ECE4058 Digital Communication

Digital Communication

Electronics and Communication EngineeringHanyang University

Haewoon Nam

Lecture 4

(ECE4058)

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ECE4058 Digital Communication

Pulse Code Modulation• PCM (Pulse-Code Modulation)

– A message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude

– The basic operation• Transmitter : sampling, quantization, encoding• Receiver : regeneration, decoding, reconstruction

• Operation in the Transmitter– Sampling

• The incoming message signal is sampled with a train of rectangular pulses• The reduction of the continuously varying message signal to a limited

number of discrete values per second– Nonuniform Quantization

• The step size increases as the separation from the origin of the input-output amplitude characteristic is increased, the large end-step of the quantizercan take care of possible excursions of the voice signal into the large amplitude ranges that occur relatively infrequently.

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ECE4058 Digital Communication

Pulse Code Modulation• Compressor

– A particular form of compression law : μ-law

– μ-law is neither strictly linear nor strictly logarithmic– A-law :

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)23.5()1log()1log(

μμ

++

=m

v

)24.5()1()1log( mvdmd μ

μμ ++=

)25.5(11,

log1)log(1

10,log1

≤≤+

+

≤≤+

=m

AAmA

Am

AmA

v

)26.5(11,)log1(

10,log1

≤≤+

≤≤+

=m

AmA

Am

AA

vdmd

ECE4058 Digital Communication

Pulse Code Modulation

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ECE4058 Digital Communication

Delta Modulation

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• DM (Delta Modulation)– An incoming message signal is oversampled to purposely increase the

correlation between adjacent samples of the signal– The difference between the input signal and its approximation is

quantized into only two levels - corresponding to positive and negative differences

)27.5()()()( ssqss TnTmnTmnTe −−=

)28.5()](sgn[)( ssq nTenTe Δ=

)29.5()()()( sqssqsq nTeTnTmnTm +−=

ECE4058 Digital Communication

Delta Modulation

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ECE4058 Digital Communication

Delta Modulation

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• System Details– Comparator

• Computes the difference between its two inputs– Quantizer

• Consists of a hard limiter with an input-output characteristic that is a scaled version of the signum function

– Accumulator• Operates on the quantizer output so as to produce an approximation to the

message signal.

(5.30) )(

)()()2(

)()()(

1

=

=

+−+−=+−=

n

isq

sqssqssq

sqssqsq

iTe

nTeTnTeTnTmnTeTnTmnTm

ECE4058 Digital Communication

Delta Modulation

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ECE4058 Digital Communication

Delta Modulation

9

• Quantization Errors– Slope-overload distortion

• The step size is too small for the staircase approximation to follow a steep segment of the original message signal

• The result that the approximation signal falls behind the message signal– Granular noise

• When the step size is too large relative to the local slope characteristic of the original message signal

• The staircase approximation to hunt around a relatively flat segment of the message signal.

ECE4058 Digital Communication

Delta Sigma Modulation

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ECE4058 Digital Communication

Noise in Analog Communications• Noise can broadly be defined as any unknown signal that affects the

recovery of the desired signal.• The received signal is modeled as

– is the transmitted signal – is the additive noise

• Lessons– Minimizing the effects of noise is a prime concern, and the ratio of signal

power is an important metric for assessing analog communication quality.– Amplitude modulation may be detected either coherently or non-

coherently by means of a simple envelope detector. However, there is a performance penalty to be paid for non-coherent detection.

– Frequency modulation is nonlinear and the output noise spectrum is parabolic when the input noise spectrum is flat. Frequency modulation allows us to trade bandwidth for improved performance.

– Pre- and de-emphasis filtering is a method of reducing the output noise of an FM demodulator without distorting the signal.

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)1.9()()()( twtstr +=)(ts)(tw

ECE4058 Digital Communication

Noise in Communication Systems

• The mean of the random process– Both noise and signal are generally assumed to have zero mean.

• The autocorrelation of the random process.– With white noise, samples at one instant in time are uncorrelated with

those at another instant in time regardless of the separation. The autocorrelation of white noise is described by

• The spectrum of the random process. For additive white Gaussian noise (AWGN), the spectrum is flat and defined as

• To compute noise power, we must measure the noise over a specified bandwidth. Equivalent-noise bandwidth is

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)3.9(2

)( 0NfSw =

)2.9()(2

)( 0 τδτ NRw =

)4.9(0 TBNN =TB

ECE4058 Digital Communication

Signal-to-Noise Ratio (SNR)

• The desired signal, , a narrowband noise signal,

• For zero-mean processes, a simple measure of the signal quality is the ratio of the variances of the desired and undesired signals.

• Signal-to-noise ratio is defined by

• The signal-to-noise ratio is often considered to be a ratio of the average signal power to the average noise power.

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)5.9()()()( tntstx +=

)(ts )(tn

)6.9()]([E)]([ESNR 2

2

tnts=

ECE4058 Digital Communication

Signal-to-Noise Ratio (SNR)

• The transmitted signal is

• Assume noise is white and Gaussian with power spectral density• The signal power

• The noise power

• The signal-to-noise ratio becomes

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)cos()( θπ += tfAts CC 2)(ts

T

C

BNA

tnts

0222 2EESNR ==

)]([)]([

20N

+=T

CC dttfAT

ts 0 22 21E ))cos(()]([ θπ

22412 20

2CT

CC AdttfT

A =++= ))cos(( θπ

TBNNtn 02E ==)]([

ECE4058 Digital Communication

Signal-to-Noise Ratio (SNR)

• SNR measurement

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ECE4058 Digital Communication

Announcement and Assignment

• Reading assignment– Digital modulations in AWGN baseband channel (Chapter 8)

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