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Electrical Communications Systems ECE.09.331 Spring 2007

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### Electrical Communications SystemsECE.09.331Spring 2007

Lecture 8bMarch 7, 2007

Shreekanth Mandayam

ECE Department

Rowan University

http://engineering.rowan.edu/~shreek/spring07/ecomms/

Plan

- Analyzing FM Signals - Battle Plan!!!!
- Single-tone FM
- Bessel Functions
- FM Spectra
- Power etc.
- Digital Communications
- Introduction
- Digital Communications Transceiver (CODEC/MODEM)

Angle Modulation Systems

- Signal Representation
- Complex Envelope
- Time Domain Representation
- Terminology
- Phase Sensitivity
- Frequency Deviation
- Instantaneous Frequency
- Phase & Frequency Modulation Indices

Phase Modulation (PM) Frequency Modulation(FM)

Instrument Demo

Matlab Demo:

anglemod.m

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

Analyzing FM Signals - Battle Plan!!!Instrument Demo

Bessel’s Differential Equation

- German mathematician and astronomer Friedrich Wilhelm Bessel (1784 - 1846)
- Discovered this equation while investigating planetary motion
- 2nd order ODE, Nonlinear, Variable Coefficients, Homogeneous
- Very important in applied mathematics and engineering
- Governing equation for problems with cylindrical geometries, e.g. waveguides, vibrating strings, and …………!!!!!!!

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');

»

Bessel Functions

Matlab Demo

%ECOMMS Spring 07 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');

http://engineering.rowan.edu/~shreek/spring07/ecomms/demos/besselfun.m

Instrument Demo

J1(b)

|S(f)| / (Ac/2)

J2(b)

J3(b)

J0(b)

0fc-3fm fc-2fm fc-fm fc fc+fm fc+2fm fc+3fm

f

FM Signal & SpectrumSingle-tone FM Signal

Single-tone FM Spectrum

Digital Communications

- Some Milestones
- Claude Shannon, 1948
- X.25 (Telephony)
- IEEE 802.3 (Ethernet)
- ARPANET, 1969
- IEEE 802.5 (FDDI)
- ISO-OSI 7-layer Network Reference Model
- CDMA
- GSM
- VOIP
- SIP

protocols.com

Digital Communications: Rationale

- Information Theory:
- What is the fundamental limit on the compression and refinement of information generated by the source?
- What is the fundamental limit on the transmission rate of information over a noisy channel?
- How do we approach these limits?

Principle

Digital message

1 1

1 0 1 0………

0 0

Digital

code

Analog

message

modulate

1 0 1 0

Sinusoidal carrier

AM

FM

PM

AM &

PM

Message 1

Message 1

Multiplexer

2

Demultiplexer

1

2

3

1

S

2

3

S

Message 2

Message 2

Message 3

Message 3

3

H

H

1

Depacket-izing

Message 1

2

H

Message 1

3

H

H

1

Depacket-izing

Packetizing

Message 2

Message 2

2

H

3

H

Message 3

Depacket-izing

H

1

Message 3

2

H

Digital Communication ParadigmsCircuit Switching

Sync bits

Packet Switching

Header

bits

Digital Communications Transceiver

Anti-

aliasing

Filter

Error

Control

Encoder

Data

Encryption

Encoder

Channel/

Line

Encoder

Source

Encoder

Sampling

Quantization

Modulator

MUX

ADC

Analog i/p

CODEC

MODEM

Multiple access channel

Analog o/p

Error

Control

Decoder

Data

Encryption

Decoder

Source

Decoder

Audio

Amp

Reconstruction/

DAC

Equalization /

Decision

Circuits

Demod-ulator

DEMUX

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