Pri rinciples nciples of of Com ommunications munications EC - - PowerPoint PPT Presentation

1

Pri rinciples nciples of

• f Com
• mmunications

munications

EC ECS S 332 32

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

Introduction

Office Hours: BKD 3601-7 Monday 14:40-16:00 Friday 14:00-16:00

Course Organization

2

 Course Website:

http://www2.siit.tu.ac.th/prapun/ecs332/

 Lectures:

 Wednesday 09:00-10:20 BKD 3206  Friday

10:40-12:00 BKD 3206

 Textbook: Communication Systems: An Introduction to

Signals and Noise in Electrical Communication

 By A. Bruce Carlson and Paul B. Crilly  5th International edition  Call No. TK5102.5 C3 2010  ISBN: 978-007-126332-0

1

Pri rinciples nciples of

• f Com
• mmunications

munications

EC ECS S 332 32

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

• 1. Intro to comm. system

Office Hours: BKD 3601-7 Monday 14:40-16:00 Friday 14:00-16:00

3

“The fundamental problem of

communication is that of reproducing at one point

either exactly or approximately a message selected at another point.”

Shannon, Claude. A Mathematical Theory Of

• Communication. (1948)

• C. E. Shannon (1916-2001)

4

 1938 MIT master's thesis: A Symbolic

Analysis of Relay and Switching Circuits

 Insight: The binary nature of Boolean

logic was analogous to the ones and zeros used by digital circuits.

 The thesis became the foundation of

practical digital circuit design.

 The first known use of the term bit to

refer to a “binary digit.”

 Possibly the most important, and also the

most famous, master's thesis of the century.

 It was simple, elegant, and important.

• C. E. Shannon (Con’t)

5

 1948: A Mathematical

Theory of Communication

 Bell System Technical Journal,

• vol. 27, pp. 379-423, July-

October, 1948.

 September 1949: Book

• published. Include a new

section by Warren Weaver that applied Shannon's theory to human communication.

 Create the architecture and

concepts governing digital communication.

 Invent Information Theory:

Simultaneously founded the subject, introduced all of the major concepts, and stated and proved all the fundamental theorems.

A Mathematical Theory of Communication

6

 Link posted in the

“references” section of the website.

[An offprint from the Bell System Technical Journal]

Shannon - Father of the Info. Age

7

[http://www.youtube.com/watch?v=z2Whj_nL-x8]

Claude E. Shannon Award

8

Claude E. Shannon (1972) David S. Slepian (1974) Robert M. Fano (1976) Peter Elias (1977) Mark S. Pinsker (1978) Jacob Wolfowitz (1979) W . Wesley Peterson (1981) Irving S. Reed (1982) Robert G. Gallager (1983) Solomon W . Golomb (1985) William L. Root (1986) James L. Massey (1988) Thomas M. Cover (1990) Andrew J. Viterbi (1991) Elwyn R. Berlekamp (1993) Aaron D. Wyner (1994)

• G. David Forney, Jr. (1995)

Imre Csiszár (1996) Jacob Ziv (1997) Neil J. A. Sloane (1998) Tadao Kasami (1999) Thomas Kailath (2000) Jack Keil Wolf (2001) Toby Berger (2002) Lloyd R. Welch (2003) Robert J. McEliece (2004) Richard Blahut (2005) Rudolf Ahlswede (2006) Sergio Verdu (2007) Robert M. Gray (2008) Jorma Rissanen (2009) Te Sun Han (2010) Shlomo Shamai (Shitz) (2011)

Information Theory

9

The science of information theory tackles the following questions [Berger]

1.

What is information, i.e., how do we measure it quantitatively?

2.

What factors limit the reliability with which information generated at one point can be reproduced at another, and what are the resulting limits?

3.

How should communication systems be designed in order to achieve or at least to approach these limits?

