Task 1
Z-transform and Inverse Z-transform
%Lab 10 Task 1 close all clear clc syms f f2 w n; f=sin(w*n); zTransformed=ztrans(f); pretty(zTransformed) pretty(iztrans(zTransformed)) f2=cos(w*n); zTransformed2=ztrans(f2); pretty(zTransformed2) pretty(iztrans(zTransformed2))
Task 2
Cross Correlation
%Lab 10 Task 2
close all
clear
clc
a=[2 -1 3 7 1 2 -3];
b=[1 -1 2 -2 4 1 -2 5];
c=xcorr(a,b);
disp(c);
figure
subplot 311
stem(a)
title('Signal 1')
ylabel('a')
subplot 312
stem(b)
title('Signal 2')
ylabel('b')
subplot 313
stem(c)
title('Cross Correlation of signal 1 and 2')
ylabel('c')
Task 3
Auto Correlation
%Lab 10 Task 3
close all
clear
clc
a=[2 -1 3 7 1 2 -3];
c=xcorr(a,a);
disp(c);
figure
subplot 211
stem(a)
title('Signal 1')
ylabel('a')
subplot 212
stem(c)
title('Auto Correlation of signal 1 ')
ylabel('c')
Task 4
Finding Transfer function of a system
%Lab 10 Task 4
close all
clear
clc
s=tf('s');
g1=1/(s+10);
g2=1/(s+1);
g3=(s^2+1)/(s^2+4*s+4);
g4=(s+1)/(s+6);
h1=(s+1)/(s+2);
h2=2;
h3=1;
t1=series(g3,g4);
t2=feedback(t1,h1,+1);
t3=series(t2,g2);
h2=h2/g4;
t4=feedback(t3,h2,-1);
t5=series(t4,g1);
t6=feedback(t5,h3,-1);
Task 5
Pole, Zero, Roots, Poly, ZPKdata and PZ map of a system. Pole zero plot of a system after Laplace Transform.
%Lab 10 Task 5 close all clear clc syms t s; ft=5*t^2+3*t+9; fs=laplace(ft); fw=fourier(ft); pretty(ft) pretty(fs) %pretty(fw) fs=simplify(fs); pretty(fs) [n,d]=numden(fs); n=sym2poly(n); d=sym2poly(d); poles=roots(d) zeroes=roots(n) [p,z]=pzmap(tf(n,d)); pzmap(tf(n,d)); sys=tf(n,d); sys pole(sys) zero(sys)