How to design digital equivalent for a lowpass Bessel filter (Thiran filter)?

In the process of applying a lowpass Bessel filter to my signal, I realized that besself function does not support the design of digital Bessel filters and the bilinear function can be used to convert an analog filter into a digital form, except for Bessel filters. The digital equivalent for Bessel filters is the Thiran filter. The only thing I know for my filter is that it should have less than 5GHz bandwidth ( let's say 3GHz bandwidth). I do appreciate if someone could help me write the code in Matlab. The code which I have so far is:

%lowpass filter  
sig = MY SIGNAL;
sig_length = 5000001;                         % my signal length
fs  = 10000e9                                 % sampling rate
fc  = 3e9;                                    % cutt off frequency
order = 4; 
wo = 2*pi*fc;
[z,p,k] = besself(order, wo,'low');           % zero, pole and gain form
% Convert to digital fileter
[zd,pd,kd] = bilinear(z,p,k,fs);              % z-domain zero/pole/gain
[sos,g] = zp2sos(zd,pd,kd);                   % convert to second order section 
filteredSignal = filtfilt(sos, g, sig);

[Mathieu NOE]

Digital Bessel filter problem - (mathworks.com)

[Amy Lg]

Thank you for the link. I've already read that post. It doesn't answer my question.

[Star Strider]

It does, actually!

[Amy Lg]

your suggested solution was that abandoning bessel filter and designing another kinds of filter. I've already tried it with your help in this post and it doesn't give me the result I want.

[Star Strider]

What result do you want?

[Star Strider]

The sampling frequency must be at least two times the cutoff frequency, and preferably several times that value.

Just use whatever filter you want. Use filtfilt to do the actual filtering, since it provides phase-neutral filtering regardless of the filter design. The Bessel analog filter has a phase-neutral characteristic, however it loses that characteristic if it is discretised.

For the result you posted, the envelope function would probably be sufficient.

[Amy Lg]

I do appreciate it if you could help me to correct the code for a normalized analog Bessel filter. I wanna try analog filter for anaother purpose.

[Star Strider]

To use an analog Bessel filter, you will need to realise it in hardware.

This is not impossible, however it will be challenging, especially to build it from discrete components. Fortunately, Active Low-Pass Filter Design tells you how to build it with operational amplifiers, and how to calculate the various component values.

[Amy Lg]

Thanks for your help!

[Star Strider]

My pleasure!