Basic elements of communication

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 Information source: produce a message  Transmitter: operate on the message to create a signal

which can be sent through a channel

Noise Source

Receiver

Transmitter Information Source

Destination

Channel

Received Signal Transmitted Signal Message Message

Basic elements (2)

11

 Channel: the medium over which the signal, carrying the

information that composes the message, is sent

 Receiver: transform the signal back into the message

intended for delivery

Noise Source

Receiver

Transmitter Information Source

Destination

Channel

Received Signal Transmitted Signal Message Message

Basic elements (3)

12

 Destination: a person or a machine, for whom or which

the message is intended

Noise Source

Receiver

Transmitter Information Source

Destination

Channel

Received Signal Transmitted Signal Message Message

Digital Communication

13

Source Encoder Channel Encoder Channel Channel Decoder Source Decoder

010100 010100 Binary Interface

Input Output

Take the bits from one place to another. Binary data stream (sequence of data) without meaning (from channel viewpoint). This is the major layering of all digital communication systems. Know the probabilistic structure of the input source. + noise & interference Waveform  sequence  symbols  bits

References

14

 A Brief History of Communications: IEEE

Communications Society - a fifty-year foundation for the future

 ประวัติย่อ "การสื่อสารโลก": ห้าสิบปีชมรมไฟฟ้า

สื่อสาร—รากฐานสู่อนาคต

 Thai Telecommunications Encyclopedia

(สารานุกรม โทรคมนาคมไทย)

 Links posted in the “references” section of

the website.

1

Pri Principles of Comm nciples of Communi unications cations

EC ECS 332 S 332

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

• 2. Frequency-Domain Analysis

Office Hours: BKD 3601-7 Monday 14:40-16:00 Friday 14:00-16:00

The Most Beautiful Equation

2

7 Equations

3

that changed the world … and still rule everyday life

4

What’s wrong with this picture?

5

Fourier Transform in Auditory System

6

Human Audiogram (Audibility Curve) [http://psyc254.uconn.edu/Lecture18/]

Approximate best frequencies of various places along the basilar membrane, in hertz. Schematic showing the cochlea unrolled, in cross-section.

[Schnupp, Nelken, and King, 2010, Fig 2.2] [Schnupp, Nelken, and King, 2010, Fig 2.1] [Schnupp, Nelken, and King, 2010, Fig 2.2]

The cochlea has sometimes been described as a biological Fourier analyzer.

Spectrum of Digital Data (1/4)

7

   

1 0, c t A t T       

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 0.2 0.4 0.6 0.8 1 f [Hz]

 

C f

A T t

 

1, 1 A T  

t A

• A

m = [-1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1]

 

s t

Can you sketch the spectrum of s(t)?

Spectrum of Digital Data (2/4)

8

   

1 0, c t A t T       

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 0.2 0.4 0.6 0.8 1 f [Hz]

 

C f

A T t

 

1, 1 A T  

t A

• A

m = [-1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1]

 

s t

   

1 n k k

s t m c t kT

 

 



 

This is also the spectrum of for any . c t kT k 

Spectrum of Digital Data (3/4)

9

   

1 0, c t A t T       

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 0.2 0.4 0.6 0.8 1 f [Hz]

 

C f

A T t

 

1, 1 A T  

t A

• A

m = [-1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1]

 

s t

   

1 n k k

s t m c t kT

 

 



   

1 2 n j fkT k k

S f C f m e

   

  



 

This is also the spectrum of for any . c t kT k 

Spectrum of Digital Data (4/4)

10

       

1 1 2 n n j fkT k k k k

s t m c t kT S f C f m e

     

    

 

   

1 0, c t A t T       

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 2 4 6 8 10 f [Hz]

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 0.2 0.4 0.6 0.8 1 f [Hz]

 

C f

 

S f

A T t

 

1, 1 A T  

t A

• A

m = [-1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1]

 

s t

 

This is also the spectrum of for any . c t kT k 

Example: Convolution

11

Important Formulas

12

                             

2 2 2 2 2

1 1 cos 2 2 2 cos sin 2cos 1 cos 2 2sin 1 cos 2 1 1 cos 2 2 2

j ft j j j j ft j f t c c c c c c

G f e j x x x x g t t e G f e g g t e dt f t f t G f f m t f t M f f f f e f f f M e

