communication 02

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7 Communication Systems

. . . transmitting messages, and possibly information . . .

Transformationof source (message) signalx(t)into transmit signal

y(t)matchedto transmission channel (frequency range, propagation

and attenuation characteristics etc.)

Mechanisms

Modulation process of embedding information-bearing signal

x(t)into y(t)

Demodulation process of extracting information-bearing sig-

nal

Multiplexing combination of independent source signals into

a composite signal suitable for transmission over a common

channel

Distinguish

Analog vs. digital message signals

analog time continuous + continuum of values digital time-discrete+ quantized values

Analog vs. digital transmission

Transmit signal varies continuously with message signal

Finiteset of transmit signals to represent information This chapter

Analog transmission of analog message signals

Lampe, Schober: Signals and Communications

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Signal Processing and Communications-IIUM


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Outline

7.1 Amplitude Modulation

7.2 Frequency Modulation7.3 Analog-Pulse Amplitude Modulation

7.4 Multiplexing


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7.1 Amplitude Modulation

Amplitude modulation (AM):Amplitudeofsinusoidal carrier signal

c(t)is varied in proportion to a message signal x(t)

AM is oldest and most simple technique for wireless transmission

and multiplexing.

Used for longwave, mediumwave, and shortwave radio and broad-

casting, for analog television, for frequency multiplexing for analog

telephone transmission, etc.

7.1.1 Modulation

Distinguish

Double-sideband AM

AM with/suppressed carrier

Quadrature AM

Single-sideband AM

Vestigial-sideband AM


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Double-sideband AM suppressed carrier

Generation of AM wave

y(t) =x(t)c(t) =x(t)

2crmscos(ct + c)with carrier signal

c(t) =

2crmscos(ct + c)

Notation

x(t): message signal, modulating signal

y(t): modulated signal c(t): carrier signal, carrier wave crms: root mean square value of sinusoidal carrier c: carrier frequency c: carrier phase

Illustration 2crmscos(ct + c)

x(t) y(t)

y(t)x(t)

t t


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Frequency domain

Spectrum of carrier waveC(j) =

2crms (

c)ejc + (+ c)e

jc Multiplication property of Fourier transformY(j) =

crms2

X(j( c))ejc +X(j(+ c))ejc

Replications of original spectrum centered aroundc

double representation of modulation signal

Bandwidthof message signal M bandwidth of modulatedsignal2

M x(t)recoverable fromy(t)only ifc> M

0

0

2crms

2crms

cc

c c c+ M

X(j)

C(j)

Y(j)

1

c M

sidebandsidebandUpper

sidebandsideband

UpperLower Lower

MM

crms2

0


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Double-sideband AM with carrier

Add carrier wave to transmit signal

Simple demodulation possible

Less power efficient, since carrier does not contain informa-tion

Modulated signal

y(t) = (A + x(t))

2crmscos(ct + c)

with

DC component A Modulation indexm=

max{|x(t)|}A

Illustration

Phase reversals

m >1

m= 1

m


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Efficiency factor

= average power of message signal

average total power

= m2S21 + m2S2

with degree of saturation

S=

average power of message signal

max{|x(t)|} Frequency domain

Superposition of message signal part and carrier waveY(j) =

crms2

X(j( c))ejc + X(j(+ c))ejc

+

2Acrms

( c)ejc + (+ c)ejc

0

X(j)

1

0c c

Y(j)

2Acrms

2Acrms

Uppersidebandsideband sideband

Lower Lower Uppersideband

crms2


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Quadrature AM

Feature

2

doubled-sideband AM using orthogonal carrier waves

cos(ct)and sin(ct)

Twoindependentmessage signals occupy same transmis-sion bandwidth (multiplexing)

Bandwidth-conservation scheme

Time-domain description (c= 0)

y(t) =

2crms(x1(t)cos(ct) x2(t)sin(ct))

Block diagram

2crmssin(ct)

2crmscos(ct)

y(t)

x2(t)

x1(t)


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Frequency domain

Spectrum of modulated signalY(j) =

crms

2 X1(j( c)) + X1(j(+c))+j

X2(j( c))X2(j(+ c))

Spectrum ofY(j) not symmetric about c no doublerepresentation

Bandwidthof modulated signal2Mequals sum of the band-

widths of the modulation signals nobandwidth expansion Illustration for real-valued spectra X1(j)andX2(j)

Im{Y(j)}

c

c

Re{Y(j)}

X2(j)

