Question

b b had a) Corle (atoul itpeuts

Solve using matlab
And solve by hand

Answer 1

Q2)

Hand calculation:

dd post

MATLAB

Function script

function y=xplt(t)
y=((sin(2*pi*100*t))+(cos(2*pi*100*t)))
end

Main script
clc;close all;clear all;
T=0.01
t=-T:T/500:T
x=xplt(t)

figure(1)
subplot(321)
plot(t,x,'linewidth',3)
xlabel('t');ylabel('x(t)')
title('x(t)')

subplot(322)
plot(t,xplt(-t),'g','linewidth',3)
xlabel('t');ylabel('x(-t)')
title('x(-t)')

xe=(xplt(t)+xplt(-t))/2
subplot(323)
plot(t,xe,'r','linewidth',3)
xlabel('t');ylabel('xe(t)')
title('Even part of x(t)')

xo=(xplt(t)-xplt(-t))/2
subplot(324)
plot(t,xo,'m','linewidth',3)
xlabel('t');ylabel('xo(t)')
title('Odd part of x(t)')

%from hand calculation
xe=cos(2*pi*100*t)
subplot(325)
plot(t,xe,'r','linewidth',3)
xlabel('t');ylabel('xe(t)')
title('Even part of x(t) from hand calculation')

xo=sin(2*pi*100*t)
subplot(326)
plot(t,xo,'m','linewidth',3)
xlabel('t');ylabel('xo(t)')
title('Odd part of x(t) from hand calculation')

x(t) x(-t) VV.VVI 0.5 0.5 -0.5 1.5 -0.01 0.005 0.005 0.01 0.0 0.005 0.005 0.01 Even part of x(t) Odd part of x(t) 0.5 0.5 0.5 0.005 0.01 0.01 -0.005 0.005 0.01 0.0 0.005 Even part of x(t) from hand calculation Odd part of x(t) from hand calculation 0.5 0.5 -0.5 0.005 0.005 0.01 0.0 0.005 0.005 0.01 -0.01

Observation:

The results of hand calculations and the results provided by matlab both are same.

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Q3)

MATLAB:

clc;close all; clear all;
t=0:0.1:3
h=ones(1,length(t))
x=(exp(-t)).*(t>=0)
subplot(231)
plot(t,x)
xlabel('t');ylabel('x(t)');title('x(t)')

subplot(232)
stem(t,h)
xlabel('t');ylabel('h(t)');title('h(t)')

m=0:0.1:6
y=conv(x,h)
subplot(233)
plot(m,y/10)
xlabel('t');ylabel('y(t)');title('y(t)')

k=0
for w=0:pi/500:pi
k=k+1
Xw(k)=trapz(t,x.*exp(-j*w*t))
end
w=0:pi/500:pi
subplot(234)
plot(w/pi,Xw)
xlabel('w');ylabel('|X(jw)|');title('X(jw)')

k=0
for w=0:pi/500:pi
k=k+1
Hw(k)=trapz(t,h.*exp(-j*w*t))
end
w=0:pi/500:pi
subplot(235)
plot(w/pi,Hw)
xlabel('w');ylabel('|H(jw)|');title('H(jw)')

Yw=Xw.*Hw
k=0
for m=0:0.1:6
k=k+1
yy(k)=trapz(w,Yw.*exp(j*w*m))
end
yy=yy/(2*pi)
m=0:0.1:6
subplot(236)
plot(m,yy)
xlabel('t');ylabel('y(t)');title('y(t) from inverse FT')

x(t) y(t) h(t) 0.8 0.8 0.6 0.6 0.8 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 H(jw) y(t) from inverse FT X(jw) 0.6 3 0.5 0.8 2 0.4 0.6 0.3 0.4 0.2 0.2 0 0.2 0.4 0.6 0.81 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6