     

      

     

               



(Will be provided on the midterm)

1

Pri Principles of Comm nciples of Communi unications cations

EC ECS 332 S 332

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

• 3. Modulation

Office Hours: BKD 3601-7 Monday 14:40-16:00 Friday 14:00-16:00

Frequency-Domain Analysis

2

Modulation:  

     

1 1 cos 2 2 2

c c c

m t f t M f f M f f    

Shifting Properties: 

  

2 j ft

g t t e G f

 



   

2 j f t

e g t G f f





Test Signal

3

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

𝑦 𝑢 = cos 𝑢 − 1 3 cos 3𝑢 + 1 5 cos 5𝑢 𝑦 𝑢 𝑧 𝑢 = ℎ 𝑢 ∗ 𝑦(𝑢) ℎ 𝑢

Distortion: Low Frequency Attenuation

4

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

𝑦 𝑢 = cos 𝑢 − 1 3 cos 3𝑢 + 1 5 cos 5𝑢 𝑧 𝑢 = 1 2 cos 𝑢 − 1 3 cos 3𝑢 + 1 5 cos 5𝑢

Distortion: High Frequency Attenuation

5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

𝑦 𝑢 = cos 𝑢 − 1 3 cos 3𝑢 + 1 5 cos 5𝑢 𝑧 𝑢 = cos 𝑢 − 1 3 cos 3𝑢 + 1 2 1 5 cos 5𝑢

Distortion: Constant Phase Shift

6

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

𝑦 𝑢 = cos 𝑢 − 1 3 cos 3𝑢 + 1 5 cos 5𝑢 𝑧 𝑢 = cos 𝑢 +  2 − 1 3 cos 3𝑢 +  2 + 1 5 cos 5𝑢 +  2 Components of the distorted signal all attain maximum or minimum values at the same time.

Surprising fact: an untrained human ear is curiously insensitive to phase distortion. The waveforms above would sound just about the same when driving a loudspeaker. Thus, phase distortion is seldom of concern in voice and music transmission.

Linear Phase Shift

7

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

• 10
• 5

5 10

• 1.5
• 1
• 0.5

0.5 1 1.5

𝑦 𝑢 = cos 𝑢 − 1 3 cos 3𝑢 + 1 5 cos 5𝑢 Same as time-shift!  

1 1 cos cos 3 3 cos 5 5 2 3 2 5 2 1 1 cos cos 3 cos 5 2 3 2 5 2 2 y t t t t t t t x t                                                                           

Multipath Propagation

8

 In a wireless mobile communication system, a transmitted

signal propagating through the wireless channel often encounters multiple reflective paths until it reaches the receiver

 We refer to this phenomenon as multipath propagation

and it causes fluctuation of the amplitude and phase of the received signal.

 We call this fluctuation multipath fading. Remark: Reflections due to mismatched impedance on a cable system produce the same effect

Similar Problem: Ghosting

9

Wireless Comm. and Multipath Fading

10

           

v i i i

r t x t h t n t x t n t  



     



• 1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

• 1
• 0.8
• 0.6
• 0.4
• 0.2

   

v i i i

h t t   



 



         

1

0.5 0.2 0.2 0.3 0.3 0.1 0.5

s s s

h t t t T t T t T           

         

2

0.5 0.2 0.7 0.3 1.5 0.1 2.3

s s s

h t t t T t T t T           

• 1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

The signal received consists of a number of reflected rays, each characterized by a different amount of attenuation and delay.

ISI (Intersymbol Interference)

Frequency Domain

11

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 f |H1(f)| 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 f |P(f)| 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.5 1 1.5 f |H2(f)|

The transmitted signal (envelope) Channel with weak multipath Channel with strong multipath

Electromagnetic Spectrum

1

[Gosling , 1999, Fig 1.1]

c f  

Wavelength Frequency

8

3 10 m/s 

Radio-frequency spectrum

2

 Commercially exploited bands c f  

Wavelength Frequency

8

3 10 m/s 

[http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum]

Note that the freq. bands are given in decades; the VHF band has 10 times as much frequency space as the HF band.

