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### Author Topic: Matched Filter (Transfer Function; Poles-Zeroes) Computer Aided Design (CAD) App  (Read 564 times)

#### OptimalDesigns

• Supporting Member
• Joined in 2018
• Posts: 68
• (retired) Mathematical Engineer
##### Matched Filter (Transfer Function; Poles-Zeroes) Computer Aided Design (CAD) App
« on: July 18, 2023, 10:24 AM »
Match-n-freq™ is a (free) Pulse Shaping Filter program that finds the pole-zero locations of a transfer function, H(s), for a matched-filter design.  H(s) equals a -desired- signal (Yout) divided by a given input signal (Yin).  Both Yout and Yin are functions of frequency.  Download at https://goal-driven....ps/match-n-freq.html .

H(s) has an option to equalize its sidelobe peak amplitudes in a Bode plot; i.e., Peak i = Peak j for all i, j.

Group delay, Td, is calculated to compliment a given dataset, thus, providing a maximally flat group delay.  A search for Group Delay definition on the internet shows various results and thus leaving the question which are true?  A textbook from 1980 differs from what is seen on the internet.  They may be equivalent but not sure.  So the basic equation is Td = Partial( H(s)) with respect to 's' / s, where s = 0 + j w.  Be careful when using some other App or even my App as they try to calculate Group delay.  If the professors don't agree, how can us developers get it 'right'?  I have worked on this problem on & off since 1979 and finally think it is done!  If you find an error, PLEASE let me know

Match-n-freq™ finds an Optimal solution for a H(s) match and maximally flat group delay; a one time process!  One must determine what Poles &/or Zeros are necessary for their datasets and this may require several runs.  But with the speed of today's PCs, a half-day should have your problem solved.
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This Matched Filter CAD App is an example of what other redundant problems can be solved using this as an example.  The source code is included in the download; search for *.fc & *.inc files plus Visual Basic code files for the front-end.
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The reason this and other Apps were developed by me was to demonstrate the simplicity & power of a Calculus-Level language/compiler; e.g., FortranCalculus visit https://goal-driven....pps/fc-compiler.html for more; freeware too.  I taught FortranCalculus from 1975 to 1979 in the SF Silicon Valley to Engineering & Science companies.  Also taught MACSYMA at Lockheed Missiles & Space Co. for 2 years... a lost cause, FortranCalculus wins hands down.
« Last Edit: July 18, 2023, 12:58 PM by OptimalDesigns »