|See Also||fnbut , fncheb2 , fnbes|
Norder = SCALAR. Requested order of transfer function. Coerced to
INTEGER before local processing. Norder >= 2.
Ap = SCALAR. Passband ripple in dB, Ap > 0.0 dB. 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 1 Chebyshev s-domain 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 >= 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. The function calls SPT function 'fnc1pole()'.
A Chebyshev TYPE 1 filter has equi-ripple behavior in the passband and monotonically increasing attenuation in the stopband. The passband peak-to-peak ripple is set via parameter 'Ap' in dB, where Ap > 0.0dB (strictly positive). Due to the nature of Chebyshev functions, even order filters cannot have a gain of unity at 0 Hz as can odd order filters. Even order filters start at Ap dB down at 0 Hz and begin passband ripple characteristics from there. All filters are passive, i.e., they can a gain of 1.0 at most at any given frequency.
A plot of the normalized CHEBYSHEV Type 1 filter apperas as:
# Design CHEBYSHEV Type 1 lowpass prototype filter, fc = 1 [radian/sec]
Norder = 5; # Filter Order
Ap = 2d0; # Passband Ripple
b = novalue; # Declare numerator polynomial
a = novalue; # Declare denominator polynomial
fncheb1(Norder, Ap, 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