Cellular Bands

3

 All cellular phone networks worldwide use a portion of the radio

frequency spectrum designated as ultra high frequency (UHF) (300 MHz to 3 GHz)

 The UHF band is also used for television, Wi-Fi and Bluetooth

transmission.

 Due to historical reasons, radio frequencies used for cellular

networks differ in the Americas, Europe, and Asia.

 Frequency bands recommended by ITU-R (in June 2003) for

terrestrial Mobile telecommunication IMT-2000:

 806-960 MHz  1710-2025 MHz  2110-2200 MHz  2500-2690 MHz

Lower limits on radio use

4

 Efficiency of an antenna in radiating radio energy is

dependent on its length expressed as a fraction of wavelength.

 Too low frequency = too large antenna

 Ex. The “Sanguine” submarine communication system

 30 Hz (10,000 km wavelength)  Designed (but never built) for the US Navy  Base antenna: 24 km square mesh of wires.  10MW RF input

 Radiate only 147 W  All the remainder of the power dissipates as heat.

[Gosling, 1999, p 11]

Upper limits on radio use

5

 Atmospheric absorption  Quasi-optical propagation

 Short wavelength = Deep

shadows behind obscuring

• bjects = Unreliable

coverage.

 Increased absorption by

building and structural materials

[Gosling , 1999, Fig 1.1]

14 dB/km @ 60 GHz Make commu. very dependent on weather conditions

(terrestrial propagation)

6

Thailand Freq. Allocations Chart

7

http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm

Spectrum Allocation

8

 Spectral resource is limited.  Most countries have government agencies responsible for

allocating and controlling the use of the radio spectrum.

 Commercial spectral allocation is governed

 globally by the International Telecommunications Union (ITU)

 ITU Radiocommunication Sector (ITU-R) is responsible for radio

communication.  in the U.S. by the Federal Communications Commission (FCC)  in Europe by the European Telecommunications Standards Institute

(ETSI)

 in Thailand by the National Telecommunications Commission

(NTC; คณะกรรมการกิจการโทรคมนาคมแห่งชาติ; กทช.)

 replaced by the National Broadcasting and Telecommunications Commission

(NBTC; คณะกรรมการกิจการกระจายเสียง กิจการโทรทัศน์และกิจการโทรคมนาคมแห่งชาติ ; กสทช.)

 Blocks of spectrum are now commonly assigned through spectral

auctions to the highest bidder.

Interesting Book

9

 Spectrum Wars: The Policy and

Technology Debate

“Designed to help you ensure that your company wins the battle for the spectrum, this text maps out the strategies required for structuring entry and operations in the spectrum. It offers advice on how to master the lobbying, technical, regulatory, legal and political tools needed for success.”

[Manner, 2003]

News: LightSquared vs. GPS industry

10

 In Jan 2011, the FCC recently granted a conditional waiver to

LightSquared allowing the expansion of terrestrial use (for launching a new LTE network) of the mobile satellite spectrum (MSS) immediately neighboring that of the GPS

 As its name suggested, MSS has been reserved for satellite services  Earlier, FCC permitted “ancillary” terrestrial uses intended to “fill in”

locations where satellite coverage was problematic.

 The new order allows a high powered nationwide terrestrial

broadband network.

 Extremely high-powered ground-based transmissions could

potentially cause severe interference to GPS receivers.

 LightSquared bought the spectrum right next door to GPS

cheaply, hoping to change the rules and make the spectrum more valuable.

[GPS World, December 2011]

11

RNSS L1 L1

Completely Separated?

12

 GPS receivers have filters that do not block signals from the

MSS band.

 These filters has enabled both low-cost and high-precision

GPS receivers.

 Assumption: Signals in MSS band were low-power.

Spectrum Allocation (Final Words)

13

 Spectrum is a scarce resource.  Spectrum is allocated in “chunks” in frequency domain.

 “Chunks” are licensed to (cellular/wireless) operators.

 Within a single cellular operator, the chunk is further divided

into many channels.

 Each channel has its own band of frequency.

