% Chapter 8: Example 8.4
%            Butterworth Lowpass Analog filter design
%
Wp = 0.2*pi; Ws = 0.3*pi; Rp = 7; As = 16;
Ripple = 10 ^ (-Rp/20); Attn = 10 ^ (-As/20);

% Analog filter design:
[b,a] = afd_butt(Wp,Ws,Rp,As);
%%*** Butterworth Filter Order =  3 

% Calculation of second-order sections:
[C,B,A] = sdir2cas(b,a)
%%C = 0.1238
%%B = 0     0     1
%%A = 1.0000    0.4985    0.2485
%%         0    1.0000    0.4985

% Calculation of Frequency Response:
[db,mag,pha,w] = freqs_m(b,a,0.5*pi);

% Calculation of Impulse response:
[ha,x,t] = impulse(b,a);

% Plots
subplot(2,2,1); plot(w/pi,mag);title('Magnitude Response')
xlabel('Analog frequency in pi units'); ylabel('|H|'); axis([0,0.5,0,1.1])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,0.5]);
set(gca,'YTickmode','manual','YTick',[0,Attn,Ripple,1]); grid
subplot(2,2,2); plot(w/pi,db);title('Magnitude in dB')
xlabel('Analog frequency in pi units'); ylabel('decibels'); axis([0,0.5,-30,5])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,0.5]);
set(gca,'YTickmode','manual','YTick',[-30,-As,-Rp,0]); grid
set(gca,'YTickLabelMode','manual','YTickLabels',['30';'16';' 7';' 0'])
subplot(2,2,3); plot(w/pi,pha/pi); title('Phase Response')
xlabel('Analog frequency in pi units'); ylabel('radians'); axis([0,0.5,-1,1])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,0.5]);
set(gca,'YTickmode','manual','YTick',[-1,-0.5,0,0.5,1]); grid
subplot(2,2,4); plot(t,ha,[0,max(t)],[0,0]); title('Impulse Response')
xlabel('time in seconds'); ylabel('ha(t)'); axis([0,max(t),min(ha),max(ha)])