How to Reduce Oscillations (not noise) in a Signal?
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How can oscillations be reduced in signals similar to the one shown in Figure 1 to achieve results like those in Figure 2? Please note that it is not a denoising or smoothing problem.
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John D'Errico
on 12 Jun 2024
Edited: John D'Errico
on 12 Jun 2024
To me, the upper signal looks like the convolution of something like a sinc with the lower signal. And that would mean, IF you knew the convolution kernel, you could recover the lower signal using decomvolution, though deconvolution is a noise amplifying process, an ill-posed problem.
But even if we ignore the issue of deconvolution as an ill-posed problem, you don't have sufficient information to perform deconvolution. It is not unlike saying you know the product of two numbers.
P=a*b
Now, given only the number P, can you recover the value of a? Or b? And of course you cannot do so. Both a and b could be infinitely many possible numbers.
So, sadly, the answer seems to be not really, and certainly not simply. I'm not a signals expert though.
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John D'Errico
on 18 Jun 2024
Yes. But I think you don't apppreciate my response. This is exactly a deconvolution problem, which is itself an ill-posed problem. But you don't know the convolution kernel. And that means there are infinitely many solutions, all equally good, or perhaps I should say equally bad.
Again, look at my simple counter-example. I'll give you a number x=123.45679. I'll tell you it is the product of two numbers, x=a*b. Now I'll ask you to tell me what were a and b? (It is a secret!) If I told you the value of a, then of course you can compute b. But my lips are sealed, and in that case, no meaningful solution exists.
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