UNIT – III I: Digital Transmission
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.
Pulse Code Modulation (PCM)Delta Modulation (DM)
Topics discussed in this section:
Pulse Modulation
Analog signal
Sample pulse
Pulse width modulation
Pulse position modulation
Pulse amplitude modulation
Pulse code modulation
8 bit
ts
PCM Transmission System
PCM Sampling
Figure 4.21 Components of PCM encoder
Figure 4.22 Three different sampling methods for PCM
According to the Nyquist theorem, the sampling rate must be
at least 2 times the highest frequency contained in the signal.
Note
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.
Input analog signal
Sampling pulse
PCM code
Quantization
PAM signal
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
max max
min
2 1resolution
nV VDR
V
DR = dynamic range (unitless)Vmin = the quantum valueVmax = the maximum voltage magnitude of the DACsn = number of bits in a PCM code (excl. sign bit)
2 1 2n nDR
20log 2 1ndBDR
For n > 4
20log 2 1 20 log 2 6ndBDR n 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 = 1.07 = 1 1V
• 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
min
minresolution 2
e e
VSQRQ Q
resolution2eQ
V
e
SQRQ
max
maxe
VSQR
Q
SQR is not constant
For input signal minimum amplitudeSQR = minimum voltage / quantization noise
For input signal maximum amplitudeSQR = maximum voltage / quantization noise
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.
Frequency-Division MultiplexingWavelength-Division MultiplexingSynchronous Time-Division MultiplexingStatistical Time-Division Multiplexing
Topics discussed in this section:
Figure 6.1 Dividing a link into channels
Figure 6.2 Categories of multiplexing
Figure 6.3 Frequency-division multiplexing
FDM is an analog multiplexing technique that combines analog signals.
Note
Figure 6.4 FDM process
Figure 6.5 FDM demultiplexing example
Figure 6.9 Analog hierarchy
Figure 6.10 Wavelength-division multiplexing
WDM is an analog multiplexing technique to combine optical signals.
Note
Figure 6.11 Prisms in wavelength-division multiplexing and demultiplexing
Figure 6.12 TDM
TDM is a digital multiplexing technique for combining several low-rate
channels into one high-rate one.
Note
Figure 6.13 Synchronous time-division multiplexing
In synchronous TDM, the data rate of the link is n times faster, and the unit
duration is n times shorter.
Note
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