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