1

Pri rinciples nciples of

• f Com
• mmunications

munications

EC ECS S 332 32

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

• 4. Amplitude Modulation

Office Hours: BKD 3601-7 Monday 14:40-16:00 Friday 14:00-16:00

DSB-SC

2

1 2 3 4 5 6 7 8 9

• 1
• 0.5

0.5 1 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude 1 2 3 4 5 6 7 8 9

• 2
• 1

1 2 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude 1 2 3 4 5 6 7 8 9

• 1
• 0.5

0.5 1 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.05 0.1 0.15 0.2 Frequency [Hz] Magnitude 1 2 3 4 5 6 7 8 9

• 1
• 0.5

0.5 1 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude

DSB-SC with Switching Demodulator

3

1 2 3 4 5 6 7 8 9

• 1
• 0.5

0.5 1 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude 1 2 3 4 5 6 7 8 9

• 1
• 0.5

0.5 1 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.05 0.1 0.15 0.2 Frequency [Hz] Magnitude 1 2 3 4 5 6 7 8 9

• 2
• 1

1 2 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.05 0.1 0.15 0.2 Frequency [Hz] Magnitude 1 2 3 4 5 6 7 8 9

• 0.5

0.5 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.05 0.1 0.15 0.2 Frequency [Hz] Magnitude

DSB-SC with Switching Demodulator

4

1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005

• 0.5

0.5 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude 1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005

• 1
• 0.5

0.5 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude 1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005

• 1
• 0.5

0.5 1 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.05 0.1 0.15 0.2 Frequency [Hz] Magnitude 1 1.0005 1.001 1.0015 1.002 1.0025 1.003 1.0035 1.004 1.0045 1.005

• 0.5

0.5 Seconds

• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 x 10

0.1 0.2 0.3 0.4 Frequency [Hz] Magnitude

(Zoomed in)

1

Pri rinciples nciples of

• f Com
• mmunications

munications

EC ECS S 332 32

• Dr. Prapun Suksompong

prapun@siit.tu.ac.th

• 7. Angle Modulation

Office Hours: BKD 3601-7 Monday 14:40-16:00 Friday 14:00-16:00

Instantaneous Frquency

2

 

 

2 1

cos 2 x t t t  

1 2 3 4 1  0.5  0.5 1 1 1  x1 t ( ) 4 t

At t = 2, frequency = ?

Instantaneous Frquency

3

 

 

2 1

cos 2 x t t t  

1 2 3 4 1  0.5  0.5 1 1 1  x1 t ( ) 4 t

At t = 2, f = t2 = 4 Hz?

 

cos 2 ft 

Correct?

Instantaneous Frquency

4

 

 

2 1

cos 2 x t t t  

1 2 3 4 1  0.5  0.5 1 x1 t ( ) cos 2   4  t  ( ) t      

Correct? At t = 2, f = t2 = 4 Hz?

 

cos 2 ft 

Instantaneous Frquency

5

 

 

2 1

cos 2 x t t t  

4 Hz is too low!!!

1 2 3 4 1  0.5  0.5 1 x1 t ( ) cos 2   4  t  ( ) t 1.9 2 2.1 1  0.5  0.5 1 x1 t ( ) cos 2   4  t  ( ) t

Instantaneous Frquency

6

 

 

2 1

cos 2 x t t t  

12 Hz?

1 2 3 4 1  0.5  0.5 1 x1 t ( ) cos 2   12  t  ( ) t 1.9 2 2.1 1  0.5  0.5 1 x1 t ( ) cos 2   12  t  ( ) t

FM vs. PM

7

Message signal Unmodulated carrier Phase-modulated signal Frequency-modulated signal

FM vs. PM

8

 

FM

x t

 

PM

x t

Remark: To see xPM(t) of time varying m(t), it is usually easier to look at the instantaneous freq. via the derivative first.

FM vs. PM

9

Message signal Unmodulated carrier Phase-modulated signal Frequency-modulated signal

AM, FM, and PM

10

FM vs. PM

11

 

FM

x t

 

PM

x t