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.net/apps/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.net/apps/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.
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.net/apps/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.