UNIT – III I: Digital Transmission

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)

Pulse Modulation Analog signal Sample pulse Pulse width modulation ts 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

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.

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 = 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

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 For input signal minimum amplitude SQR = minimum voltage / quantization noise For input signal maximum amplitude SQR = maximum voltage / quantization noise SQR is not constant

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

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

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 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

WDM is an analog multiplexing technique to combine optical signals. 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