X1(j)


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Single-sideband AM

Observation from double-sideband AM

Redundant representation of message signal in upper and

lower sideband

Twice the signal bandwidth M is required

Therefore

No information lost if one sideband is suppressed!single-sideband AM

Frequency-domain description

2crms

0

X(j)

1

0c c

Y(j)

Upper sideband

Lower sideband

0c c

Y(j)

2crms


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Spectrum (c= 0)

Upper sidebandY(j) =

2crms1

2

(sign(

c) + 1) X(j(

c))

12

(sign(+ c) 1) X(j(+ c))

Lower sidebandY(j) =

2crms

12

(sign(+ c) + 1) X(j(+ c))

1

2

(sign(

c)

1) X(j(

c))

Remark:

We note that from the convolution property of the Fourier transform

andF{1/t} = jsign()we have the Fourier pair1

x(t) 1

tF jX(j)sign().

The left-hand side operation is called Hilbert transform, and is de-fined as

H{x(t)} = 1

x(t) 1t

= 1

x()

t d

and thus

H{x(t)} = F1{jX(j)sign()}


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Single-sideband signal

Upper sidebandy(t) =

F1

{Y(j)

}= 2crms

12

(x(t) +jH{x(t)}) e+jct

+1

2(x(t)jH{x(t)}) ejct

y(t) =

2crms(x(t)cos(ct)H{x(t)}sin(ct))

Lower sidebandy(t) =

2crms(x(t)cos(ct) + H{x(t)}sin(ct))

Block diagram

x(t)

2crmssin(ct)

2crmscos(ct)y(t)

H{}

Observe

Single-sideband AM is QAM withx2(t) = H{x1(t)}


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Illustration for real-valued spectrumX(j)

Im

F{cos(ct)}

F{sin(ct)}

Re

+

Y(j)

Im

Re

Y(j)

Im

Re

=

Im

Re

++

Im

=

Re

Im Im

ReRe

Im

Re

X(j)

F{H{x(t)}} = jsign()X(j)


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Implementation of exact Hilbert-transform filter impossible

For DC-free message signals soft-Hilbert filter possible

Method by Weaver

0

X(j)

1

uo ou

y(t)

2crmscos(2t)

2crmssin(2t)

2cos(1t)

2sin(1t)x(t)

Lowpass

Lowpass

1

1

1= o+u

2

ou2

1

Lowpass

1= o+ u2

2=c 1

+ : upper sideband

: lower sideband

Lowpass filter with finite edge steepnessLampe, Schober: Signals and Communications

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Vestigial-sideband AM

Single-sideband modulation not applicable when message signal

contains significant low-frequency components, e.g., for televi-

sion signals

Compromise between double- and single-sideband AM

Vestigial-sideband AM One sideband is passed almost completely Onlyvestigeof other sideband is retained

Sideband-shaping filtersymmetric about c

Illustration

c

Y(j)

c+ Mc M

X(j)

MM

cc

Bandwidth-expansion factor (roll-off factor) [0, 1]


15


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7.1.2 Demodulation

Assumption: No overlap (c> M), transmitted signaly(t)is also

received signal (no noise, distortion etc.)

Distinguish

Synchronous demodulation

Asynchronous demodulation

Synchronous Demodulation

Demodulation of high-frequency signal into low-frequency signal

with locally generated carrier wave

c(t) =

2

crmscos(ct +

c)

Carrier frequency offset: c= c c Carrier phase offset: c=c c

Subsequent lowpass filtering with cutoff frequency co

Transmitter-receiver structure for general QAM

w2(t)

w1(t)

y(t)

2crmssin(ct + c)

2crmscos(ct + c)

x2(t)

x1(t)

v2(t)

v1(t)co

Lowpass

co

Lowpass

2crms sin(ct + c)

2

crmscos(ct +

c)

Lampe, Schober: Signals and CommunicationsSignal Processing and Communications-IIUM


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Signals after multiplication with carrier

w1(t) = 2x1(t)cos(ct + c)cos(ct +

c)

2x2(t)sin(ct + c)cos(

ct +

c)

= x1(t) [cos(ct + c) +cos((c+ c)t + c+c)]+x2(t) [sin(ct + c) sin((c+c)t + c+ c)]

w2(t) = 2x2(t)sin(ct + c)sin(ct +

c)

