## EE 451

Plots for Problem 1.13 from Orfanidis

```fmin = 0;
fmax = 3;
df = (fmax-fmin)/10000;
f=fmin:df:fmax;
a = 0.2;
fo = 0.5;
fs1 = 1;
fs2 = 2;
T1 = 1/fs1;
T2 = 1/fs2;
Xf2 = 1./(a^2 + ((2*pi*(f-fo)).^2));
T1Xhf2 = T1^2./(1-2*exp(-a*T1)*cos(2*pi*(f-fo)*T1)+exp(-2*a*T1));
T2Xhf2 = T2^2./(1-2*exp(-a*T2)*cos(2*pi*(f-fo)*T2)+exp(-2*a*T2));
figure(1)
hold off
plot(f,20*log10(Xf2));
hold on
plot(f,20*log10(T1Xhf2),':');
plot(f,20*log10(T2Xhf2),'--');
axis([0 3 -30 30])
title('|X(f)|^2 and |T hat(X)(f)|^2')
xlabel('f (Hz)')
text(1.6,20,'fs = 1 Hz')
text(2.,-20,'fs = 2 Hz')
text(.7,-25,'Continuous')

L1 = 10;
T2XL1hf2=T2^2.*(1-2*exp(-a*T2*L1)*cos(2*pi*(f-fo)*T2*L1)+exp(-2*a*T2*L1))./ ...
(1-2*exp(-a*T2  )*cos(2*pi*(f-fo)*T2  )+exp(-2*a*T2  ));
figure(2)
hold off
plot(f,20*log10(Xf2),'--');
hold on
plot(f,20*log10(T2Xhf2),':');
plot(f,20*log10(T2XL1hf2));
axis([0 3 -30 30])
title('|X(f)|^2, |T hat(X)(f)|^2 and |T hat(X)_L(f)|^2, L = 10')
xlabel('f (Hz)')

L2 = 20;
T2XL2hf2=T2^2.*(1-2*exp(-a*T2*L2)*cos(2*pi*(f-fo)*T2*L2)+exp(-2*a*T2*L2))./ ...
(1-2*exp(-a*T2  )*cos(2*pi*(f-fo)*T2  )+exp(-2*a*T2  ));
figure(3)
hold off
plot(f,20*log10(Xf2),'--');
hold on
plot(f,20*log10(T2Xhf2),':');
plot(f,20*log10(T2XL2hf2));
axis([0 3 -30 30])
title('|X(f)|^2, |T hat(X)(f)|^2 and |T hat(X)_L(f)|^2, L = 20')
xlabel('f (Hz)')
```

Bill Rison, <rison@ee.nmt.edu >