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.
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.
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.