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ECE4058 Digital Communication

Digital Communication

Electronics and Communication EngineeringHanyang University

Haewoon Nam

Lecture 2

(ECE4058)

1


Analog and Digital Signals

• Analog– Most of the signals in daily life are analog in nature.– Signals are functions of time, frequency, and space and usually

take values in a continuous range.– The signals can be directly processed in its analog form.

• Digital– Signals are represented by discrete variables and discrete time.

2

Analog input signal

Analog output signal

Analog signalprocessor

Digitalinput signal

Digitaloutput signal

Digital signalprocessor

D/Aconverter

A/Dconverter


Analog input signal


Comparison of Digital and Analog

• Advantages of digital signal processing– Easy (software) and stable processing by microprocessor– Easily stored in memory without deterioration– Lower cost due to VLSI technology (lower costs of memory, etc)– Efficient resource management (e.g. data compression)– More robust data management (e.g. coding)

• Limits of digital signal processing– Speed of operation is limited by A/D and D/A converters and

digital signal processors

3

Digitalinput signal

Digitaloutput signal

Digital signalprocessor

D/Aconverter

A/Dconverter


Analog input signal


Classification of Signals

• Continuous-Time versus Discrete-Time signals• Continuous-Valued versus Discrete-Valued signals• Deterministic versus Random signals

– Deterministic signal• All past, present, and future values of the signal are known precisely with no

uncertainty.

– Random signal• Signals can not be described accurately (noise signals, seismic signal, etc).• Probability and stochastic theory provides the mathematical framework for

the theoretical analysis of random signals.

• Periodic versus Aperiodic signals

4

T


Classification of Signals• Continuous and discrete signals

– Continuous-time andcontinuous-valued signal

– Discrete-time andcontinuous-valued signal

5

f(t)

f(n)

t

n

– Continuous-time and discrete-valued signal

– Discrete-time and discrete-valued signal

g(t)

t

g(n)

n

Sampling

Quantization


Sampling Process

• What is sampling?

• Nyquist sampling theorem

• Aliasing problem

6


Quantization Process

7


Digital Modulations

• Pulse modulations– Pulse amplitude modulation (PAM)– Pulse width modulation (PWM)– Pulse position modulation (PPM)– Pulse coded modulation (PCM)– Delta modulation (DM)– Delta sigma modulation

• Digital base-band modulations– Amplitude shift keying (ASK)– Frequency shift keying (FSK)– Phase shift keying (PSK)

8


Pulse Amplitude Modulation

• Pulse-Amplitude Modulation (PAM)– The amplitude of pulses is varied corresponding to the sample value of

a continuous message signal.• Sample-and-Hold Filter : Analysis

– The PAM signal is

– The h(t) is a standard rectangular pulse

9

∞

−∞=

−=n

ss nTthnTmts )8.5()()()(


Pulse Position Modulation

• PDM (Pulse-duration modulation) or PWM (Pulse width modulation)– Pulse-width or Pulse-length modulation.– The sample values of the message signal are used to vary the duration

of the individual pulses.– PDM is wasteful of power

• PPM (Pulse-position modulation)– The position of a pulse relative to its unmodulated time of occurrence is

varied in accordance with the message signal.

10

)20.5()2/()(max sp Ttmk <

)19.5()()2/(,0)(max

tmkTttg ps −>=

)18.5())(()( ∞

−∞=

−−=n

sps nTmknTtgts


Pulse Position Modulation

11


Quantization Process

• Amplitude quantization– The process of transforming a sample amplitude of a baseband signal

m(t) into a discrete amplitude v(t) taken from a finite set of possible levels.

– Representation level (or Reconstruction level)• The amplitudes vk , k=1,2,3,……,L

– Quantum (or step-size)• The spacing between two adjacent representation levels

12

)21.5(,...,2,1},{: 1 LkmmmI kkk =≤< +

)22.5()(mgv =


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.

13


Pulse Code Modulation• Compressor

– A particular form of compression law : μ-law

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

14

)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


Pulse Code Modulation

15


Delta Modulation

16

• 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 +−=


Delta Modulation

17


Delta Modulation

18

• 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


Delta Modulation

19


Delta Modulation

20

• 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.


Delta Sigma Modulation

21


Announcement and Assignment

• Reading assignment– Analog-to-digital conversion (Chapter 7)

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