Transfer function to FIR hiccup, help!

About half a year a go I found an excellent book on Costas: There are three models of Costas loops for BPSK presented in the book, in-detail explanation of the static and dynamic analysis and mathematical models: conventional circuit on real input, pre-envelope circuit on complex input and finally a phasor rotation circuit on complex input as well. There are explicit mathematical expressions for lock time, lock range, pull-in range, and pull-in time for the Costas loop.

I have implemented the presented pre-envelope model, in Matlab, and using the code that was described in a previous post ( I have fed it with Inmarsat-C signal from one of the channels kindly made available through SDR# spyserver (sdr:// at 12 kHz SR.

Above, the lock time in samples for a 200 Hz frequency difference.

Above, the symbols are also almost centered after 50 samples (~4 ms), and definitely centered not long after that.

At this stage the only hiccup from having an SDR# Inmarsat-C plugin are two transfer functions that I would like to implement as FIR filter approximations in C#. I have found a fast C# FIR implementation at:

The first one is the transfer function of the loop filter, this is a “proportional-integral” filter whose transfer function is:

and the second one is the VCO “simple integrator” filter having the following transfer function:

For my particular case, the loop filter is:

>> tf(F3_num, F3_den, 1/12000)

ans =
 8.916 z - 6.916
 0.48 z - 0.48
Sample time: 8.3333e-05 seconds
Discrete-time transfer function.

and the VCO:

>> tf(F4_num, F4_den, 1/12000)

ans =
 z - 1
Sample time: 8.3333e-05 seconds
Discrete-time transfer function.

Currently I do not know enough math to be able to transform these into FIR coefficients, I am currently trying a FIR from frequency response method. Can this be done?

Any help would be greatly appreciated.

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