 Signals and Systems  What is a signal?  Signal Basics  Analog / Digital Signals  Real vs Complex  Periodic vs. Aperiodic  Bounded vs. Unbounded  Causal vs. Noncausal  Even vs. Odd  Power vs. Energy

1. EE344 Communication Systems

2. Outline
 Signals and Systems
2
 Signals and Systems
 What is a signal?
 Signal Basics
 Analog / Digital Signals
 Real vs Complex
 Periodic vs. Aperiodic
 Bounded vs. Unbounded
 Causal vs. Noncausal
 Even vs. Odd
 Power vs. Energy
 What is a communications
system?
 Block Diagram
 Why go to higher frequencies?
 Telecommunication
 Wireless Communication
 Another Classification of
Signals (Waveforms)
 Power, Distortion, Noise
 Shannon Capacity
 How transmissions flow over
media
 Coaxial Cable
 Unshielded Twisted Pair
 Glass Media
 Wireless
 Connectors
 The Bands

3.  Signals are variables that carry information
 System is an assemblage of entities/objects, real or abstract,
comprising a whole with each every component/element
interacting or related to another one.
Systems process input signals to produce output signals
Signal and System
3
 Examples
i. Motion, sound, picture, video, traffic light…
ii. Natural system (ecosystem), human-made system
(machines, computer storage system), abstract system
(traffic, computer programs), descriptive system (plans)

4. Signal Examples
4
 Electrical signals --- voltages and currents in a
circuit
 Acoustic signals --- audio or speech signals
(analog or digital)
 Video signals --- intensity variations in an image
(e.g. a CAT scan)
 Biological signals --- sequence of bases in a gene
 Noise: unwanted signal
:

5. Measuring Signals
5
-0.2
-0.4
-0.6
-0.8
-1
1
0.8
0.6
0.4
0.2
0 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 463 484 505 526 547 568 589 610 631 652 673 694 715
Period
Amplitude

6. Definitions
6
 Voltage – the force which moves an electrical current
against resistance
 Waveform – the shape of the signal (previous slide is a
sine wave) derived from its amplitude and frequency over
a fixed time (other waveform is the square wave)
 Amplitude – the maximum value of a signal, measured
from its average state
 Frequency (pitch) – the number of cycles produced in a
second – Hertz (Hz). Relate this to the speed of a
processor eg 1.4GigaHertz or 1.4 billion cycles per second

7. Signal Basics
7
 Continuous time (CT) and discrete time (DT) signals
CT signals take on real or complex values as a function of an independent
variable that ranges over the real numbers and are denoted asx(t).
DT signals take on real or complex values as a function of anindependent
variable that ranges over the integers and are denoted asx[n].
Note the subtle use of parentheses and square brackets to distinguishbetween
CT and DT signals.

8. Analog Signals
 Human Voice – best example
 Ear recognises sounds 20KHz or less
 AM Radio – 535KHz to 1605KHz
 FM Radio – 88MHz to 108MHz
8

9. Digital signals
9
 Represented by Square Wave
 All data represented by binary values
 Single Binary Digit – Bit
 Transmission of contiguous group of bits is a bit
stream
 Not all decimal values can be represented by
binary
1 0 1 0 1 0 1 0

10. Analogue vs. Digital
10
Analogue Advantages
 Best suited for audio and video
 Consume less bandwidth
 Available world wide
 Less susceptible to noise
Digital Advantages
 Best for computer data
 Can be easily compressed
 Can be encrypted
 Equipment is more common and less expensive
 Can provide better clarity

11. Analog or Digital
11
 Analog Message: continuous in amplitude and over
time
 AM, FM for voice sound
 Traditional TV for analog video
 First generation cellular phone (analog mode)
 Record player
 Digital message: 0 or 1, or discrete value
 VCD, DVD
 2G/3G cellular phone
 Data on your disk
 Your grade
 Digital age: why digital communication will prevail

12. A/D and D/A
12
 Analog to Digital conversion; Digital to Analog
conversion
 Gateway from the communication device to the
channel
 Nyquist Sampling theorem
 From time domain: If the highest frequency in the
signal is B Hz, the signal can be reconstructed from
its samples, taken at a rate not less than 2B samples
per second

13.  Quantization
 From amplitude domain
 N bit quantization, L intervals L=2N
 Usually 8 to 16 bits
 Error Performance: Signal to noise ratio
A/D and D/A
13

14. Real vs. Complex
Q. Why do we deal with comple1x4signals?
A. They are often analytically simpler to deal with than real signals,
especially in digital communications.

