% Chapter 8: Example 8.21
%            Butterworth Lowpass Filter Design:
%                Use of the BUTTER 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:
N =ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(OmegaP/OmegaS)));
fprintf('\n*** Butterworth Filter Order = %2.0f \n',N)
%%*** Butterworth Filter Order =  6 
OmegaC = OmegaP/((10^(Rp/10)-1)^(1/(2*N))); %Analog BW prototype cutoff
wn = 2*atan((OmegaC*T)/2);            %Digital BW cutoff freq

% Digital Butterworth Filter Design:
wn = wn/pi;                           %Digital Butter cutoff in pi units
[b,a]=butter(N,wn);
[b0,B,A] = dir2cas(b,a)
%%C = 5.7969e-004
%%B = 1.0000    2.0297    1.0300
%%    1.0000    1.9997    1.0000
%%    1.0000    1.9706    0.9709
%%A = 1.0000   -0.9459    0.2342
%%    1.0000   -1.0541    0.3753
%%    1.0000   -1.3143    0.7149