Bessel filter transfer function

According to reverse Bessel polynomials from https://en.wikipedia.org/wiki/Bessel_filter#Bessel_polynomials the 4th order looks like this:

s^4+10s^3+45s^2+105s+105.

I create the transfer function of the filter like this:

T = 1;
Bessel4 = tf(105,[1 10 45 105 105].*T.^[4 3 2 1 0])

Bessel4 =
 
                  105
  -----------------------------------
  s^4 + 10 s^3 + 45 s^2 + 105 s + 105
 
Continuous-time transfer function.

Is that correct so far? However, I don't understand the relation or difference to the MATLAB functions besself and besselap:

%% besselap
[z,p,k] = besselap(4);
[num,den] = zp2tf(z,p,k);
Bessel4_besselap = tf(num,den)

% Bessel4_besselap =
%  
%                       1
%   -----------------------------------------
%   s^4 + 3.124 s^3 + 4.392 s^2 + 3.201 s + 1
%  
% Continuous-time transfer function.

%% besself
[num,den] = besself(4,1/T);
Bessel4_besself = tf(num,den)

% Bessel4_besself =
%  
%                       1
%   -----------------------------------------
%   s^4 + 3.124 s^3 + 4.392 s^2 + 3.201 s + 1
%  
% Continuous-time transfer function.

Obviously, the resulting transfer functions are different. Should I use the results from besself/besselap or my own implementation from above?

[RAN]

Hi,

Did you find the solution? I am facing the same problem like yours.

[Thomas Becker]

Hi Rahul,

I'm sorry, that I don't have a solution so far. We skipped the attempt to use the Bessel filter and switched to an easy moving average filter due different reasons...

Best regards

Thomas

Answer 1

[Star Strider]

The besselap function creates a Bessel lowpass filter prototype. The besself function transforms the besselap design to create different filter types from it. The advantage of Bessel filters is that they have linear (neutral) phase response, so are perfect for hardware anti-aliasing filters, however the continuous Bessel filter designs cannot be converted to discrete (digital) filters.

The filtfilt function makes all digital filters phase-neutral, so create whatever digital (discrete) filter suits your needs, then use filtfilt to filter your signals with it.