15. Periodic vs. Aperiodic Signals
15
 Periodic signals have the property that x(t + T) = x(t) for all t.
 The smallest value of T that satisfies the definition is calledthe
period.
 Shown below are an aperiodic signal (left) and a periodicsignal
(right).

16.  A causal signal is zero for t < 0 and an non-causal signal iszero
for t > 0
Causal vs. Non-causal
16
 Right- and left-sided signals
A right-sided signal is zero for t < T and a left-sided signal iszero
for t > T where T can be positive or negative.

17. Bounded vs. Unbounded
 Every system is bounded, but meaningful signal is always
bounded
17

18. Even vs. Odd
18
 Even signals xe(t) and odd signals xo(t) are defined as
xe(t) = xe(−t) and xo(t) = −xo(−t).
 Any signal is a sum of unique odd and even signals. Using
x(t) = xe(t)+xo(t) and x(−t) = xe(t) − xo(t), yields xe(t)
=0.5(x(t)+x(−t)) and xo(t) =0.5(x(t) − x(−t)).

19. Signal Properties: Terminology
19
 Waveform
 Time-average operator
 Periodicity
 DC value
 Power
 RMS Value
 Normalized Power
 Normalized Energy

20. Power and Energy Signals
 Energy Signal
20
 Power Signal
 Infinite duration
 Normalized power is
finite and non-zero
 Normalized energy
averaged over
infinite time is
infinite
 Mathematically
tractable
 Finite duration
 Normalized energy is
finite and non-zero
 Normalized power
averaged over
infinite time is zero
 Physically realizable
• Although “real” signals are energy signals, we
analyze them pretending they are power signals!

21. The Decibel (dB)
21
 Measure of power transfer
 1 dB = 10 log10 (Pout / Pin)
 1 dBm = 10 log10 (P / 10-3) where P is inWatts
 1 dBmV = 20 log10 (V / 10-3) where V is inVolts

22. Communication System
A B
Engineering System
Social System
22
Genetic System
History and fact of communication

23. What is a communications system?
 Communications Systems: Systems designed
to transmit and receive information
23
Info
Source
Info
Sink
Comm
System

24. Block Diagram
m(t)
message
from
source
Info
Source
n(t)
noise
24
Receiver
Rx
sink
m~(t)
received
message
to
Transmitter
Tx s(t)
transmitted
signal
Channel
r(t)
received
signal
Info
Sink

25. Telecommunication
25
 Telegraph
 Fixed line telephone
 Cable
 Wired networks
 Internet
 Fiber communications
 Communication bus inside computers to
communicate between CPU and memory

26. Wireless Comm. Evolution: UMTS (3G)
26
http://www.3g-generation.com/
http://www.nttdocomo.com/reports/010902_ir_presentation_january.pdf

27. Wireless Communications
27
 Satellite
 TV
 Cordless phone
 Cellular phone
 ireless LAN, WIF
 Wireless MAN, WIMAX
 Bluetooth
 Ultra Wide Band
 Wireless Laser
 Microwave
 GPS
 Ad hoc/Sensor Networks

28. Comm. Sys. Bock Diagram
m~(t)Tx
s(t)
Channel
r(t)
m(t) Rx
Baseband Baseband
28
Noise
Signal Signal
Bandpass
Signal• “Low” Frequencies
• <20 kHz
• Original data rate
• “High” Frequencies
• >300 kHz
• Transmission data rate
Modulation
Demodulation
or
Detection
Formal definitions will be provided later

29. Aside: Why go to higher frequencies?
Tx /2
29
Half-wave dipole antenna
c = f 
c = 3E+08 ms-1
Calculate  for
f = 5 kHz
f = 300 kHz
There are also other reasons for going from baseband tobandpass

30. Another Classification of Signals (Waveforms)
 Deterministic Signals: Can be modeled as a
completely specified function of time
30
 Random or Stochastic Signals: Cannot be
completely specified as a function of time; must
be modeled probabilistically
 What type of signals are information bearing?

