To Investigate The Properties Of Dtft

Objective:

To investigate the properties of DTFT

Example2
x1=rand(1,11);
x2=rand(1,11);
alpha=2;
beta=3;
x3=alpha*x1+beta*x2
n=0:10;
k=0:500;
w=(pi/500)*k;
m=n*k
X11=(exp(-j*pi/500)).^m
X1=x1*X11
X2=x2*X11
X3=x3*X11
X_check=alpha*X1+beta*X2;
error=max(abs(X3-X_check))

error =
1.1235e-014

Example 3
x=rand(1,11)
n=0:10
K=0:500
w=(pi/500)*k
m=n*k
X11=(exp(-j*pi/500)).^m
X=x*X11
y=x;
n_new=n+2;
m=n_new*k
X11=(exp(-j*pi/500)).^m
Y=y*X11;
Y_check=exp(-j*2*w).*X;
error=max(abs(Y-Y_check))

error =
9.2115e-015
Example 4
n=0:100
x=cos(pi*n/2)
K=-100:100
w=(pi/100)*k
m=n*k
X11=(exp(-j*pi/100)).^m
X=x*X11
subplot(211)
plot(w,abs(X))
y=exp(j*pi*n/4).*x
Y=y*X11
subplot(212)
plot(w,abs(Y))

Example 5
h=[1 -2 3 -2 1]
X=freqz(x,1,w)
H=freqz(h,1,w)
XP=X.



*H;
subplot(221)
plot(w/pi,abs(XP))
title(product of magnitude spectrum)
subplot(222)
plot(w/pi,angle(XP))
title(phase spectrum)
y=conv(x,h)
Y=freqz(y,1,w)
subplot(223)
plot(w/pi,abs(Y))
title(magnitude spectrum of convolved sequence)
subplot(224)
plot(w/pi,angle(Y))
title(phase of convolved sequence)

Questions:
1
x1=rand(1,11);
x2=rand(1,11);
alpha=2;
beta=3;
x3=alpha*x1+beta*x2
n=0:10;
k=0:500;
w=(pi/500)*k;
m=n*k
X11=(exp(-j*pi/500)).^m
X1=x1*X11
subplot(2, 1, 1)
plot(k,X1, r);
patronage on;
X2=x2*X11
plot(k,X2, b);
affirm on;
X3=x3*X11
plot(k,X3, g);
X_check=alpha*X1+beta*X2;
error=max(abs(X3-X_check))
subplot(2, 1, 2);
plot(k,X3, r);
hold on;
plot(k, X_check, b)
hold on;
plot(k, error,g)

2
X11=(exp(-j*pi/500)).^m
X=x*X11
y=x;
n_new=n+2;
m=n_new*k
X11=(exp(-j*pi/500)).^m
Y=y*X11;
subplot(2, 1, 1)
plot(k,X, r);
hold on;
plot(k,Y, b);
Y_check=exp(-j*2*w).*X;
error=max(abs(Y-Y_check))
subplot(2, 1, 2);
plot(k,Y, r);
hold on;
plot(k, Y_check, b)
hold on;
plot(k, error,g)If you want to get a full essay, order it on our website: Orderessay



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