2x1(t)cos(ct + c)sin(ct + c)= x2(t) [cos(ct + c) cos((c+ c)t +c+ c)]x1(t) [sin(ct + c) +sin((c+c)t + c+ c)]

Signals after lowpass filtering with

M< oc 2c M

v1(t) = x1(t)cos(ct + c) + x2(t)sin(ct + c)

v2(t) = x2(t)cos(ct + c) x1(t)sin(ct + c)

Convenient combination to complex demodulated signal

v1(t) +jv2(t) = x1(t) [cos(ct + c) jsin(ct + c)]+jx2(t) [cos(ct + c) jsin(ct + c)]

v1(t) +jv2(t) = (x1(t) +jx2(t))ej(ct+c)


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Double-sideband AM:x1(t) =x(t), x2(t) 0 Only real part used

v(t) =v1(t) =x(t)cos(ct + c)

Forv(t) = x(t)c= 0andc=k , k ZZ

Synchronous carriers required!

In case of AM with carrier: highpass to suppress carrier

QAM

v1(t) = x1(t)cos(ct + c) + x2(t)sin(ct + c)

v2(t) = x2(t)cos(ct + c) x1(t)sin(ct + c) c= 0 andc =k , k ZZ: Coupling of signals

c= 0 andc=k , k ZZ: Separation of signals Single-sided AM: x1(t) =x(t), x2(t) = H{x(t)} Only real part used

v(t) = v1(t) =Re

(x(t)jH{x(t)})ej(ct+c)

= x(t)cos(ct + c)

H{x(t)

}sin(ct + c)

c= 0, phase offset:v(t) =x(t)cos(c)H{x(t)}sin(c)


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Frequency offset

Lowpass|W(j)|

c> c

Upper sideband |Y(j)|

cc

Lowpass|W(j)

|

c< c

Lower sideband

|W(j)|Lowpass

c> c

|Y(j)|

cc

Lowpass|W(j)

|

c< c


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Asynchronous Demodulation

No demodulation with carrier wave no need for synchroniza-tion

Evaluation ofenvelopeof received signal envelope detector Only applicable for Double-sideband AMwithcarrier andm 1

y(t)

t

2crms(A + x(t))

How to get rid of carrier wave?

For non-overlapping sidebands

H{y(t)} = H{(A +x(t)) 2crmscos(ct + c)}= (A + x(t)) 2crmssin(ct + c)

cos2(ct +c) +sin2(ct + c) = 1

env{y(t)} = 12y2(t) + H2{y(t)}

Envelopeenv{y(t)} = crms|A + x(t)|

m1= crms(A + x(t))


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Envelope detector

Hv(t): Bandpass filter to suppress DC component and highfrequencies|| > M

Non-overlapping sidebands andm 1 v(t) =x(t)

()/2

()2

y(t) Hv(j) v(t)

()2

H{}

Practical implementation

v(t)v(t)

y(t)

y(t) v(t) v(t)

ttt


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7.2 Frequency Modulation

Belongs to class ofangle modulation techniques

Representation of message in phaseof carrier wave

Average power= maximum power

zero dynamic of envelope efficient power amplification

Higher quality than amplitude modulation

higher power efficiency than amplitude modulation Requires higher bandwidth than amplitude modulation

trade-off between power and bandwidth efficiency Angle-modulated signal

y(t) =

2crmscos(ct + (t))

with information bearing phase (t)

Instantaneous frequency

i(t) =c+d(t)

dt

Types of angle modulation

Phase modulation (PM)

(t) =kpx(t)

Frequency modulation (FM)

i(t) c=kfx(t)(x(t): modulating signal)


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Frequency modulation

Modulated signal

y(t) = 2crmscosct +

t

(i() c) d

with

i(t) c=kfx(t)

Phase signal

(t) =kft

x() d

Maximum frequency deviation

=kfmax{|x(t)|}

kf issystem parameter Usually max{|x(t)|}adjusted through limiter is sys-

tem parameter


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Example:

Cosine message signal

x(t) =Acos(Mt) =kfA

i(t) c= cos(Mt) (t) = Msin(Mt)

FM signal

y(t) = 2crmscosct +Msin(Mt)(= PM signal with x(t) =Asin(Mt) andkp=kf/A)

t

t

t

y(t)

y(t)

x(t)

PM

FM


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Spectrum of FM signals for cosine signal x(t)

y(t) =

2crmscosct +

Msin(Mt)

