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+//Example 8.11

+clc;clear;close;

+rp=0.707                       //passband ripple

+rs=0.2                        //stopband ripple

+wp=%pi/2;                     //passband frequency

+ws=3*%pi/4;                   //stopband frequency

+T=1;

+fp=wp/T;

+fs=ws/T;

+s=poly(0,'s');

+z=poly(0,'z');

+hs=1;

+//Calculating the order of filter

+num=log((rs^-2 -1)/(rp^-2 -1));

+den=2*log(fs/fp);

+N=ceil(num/den);

+

+//Calculation of cut-off frequency

+fc=fp/(rp^-2 -1)^(0.5/N);

+

+//Calculating filter response

+if modulo(N,2)==1 then

+    b=-2*sin(%pi/(2*N));

+    hs=hs*fc/(s+fc);

+end

+for k=1:N/2

+    b=2*sin((2*k-1)*%pi/(2*N));

+    hs=hs*fc^2/(s^2+b*fc*s+fc^2);

+end

+hs=clean(hs);

+sys=syslin('c',hs);                

+hz=horner(ss2tf(dscr(sys,T)),1/z);        //converting H(s) to H(z)

+

+//Displaying filter response

+[hzm,fr]=frmag(hz,256);

+disp(hz,'Filter Transfer function: ');

+plot(fr,hzm);

+title('Lowpass Butterworth Filter Response');ylabel('Amplitude-->');xlabel('Normalised frequency f/fs-->');
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