31. Power, Distortion, Noise
31
 Transmit power
 Constrained by device, battery, health issue, etc.
 Channel responses to different frequency and different time
 Satellite: almost flat over frequency, change slightly over time
 Cable or line: response very different over frequency, change
slightly over time.
 Fiber: perfect
 Wireless: worst. Multipath reflection causes fluctuation in
frequency response. Doppler shift causes fluctuation over time
 Noise and interference
 AWGN: Additive White Gaussian noise
 Interferences: power line, microwave, other users (CDMA phone)

32. Shannon Capacity
32
 Shannon Theory
 It establishes that given a noisy channel with information capacity
C and information transmitted at a rate R, then if R<C, there exists
a coding technique which allows the probability of error at the
receiver to be made arbitrarily small. This means that
theoretically, it is possible to transmit information without error
up to a limit, C.
 The converse is also important. If R>C, the probability of error at
the receiver increases without bound as the rate is increased. So no
useful information can be transmitted beyond the channel
capacity. The theorem does not address the rare situation in which
rate and capacity are equal.
 Shannon Capacity
bit /sC  Blog2 (1 SNR)

33. How transmissions flow over media
33
 Simplex – only in one direction
 Half-Duplex – Travels in either direction, but not
both directions at the same time
 Full-Duplex – can travel in either direction
simultaneously

34. Coaxial Cable
34
•First type of networking
media used
•Available in different
types (RG-6 – Cable TV,
RG58/U – Thin Ethernet,
RG8 – Thick Ethernet
•Largely replaced by
twisted pair for networks

35. Unshielded Twisted Pair
35
 Advantages
 Inexpensive
 Easy to terminate
 Widely used, tested
 Supports many network
types
 Disadvantages
Susceptible to interference
Prone to damage during
installation
Distance limitations not
understood or followed

36. Glass Media
• Core of silica, extruded glass or plastic
• Single-mode is 0.06 of a micron in diameter
• Multimode = 0.5 microns
• Cladding can be Kevlar, fibreglass or even steel
• Outer coating made from fire-proof plastic
36
 Advantages
 Can be installed over long distances
 Provides large amounts of
bandwidth
 Not susceptible to EMI RFI
 Can not be easily tapped (secure)
 Disadvantages
 Most expensive media to
purchase and install
 Rigorous guidelines for
installation

37. Wireless
37

38. Wireless (2)
38
 Radio transmits at 10KHz to 1KHz
 Microwaves transmit at 1GHz to 500GHz
 Infrared transmits at 500GHz to 1THz
 Radio transmission may include:
 Narrow band
 High-powered
 Frequency hopping spread spectrum (the hop is controlled
by accurate timing)
 Direct-sequence-modulation spread spectrum (uses
multiple frequencies at the same time, transmitting data in
‘chips’ at high speed)

39. Connectors
39
Fibre Optic
Thicknet
RJ45
T-Piece
Token Ring

41. The Bands
MF HF VHF UHF SHF EHF
Submillimeter
Range
ELF VLF LF
Far
Infra-
Red
41
3KHz 30KHz300KHz 3MHz 30MHz300MHz 3GHz 30GHz 300GHz 3THz
Radio Optical
Near
Infra-
Red
700nm
1PetaHz
R
e
d
O
r
a
n
g
e
Y
e
l
l
o
w
G
r
e
e
n
B
l
u
e
I
V
n i
d o
i l
g e
o t
600nm 400nm500nm
Ultraviolet
1ExaHz
300m1500nm

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The ITU radio bands are designations defined in the ITU Radio
Regulations. Article 2, provision No. 2.1 states that "the radio
spectrum shall be subdivided into nine frequency bands, which shall
be designated by progressive whole numbers in accordance with the
following table[2]".
The table originated with a recommendation of the IVth CCIR meeting,
held in Bucharest in 1937, and was approved by the International
Radio Conference held at Atlantic City in 1947. The idea to give each
band a number, in which the number is the logarithm of the
approximate geometric mean of the upper and lower band limits in Hz,
originated with B.C. Fleming-Williams, who suggested it in a letter to
the editor of Wireless Engineer in 1942. (For example, the
approximate geometric mean of Band 7 is 10 MHz, or 107 Hz.)[3]

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