% Chapter 8: Example 8.22
%            Butterworth Lowpass Filter Design:
%                Use of the CHEBY1 function
%
% Digital Filter Specifications:
wp = 0.2*pi;                         %digital Passband freq in Hz
ws = 0.3*pi;                         %digital Stopband freq in Hz
Rp = 1;                              %Passband ripple in dB
As = 15;                             %Stopband attenuation in dB

% Analog Prototype Specifications:
T = 1;                               %Set T=1
OmegaP = (2/T)*tan(wp/2);            %Prewarp Prototype Passband freq
OmegaS = (2/T)*tan(ws/2);            %Prewarp Prototype Stopband freq
ep = sqrt(10^(Rp/10)-1);             % Passband Ripple parameter
Ripple = sqrt(1/(1+ep*ep));          % Passband Ripple
Attn = 1/(10^(As/20));               % Stopband Attenuation

% Analog Prototype Order Calculation:
ep = sqrt(10^(Rp/10)-1);             %Passband Ripple Factor
A = 10^(As/20);                      %Stopband Attenuation Factor
OmegaC = OmegaP;                     %Analog Prototype Cutoff freq
OmegaR = OmegaS/OmegaP;              %Analog Prototype Transition Ratio
g = sqrt(A*A-1)/ep;                  %Analog Prototype Intermediate cal.
N = ceil(log10(g+sqrt(g*g-1))/log10(OmegaR+sqrt(OmegaR*OmegaR-1)));
fprintf('\n*** Chebyshev-1 Filter Order = %2.0f \n',N)
%%*** Chebyshev-1 Filter Order =  4 

% Digital Chebyshev-I Filter Design:
wn = wp/pi;                          %Digital Passband freq in pi units
[b,a]=cheby1(N,Rp,wn);
[b0,B,A] = dir2cas(b,a)
%%b0 = 0.0018
%%B = 1.0000    2.0000    1.0000
%%    1.0000    2.0000    1.0000
%%A = 1.0000   -1.4996    0.8482
%%    1.0000   -1.5548    0.6493