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UNIT – III
I: Digital Transmission
4-2 ANALOG-TO-DIGITAL CONVERSION
We have seen that a digital signal is superior to an
analog signal. The tendency today is to change an
analog signal to digital data. In this section we
describe two techniques, pulse code modulation and
delta modulation.
Topics discussed in this section:
Pulse Code Modulation (PCM)
Delta Modulation (DM)
ts
Pulse Modulation
Analog signal
Sample pulse
Pulse width modulation
Pulse position modulation
Pulse amplitude modulation
Pulse code modulation
8 bit
PCM Transmission System
PCM Sampling
Figure 4.21 Components of PCM encoder
Figure 4.22 Three different sampling methods for PCM
Note
According to the Nyquist theorem, the
sampling rate must be
at least 2 times the highest frequency
contained in the signal.
Figure 4.23 Nyquist sampling rate for low-pass and bandpass signals
Figure 4.24 Recovery of a sampled sine wave for different sampling rates
Figure 4.26 Quantization and encoding of a sampled signal
Quantization
Quantization
• With a folded binary code, each voltage level has one code
assigned to it except zero volts, which has two codes, 100 (+0)
and 000 (-0).
• The magnitude difference between adjacent steps is called
the quantization interval or quantum.
• For the code shown in Table 10-2, the quantization interval is
1 V.
• If the magnitude of the sample exceeds the highest
quantization interval, overload distortion (also called peak
limiting) occurs.
Quantization
• Assigning PCM codes to absolute magnitudes is called
quantizing.
• The magnitude of a quantum is also called the resolution.
• The resolution is equal to the voltage of the minimum step
size, which is equal to the voltage of the least significant bit
(Vlsb) of the PCM code.
• The smaller the magnitude of a quantum, the better (smaller)
the resolution and the more accurately the quantized signal
will resemble the original analog sample.
Quantization
Input analog signal
Sampling pulse
PAM signal
PCM code
Quantization
• For a sample, the voltage at t3 is approximately +2.6 V. The
folded PCM code is
sample voltage = 2.6 = 2.6
resolution
1
• There is no PCM code for +2.6; therefore, the magnitude of
the sample is rounded off to the nearest valid code, which is
111, or +3 V.
• The rounding-off process results in a quantization error of 0.4
V.
Quantization
• The likelihood of a sample voltage being equal to one of the
eight quantization levels is remote. Therefore, as shown in the
figure, each sample voltage is rounded off (quantized) to the
closest available level and then converted to its corresponding
PCM code.
• The rounded off error is called the called the quantization
error (Qe).
• To determine the PCM code for a particular sample voltage,
simply divide the voltage by the resolution, convert the
quotient to an n-bit binary code, and then add the sign bit.
Figure 4.27 Components of a PCM decoder
Dynamic Range
DR 
V m ax

V m in
V m ax
 2 1
n
resolution
DR = dynamic range (unitless)
Vmin = the quantum value
Vmax = the maximum voltage magnitude of the DACs
n = number of bits in a PCM code (excl. sign bit)
For n > 4
DR  2  1  2
n

n

D R  dB   20 log 2  1  20 n log 2  6 n
n

D R  dB   20 log 2  1
n

Example 2
• For the PCM coding determine the quantized voltage,
quantization error (Qe) and PCM code for the analog
sample voltage of + 1.07 V.
• To determine the quantized level, simply divide the
sample voltage by resolution and then round the
answer off to the nearest quantization level:
+1.07V
1V
= 1.07 = 1
• The quantization error is the difference between the
original sample voltage and the quantized level, or Qe =
1.07 -1 = 0.07
• From Table 10-2, the PCM code for + 1 is 101.
Signal-to-Quantization Noise Efficiency
SQ R 
V
Qe 
resolution
Qe
For input signal minimum amplitude
SQR = minimum voltage / quantization noise
SQR  min  
V min

resolution
Qe
Qe
For input signal maximum amplitude
SQR = maximum voltage / quantization noise
SQ R  m ax  
V m ax
Qe
SQR is not constant
2
2
Figure 4.28 The process of delta modulation
DELTA MODULATION
Differential DM
• In a typical PCM-encoded speech waveform, there are often
successive samples taken in which there is little difference
between the amplitudes of the two samples.
•
This necessitates transmitting several identical PCM codes,
which is redundant.
• Differential pulse code modulation (DPCM) is designed
specifically to take advantage of the sample-to-sample
redundancies in typical speech waveforms.
Differential DM
• With DPCM, the difference in the amplitude of
two successive samples is transmitted rather
than the actual sample. Because the range of
sample differences is typically less than the
range of individual samples, fewer bits are
required for DPCM than conventional PCM.
Figure 4.29 Delta modulation components
Figure 4.30 Delta demodulation components
UNIT – III
II: Multiplexing & T-Carriers
6-1 MULTIPLEXING
Whenever the bandwidth of a medium linking two
devices is greater than the bandwidth needs of the
devices, the link can be shared. Multiplexing is the set
of techniques that allows the simultaneous
transmission of multiple signals across a single data
link. As data and telecommunications use increases,
so does traffic.
Topics discussed in this section:
Frequency-Division Multiplexing
Wavelength-Division Multiplexing
Synchronous Time-Division Multiplexing
Statistical Time-Division Multiplexing
Figure 6.1 Dividing a link into channels
Figure 6.2 Categories of multiplexing
Figure 6.3 Frequency-division multiplexing
Note
FDM is an analog multiplexing technique
that combines analog signals.
Figure 6.4 FDM process
Figure 6.5 FDM demultiplexing example
Figure 6.9 Analog hierarchy
Figure 6.10 Wavelength-division multiplexing
Note
WDM is an analog multiplexing
technique to combine optical signals.
Figure 6.11 Prisms in wavelength-division multiplexing and demultiplexing
Figure 6.12 TDM
Note
TDM is a digital multiplexing technique
for combining several low-rate
channels into one high-rate one.
Figure 6.13 Synchronous time-division multiplexing
Note
In synchronous TDM, the data rate
of the link is n times faster, and the unit
duration is n times shorter.
Figure 6.15 Interleaving
Figure 6.18 Empty slots
Figure 6.19 Multilevel multiplexing
Figure 6.20 Multiple-slot multiplexing
Figure 6.21 Pulse stuffing
Figure 6.22 Framing bits
Figure 6.23 Digital hierarchy
Table 6.1 DS and T line rates
Figure 6.24 T-1 line for multiplexing telephone lines
Figure 6.25 T-1 frame structure
Table 6.2 E line rates
Figure 6.26 TDM slot comparison