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Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary PSK (BPSK) Frequency shift keying Typical spectra Modulation/demodulation principles Main difference between digital and analog systems: goal of transmission. Advantages of digital modulation: More flexibility through DSP (processing, services, etc.) Noise/interference immunity; security Fits to computer/data communications Lecture 10 22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 1(20)
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Page 1: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Digital Modulation

On-Off keying (OOK), or amplitude shift keying (ASK)

Phase shift keying (PSK), particularly binary PSK (BPSK)

Frequency shift keying

Typical spectra

Modulation/demodulation principles

Main difference between digital and analog systems: goal of

transmission.

Advantages of digital modulation:

More flexibility through DSP (processing, services, etc.)

Noise/interference immunity; security

Fits to computer/data communications

Lecture 10

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 1(20)

Page 2: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Baseband Binary Modulation• Binary data representation: 0 or 1.

• Unipolar modulation: high level (e.g., 5V) / zero, or 1/0

• Bipolar modulation: +high level / -high level, or +1/-1

1

b

RT

= bit (data) rate, bit/s

L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.

NRZ

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 2(20)

Page 3: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Amplitude Shift Keying (ASK)• Switch on-off the carrier:

• Signal representation:

• Is it similar to something?

• Signal spectrum?

( ) ( ) ( )cos 2c c

x t A m t f t= π

( ) 1 or 0m t =

L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.

binary ASK:

general case: a fixed number of levels

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 3(20)

Page 4: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

L.W

. C

ouch II,

Dig

ital and A

nalo

g C

om

munic

ation S

yste

ms, P

rentice H

all, 2001.

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 4(20)

Page 5: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Amplitude Shift Keying (ASK)

• Signal spectrum (FT):

• Square-wave message:

• Random message PSD:

• How to detect?

( ) ( ) ( )2

c

x m c m c

AS f S f f S f f= − + +

0

20

( ) ( ),

1 1sinc ,

2 2 2 2

m n

n

j n

nb

S f c f nf

n Rc e f

T

+∞

=−∞

π

= δ −

= = =

L.W

. C

ouch II,

Dig

ital and A

nalo

g C

om

munic

ation S

yste

ms, P

rentice H

all, 2001.

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 5(20)

Page 6: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Binary Phase Shift Keying

• BPSK signal representation:

where is bipolar message.

• Another form of the BPSK signal ->

( ) ( )cos ( )c c

x t A t m t= ω + ∆ϕ⋅

( ) 1m t = ±

( ) cos cos

sin ( )sin

c c

c c

x t A t

A m t t

= ∆ϕ ω −

− ∆ϕ⋅ ω

L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 6(20)

Page 7: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Binary Phase Shift Keying

• Digital modulation index:

• Important special case (random message)

• Compare with ASK!

• How to detect?

2

d

∆ϕβ =

π

1d

β =

L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.

PSD

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 7(20)

Page 8: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Detection of BPSK

• Same as analog PM

• Add a quantizer (sign(*) function) to improve performance

(noise immunity)

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka

sign(.)out (+/-1)

8(20)

Page 9: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Frequency Shift Keying

• Discontinuous FSK: ( )( )

( )1 1

2 2

cos , mark (1)

cos , space (0)

c

c

A tx t

A t

ω + θ=

ω + θ

Not popular (spectral noise + PLL problems)

L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 9(20)

Page 10: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Frequency Shift Keying

• Continuous FSK:

L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.

( ) ( )0

cos

t

c cx t A t m d

= ω + ∆Ω τ τ

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 10(20)

Page 11: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Pulse-Amplitude Modulation (PAM)

• Baseband modulation (no carrier yet)

• Baseband signal represents digital data (e.g. binary)

• PAM: a conversion of an analog signal to a pulse-type signal in

which the pulse amplitude carriers the analog information.

• This is the 1st step in converting an analog signal (waveform) to a

digital signal.

1 1

1

... ... ( ) ( )

n

n n k

k

b b A A x t A s t kT

=

→ → = −∑

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 11(20)

Page 12: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Pulse-Amplitude Modulation

• Based on the sampling theorem: analog band-limited (to Fmax

)

signal can be represented by its samples taken at

• PAM provides pulse-like waveform that contains the same

information as the original analog signal. Pulse rate [pulses/s] is

the same as fs .

• Pulse shape can be any. Discuss rectangular pulse waveform

first.

