% 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);% Plotssubplot(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]); gridsubplot(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]); gridset(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]); gridsubplot(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)])