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I was wondering if there is something like a Hilbert Transform but that can implement an arbitrary phase shift to every frequency component.

I mean, I know that the magnitude response of a "Hilbert filter" is 1 for all frequencies and the phase response is $-\pi/2$ for all positive frequencies, but I would like to obtain different phase shifts like $\pi/3, \pi/4, \ldots$ etc.

Is there a transform that can accomplish that? I guess it would be something like a "trascendental Hilbert Transform"

Gilles
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Victor Manuel
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  • This is easily achieved with a Hilbert transformer, two multipliers, and an adder. See [this question](https://dsp.stackexchange.com/q/31597/4298) and its answers for more details. – Matt L. Dec 14 '20 at 21:59
  • Thank you... yes this answers my question, from a theoretical point of view. **do you know a reference for this?** I am not sure how to implement it in a discrete sense, even though there is an inkling in the response. I'll try to implement it anyway. **do you have any idea about how to implement it?** Thank you very much for your prompt response. – Victor Manuel Dec 14 '20 at 22:21
  • The block diagram in the answer by MBaz is pretty clear -- if you're going to do signal processing, you have to write code (or build circuits, if you're going analog). If you have trouble with that, then I suggest you ask a question titled "How do I implement code from a Block Diagram", with the obvious question body and using that block diagram as your example. – TimWescott Dec 15 '20 at 02:50
  • @VictorManuel: The last sentence in [my answer](https://dsp.stackexchange.com/a/31616/4298) is actually a pretty concrete hint at how to implement such a system. – Matt L. Dec 15 '20 at 11:37
  • Yep, I can understand what you both say. Sorry if it was too much. I'll just go and try. Maaaaaaaaany thanks – Victor Manuel Dec 15 '20 at 18:31
  • @VictorManuel: Yes, go and try and come back with a concrete implementation question if you should have one. – Matt L. Dec 15 '20 at 20:27

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