Given an arbitrary frequency response, what signal processing methods might exist that could guess, estimate or determine a transfer function (pole and zero constellation) which gives a "reasonably good" approximation (for some given estimation quality criteria) to that given frequency response? What means exist to estimate the number of poles and zeros required for a given transfer function plus a given approximation error allowance? Or how could one determine these constraints can't be met, if possible?
If the given frequency response was actually produced by a known transfer function, will any of these methods converge on that original transfer function? How about if the given frequency response were subject to (assumed Gaussian) measurement errors?
Assume working in the Z-plane with sampled spectrum, although continuous domain answers might also be interesting.
Added: Are the solution methods any different if only the magnitude of the frequency response is given (e.g. a solution with any phase response is allowed)?
Added: The latter problem is what I'm most interested in, given a known magnitude response around the unit circle, but unknown/unmeasured phase response, can the measured system be estimated, and if so under what conditions?
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