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Given a desired frequency and phase response, is it possible to find a transfer function that matches/approximates both the frequency and phase response? Basically once you have a Bode plot, invert it to find the a transfer function. Is that even possible, or is the problem overconstrained?

I'm aware of the Remez exchange method of optimizing FIR filters, but that only constrains frequency response and I can't find anything about phase response.

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  • $\begingroup$ Isn't this basically the same question? dsp.stackexchange.com/questions/82619/… $\endgroup$
    – Dan Boschen
    Commented Apr 17, 2022 at 1:06
  • $\begingroup$ What a coincidence! I did not notice that one. However, it's not clear to me that the question is asking for both frequency and phase response to be satisfied simultaneously by the same transfer function, and the title also does not include anything about phase response to reflect that. If that is the case, would you consider revising the question to clarify? then I can remove this one as duplicate $\endgroup$
    – goweon
    Commented Apr 17, 2022 at 1:35
  • $\begingroup$ Yes that was exactly the question-- as like you said it is easy to get the transfer function from a magnitude response using least squares (with linear phase). I will edit! Great minds think alike $\endgroup$
    – Dan Boschen
    Commented Apr 17, 2022 at 1:36

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