1. Electrical Communications Systems ECE.09.331 Spring 2008
Lecture 8a March 11, 2008
Shreekanth Mandayam
ECE Department
Rowan University

2. Plan SSB Angle Modulation Systems Hilbert Transform
Definitions - Phase and Frequency Modulation
Complex Envelope
Time Domain
Analyzing FM Signals - Battle Plan!!!!
Single-tone FM
Bessel Functions

3. ECOMMS: Topics

4. Single Sideband (SSB) Modulation
Recall: DSB-SC Spectrum
USSB - Signal with zero-valued spectrum for |f| < fc
LSSB - Signal with zero-valued spectrum for |f| > fc
-fc-B -fc fc+B fc-B fc fc+B
|S(f)| f

5. The Hilbert Transform time, t in sec -1 -0.5 0.5 1 1.5 2 3 4 5 6 7
0.5 1
1.5 2 3 4 5 6 7
time, t in sec
» t=0:0.1:2*pi;
» w=sin(t);
» plot(t,w)
» hold
Current plot held
» H=hilbert(w);
» plot(t,imag(H),'r');
» xlabel('time, t in sec')

6. SSB Generation S Phasing Method Filter Method m(t) s(t) m(t) s(t)
Product
Modulator
Carrier
-90o
Phase Shift
m(t) S
s(t)
Filter Method
Sideband
Filter
Carrier
Product
Modulator
m(t)
s(t)

7. SSB Generation: Weaver’s Method

8. Angle Modulation Systems
Phase Modulation (PM) Frequency Modulation(FM)
Instrument Demo
Signal Representation
Complex Envelope
Time Domain Representation
Terminology
Phase Sensitivity
Frequency Deviation
Instantaneous Frequency
Phase & Frequency Modulation Indices
Matlab Demo:
anglemod.m

9. Analyzing FM Signals - Battle Plan!!!
Instrument Demo
Signals Systems
Time Domain
Complex Envelope
Spectrum
Single-tone FM
Narrowband FM
Wideband FM
Bessel Functions
Power
Performance
Transmitters
Receivers
Standards
Modulation
Index
Efficiency
Bandwidth
Noise

10. Bessel Functions Matlab Demo » help besselj
BESSELJ Bessel function of the first kind.
J = BESSELJ(NU,Z) is the Bessel function of the first kind, J_nu(Z).The order NU need not be an integer, but must be real.The argument Z can be complex. The result is real where Z is positive.
» x=0:0.1:10;
» plot(x,besselj(0,x));
» title('Bessel Function of Order Zero, J_0(x)');
» xlabel('x');

11. Bessel Functions Matlab Demo Instrument Demo
%ECOMMS Spring 08 Classroom Demo
%S. Mandayam, ECE, Rowan University
clear;close all;
n=0:6;
beta=0:0.1:10;
Jn=besselj(n,beta');
plot(beta',Jn);
grid on;
xlabel('Frequency Modulation Index: \beta');
ylabel('J_n(\beta)');
legend('J_0(\beta)','J_1(\beta)','J_2(\beta)',
'J_3(\beta)','J_4(\beta)','J_5(\beta)','J_6(\beta)');
title('J_n(\beta): Spectral Amplitudes of an FM signal at f_c \pm nf_m');
Instrument Demo

12. FM Signal & Spectrum Single-tone FM Signal Single-tone FM Spectrum
fc-3fm fc-2fm fc-fm fc fc+fm fc+2fm fc+3fm
|S(f)| / (Ac/2) f
J0(b)
J1(b)
J2(b)
J3(b)

13. Summary