ECE4058 Digital Communication

Digital Communication

Electronics and Communication EngineeringHanyang University

Haewoon Nam

Lecture 3

(ECE4058)

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ECE4058 Digital Communication

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)

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ECE4058 Digital Communication

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

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∞

−∞=

−=n

ss nTthnTmts )8.5()()()(

ECE4058 Digital Communication

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.

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

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

tmkTttg ps −>=

)18.5())(()( ∞

−∞=

−−=n

sps nTmknTtgts

ECE4058 Digital Communication

Pulse Position Modulation

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ECE4058 Digital Communication

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

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)21.5(,...,2,1},{: 1 LkmmmI kkk =≤< +

)22.5()(mgv =

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

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• 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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