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Normalized Bessel Lowpass Filter Transfer Function
Syntax fnbes(Norder, b, a)
Include: include spt\fnbes.oms
See Also fnbut , fncheb1 , fncheb2

      Norder = SCALAR. Requested order of transfer function. Coerced to
               INTEGER before local processing. Norder >= 2.
      b      = VECTOR, COLUMN, for return (type disregarded on input).
               Numerator polynomial coefficients. Type DOUBLE.
      a      = VECTOR, COLUMN, for return (type disregarded on input).
               Denominator polynomial coefficients. Type DOUBLE.
   RETURN: novalue. Filter functions are returned in 'b' and 'a'.


This function creates a normalized Bessel s-domain lowpass transfer function. The 3-dB cutoff frequency is set to 1 radian/sec. The requested filter order 'Norder' must be >= 2. The numerator polynomial of the transfer function is returned through argument 'b', and is a column vector where the elements form a polynomial as follows:

b => b(1) + b(2)*s + b(3)*s^2 + ...

Denominator polynomial is returned in argument 'a', and is of the same form.

Bessel filters approximate a maximally flat group delay characteristic. The filter's selectivity is relatively poor since it has a slow magnitude cutoff rate. But these filters have very low overshoot in their transient responses.


include spt\fnbes.oms

# Design BESSEL lowpass prototype filter, fc = 1 [radian/sec]
Norder = 5;           # Filter Order
b      = novalue;     # Declare numerator
a      = novalue;     # Declare denominator
fnbes(Norder, b, a);  # Make the prototype

# Evaluate this filter around its cutoff.
fmin    =  1d-2; # Plotting Limits
fmax    =  1d0;
ymax    =  10d0;
ymin    = -60d0;

N       = 201; # Plotting information
n       = seq(N)'-1d0;
f       = logspace(log10(fmin),log10(fmax),N)';
H       = gains(b,a,f);
HdB     = db20(H);
fc      = 1d0/2/PI; # 3dB down at this cutoff

A plot of the normalized BESSEL filter appears as: