                                                % Stopband Frequency Vector (Normalised)
Rp =   1;                                                   % Passband Ripple (dB)
Rs = 150;                                                   % Stopband Attenuation (dB)
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                             % Calculate Filter Order
[z,p,k] = ellip(n,Rp,Rs,Wp,'high');                         % Default Here Is A Lowpass Filter
[sos,g] = zp2sos(z,p,k);                                    % Use Second-Order-Section Implementation For Stability
sr_filtered = filtfilt(sos,g,sr);                           % Filter Signal (Here: ‘sr’)
figure
freqz(sos, 2^14, Fs)                                        % Bode Plot Of Filter
set(subplot(2,1,1), 'XLim',[0 Fn])                          % Optional, Change Limits As Necessary

set(subplot(2,1,2), 'XLim',[0 Fn])                          % Optional, Change Limits As Necessary
figure
plot(tr, sr_filtered)
grid

I use an elliptical filter here rather than a Butterworth filter because it is shorter and therefore computationally more efficient. It also gives the filter characteristics I want.

MATLAB: How to create low pass filter for audio file

You gave enough information for the Signal Processing Toolbox (with a bit of help from me) to be able to design your filter:

Fs  = 8000;                                 % Sampling Frequency (Hz)
Fn  = Fs/2;                                 % Nyquist Frequency
Fco =   20;                                 % Passband (Cutoff) Frequency
Fsb =   30;                                 % Stopband Frequency
Rp  =    1;                                 % Passband Ripple (dB)
Rs  =   10;                                 % Stopband Ripple (dB)
[n,Wn]  = buttord(Fco/Fn, Fsb/Fn, Rp, Rs);  % Filter Order & Wco
[b,a]   = butter(n,Wn);                     % Lowpass Is Default Design
[sos,g] = tf2sos(b,a);                      % Second-Order-Section For STability
figure(1)
freqz(sos, 2048, Fs)                         % Check Filter Performance

Then use the filtfilt function to filter your signal.

I chose a Butterworth design, but if you want a steeper cutoff, consider using a Chebychev design instead. You may want to experiment with the design to get the exact result you want with respect to your signal. See the relevant documentation for details.

Best Answer

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