= crms2

y(t)ejct + (y(t)ejct)

with

y(t) =ejM

sin(Mt)

y(t)periodic with period 2/M

Fourier series description ofyt)

y(t) =

k=Jk

M

ejkMt

with Bessel function of the first kind,nth order

Jk(u) = 1

2

ej(usin(v)kv) dv

Spectrum ofy(t)

Y(j) = 2

k=Jk

M

( kM)

Spectrum of FM signal

Y(j) =crms

2[Y(j( c)) + Y(j( c))]


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Illustration

0 2 4 6 8 10 12 14 160.5

0

0.5

1

6 4 2 0 2 4 60.4

0.2

0

0.2

0.4

u

J0(u)

J1(u) J2(u)

Y(j)

/M= 5

/M

J0(5)

J1(5)

J2(5)J2(5)

Interpretation:

Discrete spectrum LargerM density decreases Larger for fixedM bandwidth increases /M 1:

J0(/M) = 1, J1(/M) (/M)/2,Jk(/M) 0 fork >1

Spectrum ofnarrowbandFM similar to double-sideband

AM with carrier


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15 10 5 0 5 10 150

0.2

0.4

0.6

0.8

15 10 5 0 5 10 150

0.05

0.1

0.15

0.2

0.25

0.3

15 10 5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

15 10 5 0 5 10 150

0.05

0.1

0.15

0.2

0.25

0.3

15 10 5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

15 10 5 0 5 10 150

0.1

0.2

0.3

0.4

15 10 5 0 5 10 15

0

0.1

0.2

0.3

0.4

15 10 5 0 5 10 15

0

0.1

0.2

0.3

0.4

0.5

0.6

M

for

=

2

(5kHz)

forM

=

2

(1kHz)

= 2 (5kHz)

M= 20

M= 10

M= 2.5

M= 5

M= 5

M= 3.8

M= 2.4

M= 1

M= 2 (1 kHz)

/(2(1kHZ))/(2(1kHZ))


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Estimation of bandwidth of FM signal for cosine message signal

Strictly speaking: infinite bandwidth

Approximation by Carson

How many discrete spectral components are required to re-tainp (100%) of the total modulated signal power?Parseval:

J20(u) + 2

Kk=1

J2k(u) p

Bandwidth limited toB = 2KM

causes loss of(1p) (100%) in signal powerCarsons approximation of bandwidth of FM signal

B =

2(+ M) forp= 0.9

2(+ 2M) forp= 0.99

Note: bandwidth measured in Hz (as usual)Bf=B/(2)[Hz]

Carsons approximation is also applicable to non-cosine message

signals.


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Demodulation

Ideal angle modulation track angle of modulated signal

v(t) = v1(t) +jv

2(t) =

|v(t)

|ej(t)

v(t) = d

dt(arg{v(t)}) = d

dt

tan1

v2(t)

v1(t)

= kfx(t)

Lowpass

Lowpass

arg{}

v1(kT)

v2(kT)

2crms

cos(ct)

2

crmssin(ct)

y(t)

T

+ v(kT)

FM-AM conversion

v(t) = d

dt

y(t)

2crms

= (c+ kfx(t)) sin(ct + (t))

and AM envelope detector (c =kfmax{|x(t)|})


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7.3 Analog Pulse-Amplitude Modulation

Analog transmission of discrete-time sample valuesof message sig-

nal

Amplitude of the pulse carrier is modulated in accordance with in-

stantaneous sample values of the message signal.

Pulse-Amplitude Modulation (PAM)

Lowpass anti-aliasing filtering of message signal band limitation to || M Sampling signal at rate T = 2/s,s>2M

Modulation of impulses h(t)

x(nT)x(t)

Mx(t)

Lowpass

h(t) y(t)

PAM signal

y(t) =

n=x(nT)h(t nT))


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Example:

Rectangular pulse of durationT0

h(t) =rect

t T0/2T0

y(t) =

n=x(nT)rect

t T0/2 nT

T0

T

x(t)

T0

y(t)

t

Sampling-and-hold operation with sampling period T and holddurationT0

Express PAM signal

y(t) =

x(t)

k=

(t kT) h(t)

Spectrum of PAM signal

Y(j) = 1

T

k=

X(j( ns))H(j)

whereH(j) = F{h(t)}


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Effect of pulse shape

E.g. h(t) =recttT0/2T0

F H(j) =T0sincT02 ejT0/2

ss

(Xj)

