1. UNIT – III
I: Digital Transmission

2. Topics discussed in this section:
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)

7. Pulse Modulation Analog signal Sample pulse Pulse width modulationts
Analog signal
Sample pulse
Pulse width modulation
Pulse position modulation
Pulse amplitude modulation
Pulse code modulation
8 bit

8. PCM Transmission System

11. PCM Sampling

12. Figure 4.21 Components of PCM encoder

13. Figure 4.22 Three different sampling methods for PCM

14. According to the Nyquist theorem, the sampling rate must be
Note
According to the Nyquist theorem, the sampling rate must be
at least 2 times the highest frequency contained in the signal.

15. Figure 4.23 Nyquist sampling rate for low-pass and bandpass signals

16. Figure 4.24 Recovery of a sampled sine wave for different sampling rates

17. Figure 4.26 Quantization and encoding of a sampled signal

18. Quantization

19. 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.

20. 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.

21. Quantization
Input analog signal
Sampling pulse
PAM signal
PCM code

22. Quantization
For a sample, the voltage at t3 is approximately +2.6 V. The folded PCM code is
sample voltage = = 2.6
resolution
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.

23. 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.

24. Figure 4.27 Components of a PCM decoder

27. Dynamic Range 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

28. Example 2
For the PCM coding determine the quantized voltage, quantization error (Qe) and PCM code for the analog sample voltage of 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 = = 0.07
From Table 10-2, the PCM code for + 1 is 101.

30. Signal-to-Quantization Noise Efficiency
For input signal minimum amplitude
SQR = minimum voltage / quantization noise
For input signal maximum amplitude
SQR = maximum voltage / quantization noise
SQR is not constant

39. Figure 4.28 The process of delta modulation

40. DELTA MODULATION

41. 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.

42. 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.

43. Figure 4.29 Delta modulation components

44. Figure 4.30 Delta demodulation components

45. UNIT – III
II: Multiplexing & T-Carriers

46. Topics discussed in this section:
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

47. Figure 6.1 Dividing a link into channels

48. Figure 6.2 Categories of multiplexing

49. Figure 6.3 Frequency-division multiplexing

50. FDM is an analog multiplexing technique that combines analog signals.
Note
FDM is an analog multiplexing technique that combines analog signals.

51. Figure 6.4 FDM process

52. Figure 6.5 FDM demultiplexing example

53. Figure 6.9 Analog hierarchy

54. Figure 6.10 Wavelength-division multiplexing

55. WDM is an analog multiplexing technique to combine optical signals.
Note
WDM is an analog multiplexing technique to combine optical signals.

56. Figure 6.11 Prisms in wavelength-division multiplexing and demultiplexing

57. Figure TDM

58. Note
TDM is a digital multiplexing technique for combining several low-rate channels into one high-rate one.

59. Figure 6.13 Synchronous time-division multiplexing

60. Note
In synchronous TDM, the data rate of the link is n times faster, and the unit duration is n times shorter.

61. Figure Interleaving

62. Figure Empty slots

63. Figure 6.19 Multilevel multiplexing

64. Figure 6.20 Multiple-slot multiplexing

65. Figure Pulse stuffing

66. Figure Framing bits

67. Figure 6.23 Digital hierarchy

68. Table 6.1 DS and T line rates

69. Figure 6.24 T-1 line for multiplexing telephone lines

70. Figure 6.25 T-1 frame structure

71. Table 6.2 E line rates

72. Figure 6.26 TDM slot comparison