Re: Optimal Crystal Filter Design
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Thanks Reg,
Perhaps the link you furnished will provide more insight.? I always felt there was a big gap between linear algebra,? and the linear programming used in business applications.? Because of complexity, the mathematical underpinnings of linear programming might not be covered in business courses.? I sense some professors teaching its use might not thoroughly understand what is going on either.
Regards,
Bruce, KG6OJI
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From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected] Sent: Sat, Jun 12, 2021 12:52 pm Subject: Re: [qex] Optimal Crystal Filter Design Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al. The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do. https://stacks.stanford.edu/file/druid:qg769wc9289/2004-09.pdf Have Fun! Reg On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote:
Reg,
I apologize for this being off topic.?
I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra.
I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry.
Regards,
Bruce, KG6OJI?
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From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected]; [email protected] Sent: Sat, Jun 12, 2021 11:41 am Subject: [qex] Optimal Crystal Filter Design 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?
Have Fun!
Reg
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ebrucehunter