|See Also||fncheb1 , fncheb2 , fnbes , fn2clp , fn2chp , fn2cbp , fn2cbs|
Norder = SCALAR. Requested order of transfer function. Coerced to
INTEGER before local processing. Norder >= 1.
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 arguments 'b' and 'a'.
This function creates a normalized Butterworth s-domain (analog) lowpass transfer function of the form: H(s) = b(s)/a(s). The 3-dB cutoff frequency is set to 1 [radian/sec]. The requested filter order 'Norder' must be >= 1. The numerator polynomial of the transfer function is returned through argument 'b', and is a column vector where the elements form an ascending 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.
A Butterworth filter has a monotonically decreasing attenuation characteristic and is maximally flat in the passband. It has moderate selectivity, being lesser than the Chebyshev family but greater than a Bessel filter.
The resulting normalized embodied in polynomials 'b' and 'a' can be further scaled to different frequencies and filter types by the functions: fn2clp , fn2chp , fn2cbp , fn2cbs .
A plot of the normalized BUTTERWORTH appears as:
# Design BUTTERWORTH lowpass prototype filter, fc = 1 [radian/sec]
Norder = 5; # Filter Order
b = novalue; # Declare numerator polynomial
a = novalue; # Declare denominator polynomial
fnbut(Norder,b,a); # Make prototype filter
# 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