|See Also||fnbut , fncheb1 , fnbes|
Norder = SCALAR. Requested order of transfer function. Coerced to
INTEGER before local processing. Norder >= 2.
Ap = SCALAR. Passband attenuation in dB at cutoff frequency,
Ap > 0.0 dB. Coerced to DOUBLE for local processing.
As = SCALAR. Stopband minimum attenuation in dB, As > Ap.
Coerced to DOUBLE for local processing.
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 TYPE 2 Chebychev s-domain lowpass transfer function of the form: H(s) = b(s)/a(s). The cutoff frequency is set to 1 radian/sec at an attenuation of 'Ap' dB, where Ap > 0.0 dB. 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.
A Chebychev TYPE 2 filter (sometimes called the Inverse Chebychev Filter) has monotonic behavior in the passband and equi-ripple attenuation in the stopband of maximum value 'As' dB, where As > Ap.
A plot of the normalized CHEBYSHEV Type 2 filter appears as:
# Design CHEBYCHEV Type 2 lowpass prototype filter, fc = 1 [radian/sec]
Norder = 5; # Filter Order
Ap = 2d0; # Passband variation
As = 45d0; # Stopband attenuation
b = novalue; # Declare numerator polynomial
a = novalue; # Declare denominator polynomial
fncheb2(Norder, Ap, As, b , a ); # Make the filter
# Evaluate this filter around its cutoff.
fmin = 1d-2; # Plotting Limits
fmax = 1d1;
ymax = 10d0;
ymin = -60d0;
N = 301; # 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; # Ap dB down at this cutoff