Signal Processing

Running head: SIGNAL PROCESSING
SIGNAL PROCESSING
Name of the Student
Name of the University
Author Note

1SIGNAL PROCESSING
Part I: Double-SideBand AM
Exercise 1: Standard AM
Given, modulated signal is
s(t) = Ac[1 + ka*m(t)]cos(2*π*fc*t)
The information bearing signal is
m(t) = sinc(2(t-2)) – sinc(2(t+2))
The carrier signal is c(t) = Ac*cos(2πfct), Ac = 1 is the amplitude of carrier and fc = 50 Hz is
the carrier frequency.
a) The plot of signal m(t) and carrier c(t) is given below.
MATLAB code:
t = -4:0.001:3.999;
Ac = 1; fc = 50;
m = sinc(2.*(t-2)) - sinc(2.*(t+2));
c = Ac*cos(2*pi*fc.*t);
plot(t,m,'b-',t,c,'r-')
title('m(t) and c(t)')
legend('m(t)','c(t)')
xlabel('t')
ylabel('information signal and carrier signal amplitude')
zoom(2)

2SIGNAL PROCESSING
Plot:
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
t
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
information signal and carrier signal amplitude
m(t) and c(t)
m(t)
c(t)
b) The modulated waveforms for different values of Ac are obtained by the following
MATLAB codes.
MATLAB code:
ka = 1/2;
s = c.*(1+ka.*m);
figure(1)
plot(t,s)
xlabel('t')
title('modulated waveform for ka= 1/2')

3SIGNAL PROCESSING
zoom(2)
ka = 1;
s = c.*(1+ka.*m);
figure(2)
plot(t,s)
xlabel('t')
title('modulated waveform for ka= 1')
zoom(2)
ka = 2;
s = c.*(1+ka.*m);
figure(3)
plot(t,s)
xlabel('t')
title('modulated waveform for ka= 1')
zoom(2)
Plots:

4SIGNAL PROCESSING
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
t
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 modulated waveform for ka= 1/2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
t
-1
-0.5
0
0.5
1
modulated waveform for ka= 1

5SIGNAL PROCESSING
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
t
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2 modulated waveform for ka= 1
Clearly from the diagram it can be seen that the phase reversal occurs for ka = 1 at t = -2.
c)
The coherent receiver output at different amplitude sensitivities are obtained by the following
MATLAB code.
MATLAB code:
ka = 1/2;
s = (c.*(1+ka.*m)).*cos(2*pi*fc.*t);
[slp,tslp] = lowpass(s,t,fc);
figure(4)
plot(tslp,slp)
xlabel('t')