% Chapter 8: Example 8.11
%            Impulse Invariance Transformation
%                  Butterworth Lowpass Filter Design
%
% 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: Inverse mapping for frequencies
T = 1;                               % Set T=1
OmegaP = wp * T;                     % Prototype Passband freq
OmegaS = ws * T;                     % 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 Butterworth Prototype Filter Calculation:
[cs,ds] = afd_butt(OmegaP,OmegaS,Rp,As);
%%*** Butterworth Filter Order =  6 

% Impulse Invariance transformation:
[b,a] = imp_invr(cs,ds,T);
[C,B,A] = dir2par(b,a)
%%C =  []
%%B = 1.8557   -0.6304
%%   -2.1428    1.1454
%%    0.2871   -0.4466
%%A = 1.0000   -0.9973    0.2570
%%    1.0000   -1.0691    0.3699
%%    1.0000   -1.2972    0.6949

% Plotting
figure(1); subplot(1,1,1)
[db,mag,pha,grd,w] = freqz_m(b,a);
subplot(2,2,1); plot(w/pi,mag); title('Magnitude Response')
xlabel('frequency in pi units'); ylabel('|H|'); axis([0,1,0,1.1])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[0,Attn,Ripple,1]); grid
subplot(2,2,3); plot(w/pi,db); title('Magnitude in dB');
xlabel('frequency in pi units'); ylabel('decibels'); axis([0,1,-40,5]);
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[-50,-15,-1,0]); grid
set(gca,'YTickLabelMode','manual','YTickLabels',['50';'15';' 1';' 0'])
subplot(2,2,2); plot(w/pi,pha/pi); title('Phase Response')
xlabel('frequency in pi units'); ylabel('pi units'); axis([0,1,-1,1]);
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[-1,0,1]); grid
subplot(2,2,4); plot(w/pi,grd); title('Group Delay')
xlabel('frequency in pi units'); ylabel('Samples'); axis([0,1,0,10])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[0:2:10]); grid