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The signal shown in the following figure is collected from a ECG sensor. The spike noise that is observed with a periodicity of 30 seconds was traced to the periodic blip of the LED as it draws current.

enter image description here

The following is one instance of the spike noise after zooming in,

enter image description here

Frequency domain filters are not effective in this case because the frequency domain characteristics of the LED blip artifact is similar to the heart beat signal(QRS).

Is there any effective way to remove this artifact..? I was think of using the blip as a mother wavelet and performing a multi-scale correlation with the ECG signal to detect the spikes. Is this the procedure for wavelet denoising? Is there any other effective way of denoising for this case?

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  • $\begingroup$ As you said the frequencies of spike noise overlaps with heart beat signal, is the same true for amplitudes(in time domain), i.e. are the amplitudes of noise spike and heart beat spike have similar magnitudes and are these magnitudes stable. because if the magnitude of noise spike is very different from heart beat spike and remains almost constant over the time, we can remove it using time domain methods. $\endgroup$ – arpit jain Jan 22 '16 at 10:38
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In the first place I would suggest you to look for some electrical methods of avoiding those spikes... If it's impossible to do so, then you must find a close enough mathematical model of your noise generation process from which you may decide to choose an adequate method of noise removal...Provided you can do so...

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  • $\begingroup$ I was thinking in the lines of taking one instance of the spike noise as a template and cross-correlating with the signal to identify the locations of the spikes in the timeseries. But it looks like normalized cross correlation isn't possible if the two inputs are not of similar size. Is there any wavelet based de-noising approach that'll work here? $\endgroup$ – Naveen Jun 8 '15 at 19:19
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If duration of this spike is a only few point in time (1 or 2) , you can use median filter (wiki) with size 3 or 5. But be careful - if useful signal has same duration, you will lose information.

P.S.
As Fat32 write above, I suggest "to look for some electrical methods of avoiding those spikes"

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Assuming that you do not need to beat-to-beat information on the EKG morphology, which would be subject signficant noise anyway, one approach would be ensemble averaging on the time domain.

As the heart rhythm has a natural arrhythmia it is very unlikely that the spikes will occur at the same point in the waveform even when the heart rate matches the periodicity of the artifact. Thus by identifying a QRS complex and averaging (most likely a median) around some window with the last couple of beats should provide a robust measure of the EKG.

As others have mentioned, the underlying electrical noise should be minimized at the signal capture stage however I appreciate this is not always appropriate and you never want to throw away otherwise good data.

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Because the frequency is known and appears to be quite consistant through out, why not create a filter.

Something like fourier transform -> remove data of the noise frequency (set equal to zero) -> inverse fourier transform.

I'm not an expert, but that seems like one means to do this.

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    $\begingroup$ As mentioned in the question, the frequency of this artifact overlaps the useful part of the signal in the frequency domain. So FD filtering will be lossy. $\endgroup$ – Naveen May 26 '15 at 19:43
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The noise in the image looks very similar to salt and pepper noise where signal goes to + or - infinity clipped by the hardware (name comes from image analysis where you will see white and black dots) A common way of removing that noise is actually the median filter( a non linear filter).

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