3
$\begingroup$

I need to locate R-peaks in an ECG signal. I'm using wavelets to extract QRS complexes:
First, I decompose the signal using a maximal overlap discrete wavelet transform with the Symlet 4 wavelet. This wavelet resembles the QRS complexes I want to detect. I then copy scales 4 and 5, because this band maximizes QRS energy. The wavelet coefficients on scales 1-3, and the level 5 approximation coefficients are set to zero. Then I perform an inverse wavelet transform on these modified coefficients. The result is a signal in the time domain that contains mostly QRS complexes, and has very high amplitude at the R-peaks.
I just use a peak detector on this signal to locate the R-peaks.

ECG signal and wavelet reconstruction

Everything is well-explained here: https://mathworks.com/help/wavelet/ug/r-wave-detection-in-the-ecg.html

This is the code I use:

wt = modwt(rawECGsignal_buffer,5);
wtrec = zeros(size(wt));
wtrec(4:5,:) = wt(4:5,:);
filtered = imodwt(wtrec,'sym4');

From what I understand, the Symlet 4 is a biorthogonal wavelet, which means that the decomposition and reconstruction can be implemented as a bank of high- and low-pass FIR filters. enter image description here

Right now, I read the live ECG data into a 5 second buffer, and then perform the wavelet filter on the buffer (as described above). This seems rather inefficient, because I have to filter the entire buffer again when new data comes in.
Is it possible to implement this in a way that allows for real-time filtering of an ECG signal without buffering?
(I.e. single value in → wavelet 'filter' → single filtered/reconstructed value out)

$\endgroup$

1 Answer 1

3
$\begingroup$

Right now, I read the live ECG data into a 5 second buffer, and then perform the wavelet filter on the buffer (as described above). This seems rather inefficient, because I have to filter the entire buffer again when new data comes in.

You cannot avoid the filtering / reconstruction steps over the buffer with this kind of processing.

Is it possible to implement this in a way that allows for real-time filtering of an ECG signal without buffering? (I.e. single value in → wavelet 'filter' → single filtered/reconstructed value out)

Yes.

For block processing, you can use the overlap add or overlap save methods which can also work straight in the time domain.

For sample-by-sample processing, you can start with the basic formula of discrete convolution:

$$ y[n] = \sum_{k=0}^{k<N} x[n-k] \cdot h[k]$$

Where $y$ is the output, $x$ is the input and $h$ is the impulse response, or "filter coefficients".

To get rid of the indexing by $n$, shift the input $x$ by one sample and place the newly acquired sample in the beginning of $x$. You can do this in MATLAB with circshift. So, this would probablly look like x=circshift(x,1);x[1]=input_value.

This now leaves us with getting the $h$ coefficients. You can get those for the wavelets you are using, in MATLAB, using wfilters.

This would cover the application of 1 filter. You will have to repeatedly do this for all the levels you need for both the directions of analysis and reconstruction plus the steps of decimation / upsampling.

So, overall, denoising the ECG in such a way is very demanding. Were the typical QRS detectors (possibly with the addition of "pulse-filters") failing to provide a robust enough R-R sequence?

Hope this helps.

$\endgroup$
2
  • $\begingroup$ Thanks a lot for your reply. I don't really see how the filter bank can be implemented. I understand how a single real-time FIR filter works, and how to find the coefficients, but I don't understand how you would cascade them together, and the down/up sampling confuses me. (I understand the diagram, but I don't know how to implement this in real-time.) $\endgroup$
    – tttapa
    Dec 11, 2017 at 19:34
  • $\begingroup$ @tttapa I got a lot of good understanding out of this article: A really friendly guide to wavelets. It describes how a wavelet transform can be implemented as a filter bank. $\endgroup$ Feb 17, 2021 at 23:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.