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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 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 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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