MM

sincT0

2

2

T02

T0

Frequency distortion

Shorter pulse duration

less distortion

Demodulation of PAM signal

Lowpass filter with cutoff frequencyM< co s M Compensate for distortion due to pulse shape

Hr(j)y(t) v(t)

E.g. for rectangular pulse shape

Hr(j) =

1

T0sinc(T0/(2))ej(TdT0) , || M

0,

|

| (s

M)

dont care, else

v(t) =x(t Td)(delay Td for causal filter)


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7.4 Multiplexing

Combination of independent message signals into a composite signal

suitable for transmission over a common channel

General structure

xI(t)

Channel

v1(t)

v2(t)

vI(t)Demultiplexer

......

x1(t)

x2(t)

Multiplexer

Basic types of multiplexing

1. Frequency-division multiplexing (FDM)

Individual signals are separated by allocating them to differ-

ent frequency bands.

Used with sinusoidal carrier-wave modulation

Examples:

Wired telephony and telegraphy Radio and TV broadcasting 1st generation (analog) cellular phone systems as the US

Advanced Mobile Phone Service (AMPS), the UK Total

Access Communications System (TACS), the German C-Netz


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2. Time-division multiplexing (TDM)

Individual signals are separated by allocating them to differ-

ent time slots within a sampling interval.

Used with (digital) pulse modulation Examples:

Digital Enhanced Cordless Telecommunications (DECT) 2nd generation digital cellular phone systems as Global

System for Mobile Communications (GSM), Digital-American

Mobile Phone Service (D-AMPS), and Personal Digital

Cellular (PDC)

3. Code-division multiplexing (CDM)

Individual signals are separated by assignment of different

codes to them.

Used with digital pulse modulation

Examples:

3rd generation mobile communication standards CDMA2000,

Universal Mobile Telecommunications System (UMTS)

4. Space-division multiplexing (SDM)

Individual signals are separated spatially.

Based on directed antennas

Examples:

GSM, UMTS

If the message signals correspond to different user which access the

same transmission medium, the above techniques are also referred

to asmultiple-accesstechniques (FDMA, TDMA, CDMA, SDMA).


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Illustration

Tim

e

Frequency

SDMCDM

Frequency

Tim

e

TDM

Tim

e

Frequency

Power

Power

Pow

er

FDM


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7.4.1 Frequency-Division Multiplexing

Multiplexing

Lowpass filtering of message signal no interference with othersignals sharing the common channel

Modulation

Shift the frequency ranges of signals so as to occupy mutuallyexclusive frequency intervals

Most widely used: single-sideband AM

Bandpass filter restrict the band of each modulated wave to itsprescribed range

Summation forms input to common channel

Modulator

Modulator

Modulator

... ...

Bandpass

Bandpass

Bandpass

x1(t) Lowpass

x2(t) Lowpass

xI(t) Lowpass

supply

Carrier

... ...


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Demultiplexing received signal

Bandpass filtering to extract the modulated signals correspond-

ing to their specific frequency range

Demodulation to recover the original signal

Lowpass filtering to reduce interference and noise

Carrier

...

supply

Demod.

Demod.

Demod.

vI(t)

...

v2(t)

v1(t)

...

Lowpass

Lowpass

Lowpass

...

Bandpass

Bandpass

Bandpass

To allow for a coexistence of different communication systems and

standards over the entire usable frequency range, the allocation of

frequencies for different purposes is controlled by several national

and international standards and regulation bodies.


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7.4.2 Time-Division Multiplexing

TDM is based on the sampling theorem.

Transmission of oneband-limitedmessage signal engages trans-mission channel for only a fraction of the sampling interval.

Time interval between adjacent samples is cleared for use by

other message signals.

Multiplexing

Lowpass filtering to restrict bandwidth to || M Commutator

Takes narrow samples of each of the Imessage signals atrate1/T > /M

Sequentially interleavesIsamples inside sampling intervalT Pulse modulation

......

LowpassxI(t)

Lowpassx2(t)

Lowpassx1(t)

Commutator

modulatorPulse-


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Demultiplexing

Pulse demodulator produces narrow samples

Decommutator distributes samples

Lowpass filtering to reconstruct message signal

Decommutator

Pulse-demodulator ...

Lowpass

Lowpass

Lowpass v1(t)

v2(t)

vI(t)

...

Timing synchronization between commutator and decommutator

critical

Appropriate choice of pulse shape and pulse demodulation to avoid

intersymbol interference

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