There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple. And the nanoVNA has made it cheap. This suggests simply multiplying the transfer functions of each possible section and using linear programming to solve for the set of N of P xtals which most closely give the desired response. The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming. David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled, even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
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