• Two types of sampling: natural sampling (gating) and

instantaneous sampling (flat-top or sample-and-hold).

max2

sf F≥

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 12(20)

Page 13: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Natural Sampling (Gating)

• The sampled (PAM) signal is

where

( ) ( ) ( ),

( )

s

s

k

x t s t x t

t kTs t

=−∞

=

− = Π τ ∑

max1/ 2

s sf T F= ≥

( )sx t

( )x t

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 13(20)

Page 14: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Natural Sampling (Gating): Spectrum

• Spectrum (FT) of the sampled (PAM) signal is

where is the duty cycle of s(t).

[ ] ( )( ) ( ) sinc( ) ,sx s x s

k

S f FT x t d kd S f kf

=−∞

= = −∑

/s

d T= τ

original signal spectrum sampled signal spectrum

( )x

S f

( )sx

S f

sinc( )d kd⋅

( )xd S f⋅

similar to ideal (delta-function) sampling?

Example:

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 14(20)

Page 15: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Natural Sampling: Proof

• Start with

• Find Fourier series of s(t):

• FT of s(t) is

• Finally,

• This concludes the proof.

• How to recover (demodulate) the original signal?

( ) ( ) ( ) ( ) ( )* ( )s

s x x sx t s t x t S f S f S f= ↔ =

( ) , sinc( )sjn t

n n

n

s t c e c d nd

ω

=−∞

= = ⋅∑

( ) ( )s n s

n

S f c f nf

=−∞

= δ −∑

( ) ( )* ( ) ( )sx x s n x s

n

S f S f S f c S f nf

=−∞

= = −∑

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 15(20)

Page 16: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Instantaneous Sampling

• Also known as flat-top PAM or sample-and-hold.

• The sampled signal is

( ) ( )

* ( ) ( )

ss s

k

s s

k

t kTx t x kT

tx kT t kT

=−∞

=−∞

− = Π τ

= Π δ − τ

( )x t

( )sx t

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 16(20)

Page 17: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Instantaneous Sampling: Spectrum

• The sampled signal spectrum (FT) is

( )1

( ) ( ) , ( ) sinc( )sx x s

s k

S f H f S f kf H f fT

=−∞

= − = τ ⋅ τ∑

Proof – homework. How to recover (demodulate) x(t) ?

original signal spectrum sampled signal spectrum

( )x

S f

( )sx

S f

sinc( )d f⋅ τ

( )sinc( )x

d f S f⋅ τ ⋅

Example:

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 17(20)

Page 18: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Baseband PAM: Generic Case

• Basic pulse shape is not necessarily rectangular. The

information is represented by the pulse amplitude Am

.

• M-ary PAM signal waveform:

• s(t) – signal waveform, T – symbol interval, M – the number of

symbols.

( ) ( ), 1,2,... , 0m mx t A s t m M t T= = ≤ ≤

2log [bits]bn M=

• The information transmitted by

one symbol:

• Transmitted signal sequence

T

( )s t

t

0

generic signal waveform

( ) ( )T k

k

x t A s t kT= −∑

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 18(20)

Page 19: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

PAM: Energy, Spectrum

• Baseband signal energy:

• Depends on m.

• Bandpass PAM signal:

• Its spectrum (FT):

• It is DSB-SC signal! The bandwidth is twice of that of baseband

signal.

• Bandpass signal energy:

• Similar modulation formats: PPM, PWM.

2 2 2

0 0

( ) , ( )

T T

m m m s sE x t dt A E E s t dt= = =∫ ∫

( ) ( ) cos , 1, 2,... , 0m m cx t A s t t m M t T= ω = ≤ ≤

( )( ) ( ) ( )2m

m

x s c s c

AS f S f f S f f= − + +

22

0

( )2

T

mm m s

AE x t dt E= =∫

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 19(20)

Page 20: Digital Modulation Lecture 10sloyka/elg3175/Lec_10_ELG3175.pdf · Digital Modulation On-Off keying (OOK), or amplitude shift keying (ASK) Phase shift keying (PSK), particularly binary

Summary

Basic digital modulation formats. Unipolar and bipolar NRZ

baseband signals. ASK (OOK), PSK and FSK. Spectra and

bandwidth.

PAM. Instantaneous and flat-top sampling. Spectra of

sampled signals. Recovery (demodulation) of the original

signal. Generic form of a PAM signal.

Homework: Reading: Couch, 3.1, 3.2, 5.9. Study carefully all

the examples, make sure you understand and can solve them

with the book closed.

22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 20(20)


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