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ECE4058 Digital Communication
Digital Communication
Electronics and Communication EngineeringHanyang University
Haewoon Nam
Lecture 4
(ECE4058)
1
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.
2
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 :
3
)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
Delta Modulation
5
• 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
7
• 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
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
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.
11
)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
12
)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.
13
)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
14
)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 ==)]([