Matlab Codes and Graphs

                                        SOLUTION TO EXERCISE 1(a)

[num1,den1]=butter(1,1,'s');

[y1,w]=freqs(num1,den1);

y1=abs(y1);

[num2,den2]=butter(2,1,'s');

[y2,w]=freqs(num2,den2);

y2=abs(y2);

[num3,den3]=butter(3,1,'s');

[y3,w]=freqs(num3,den3);

y3=abs(y3);

[num4,den4]=butter(4,1,'s');

[y4,w] = freqs(num4,den4);

y4=abs(y4);

plot(w,y1,'g',w,y2,'r',w,y3,'b',w,y4,'k') ;

title('Junaid Shaikh, 05ES42') ;

[pic 1]

                                SOLUTION TO EXERCISE 1(b)

POLE-ZERO MAP OF FIRST ORDER

[num1,den1] =butter(1,1,'s');

pzmap(num1,den1)

grid;

title('Junaid Shaikh, 05ES42') ;

[pic 2]

POLE-ZERO MAP OD 2ND ORDER

[num2,den2] =butter(2,1,'s');

pzmap(num2,den2)

grid;

title('Junaid Shaikh, 05ES42') ;

[pic 3]

POLE-ZERO MAP OF 3rd   ORDER

[num3,den3] =butter(3,1,'s');

pzmap(num3,den3)

grid;

title('Junaid Shaikh, 05ES42') ;

[pic 4]

POLE-ZERO MAP OF 4th  ORDER

  [num4,den4] = butter(4,1,'s');

   pzmap(num4,den4)

   grid;

   title('Junaid Shaikh, 05ES42') ;

[pic 5]

                                           SOLUTION OF EXERCISE 1(C)

[num1,den1]=butter(1,1,'high','s');

[num2,den2]=butter(2,1,'high','s');

[num3,den3]=butter(3,1,'high','s');

[y1,w]=freqs(num1,den1);

[y2,w]=freqs(num2,den2);

[y3,w]=freqs(num3,den3);

y1=abs(y1);

y2=abs(y2);

y3=abs(y3);

plot(w,y1,'g',w,y2,'k',w,y3,'m');

title('05ES42,Junaid Shaikh');

xlabel('Frequency in HZ') ;

ylabel('Magnitude Response');

[pic 6]

                                              SOLUTION TO EXERCISE 1(d)

wn=[50 200];

[num1,den1]=butter(1,wn,'stop','s');

[y1,w]=freqs(num1,den1);

y1=abs(y1);  

[num2,den2]=butter(2,wn,'stop','s');

[y2,w]=freqs(num2,den2);