[FEATURE REQUEST] add Hilbert transform

[labodezao]

Hi,
I wonder if it's possible to implement the hilbert transform with micropython ulab.
Best regards

[v923z]

I assume, you want the implementation of https://docs.scipy.org/doc/scipy/reference/generated/scipy.fftpack.hilbert.html. However, before we add that, I wanted to ask, whether you could already calculate the Hilbert transform via the Fourier transform by applying the relation: Relationship with the Fourier transform.

[labodezao]

Hi, this is the right feature.
It's certainly possible to code this manually, yes, but some of my tries where hazardous :)

[v923z]

OK, but the question is, whether this has to be implemented, if the same functionality can be gotten with the already available tools. In order to keep the flash size small, I would rather implement things with some python wrapper. https://github.com/v923z/micropython-ulab/tree/master/snippets

[labodezao]

Hmm yes i did not think about it :)

[v923z]

@labodezao I am not sure, where this issue stands now. Do you want to implement this functionality as a snippet, or should we close it?

[labodezao]

This could be a good idea, but I don't have the knoloedge to modify the code :)

[v923z]

This could be a good idea, but I don't have the knowledge to modify the code :)

But if it is supposed to be a snippet, then you would write the code in python, so you would not have to change anything in the code base. That's the beauty of it.

[labodezao]

How can I do that ?

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[v923z]

You have access to the Fourier transform, and then you use what is written in https://en.wikipedia.org/wiki/Hilbert_transform#Relationship_with_the_Fourier_transform. You can calculate the phase of your signal by calling np.atan2, and then shift the phase by +/-90 degrees. This all can be done in python.

EDIT: if this is performance-critical, we could move the calculations to C, but first I would like to see a working implementation in python.