PULSE CODE MODULATION (PCM) , CONCEPT OF QUANTIZATION , discretization in time and amplitude modulation

By   November 23, 2019

CONCEPT OF QUANTIZATION , discretization in time and amplitude modulation , PULSE CODE MODULATION (PCM) :-
WAVEFORM CODING TECHNIQUES
Inside this Chapter

r   Introduction r  Discretization in Time and Amplitude
r   Concept of Quantization r  Pulse Code Modulation (PCM)
r   A PCM Generator or Transmitter r  PCM Transmission Path
r   PCM Receiver r  Quantizer
r   Working Principle of Quantizer r  A Uniform Quantizer with Incorrect
r   Transmission Bandwidth in a PCM System r  Quantization Noise/Error in PCM
r  Signal to Quantization Noise Ratio for Linear Quantization
r  Influence of Noise on the PCM System
r  Various important aspects related to PCM
r  Performance evaluation of PCM : Probability of Error for PCM
r  Comparison of PCM and Analog Modulation
r  Robust Quantization: Necessity of Non-uniform Quantization in a PCM System
r  Necessity of Nonuniform Quantization for Speech Signal
r   Nonuniform Quantization r  Companding (i.e., Companded PCM)
r   Compander Characteristic r  Applications of PCM
r  Different Types of Compressor Characteristics
r  Advantages of PCM : Salient Features of PCM
r   Drawbacks of PCM r  Delta Modulation
r  Evaluation of Maximum Output Signal to Noise Ratio
r   Delta-sigma Modulation r  Adaptive Delta Modulation
r  Differential Pulse Code Modulation (DPCM)
r  Evaluation of Output Signal to Noise (SIN) Ratio
r  Comparison of Digital Pulse Modulation Methods

4.1       INTRODUCTION
            To transport an information-bearing signal from one point to another point over a communication channel, we can use digital or analog techniques. As discussed earlier in chapter 1, the use of digital communication offers several important advantages as compared to analog communication. In particular, a digital communication system offers the following highly attractive features:
(i)         ruggedness to channel noise and external interference unmatched by any analog communication system.
(ii)        flexible operation of the system.
(iii)       integration of diverse sources of information into a common format.
(iv)       security of information in the course of its transmission from source to the destination.
In view of above reasons, digital communi-cations have become the dominant form of communication technology in our society.
However, to handle the transmission of analog message signals (i.e., voice and video signals)* by digital means, the signal has to undergo an analog-to-digital conversion. We already know about the pulse amplitude modulation (PAM) technique. We also know the disadvantages of using PAM technique. Using the waveform coding technique, we convert the analog PAM signal into a digital signal. This digital signal is in the form of a train or stream of binary digits 0 and 1. Thus, with waveform coding techniques, we enter into the world of digital communication. After sampling an analog signal, the next step in its digital transmission is the generation of the “coded version” (digital representation) of the signal. Pulse Code Modulation (PCM) provides one method to meet such a requirement.
In PCM, the message signal is sampled and amplitude of each sample is approximated (rounded off) to the nearest one of a finite set of discrete levels. This will enable us to represent both time and amplitude in discrete form. Hence, it is possible to transmit the message signal by means of a digital (coded) waveform. Conceptually PCM is simple to understand. It was the first method which was developed for the digital coding of the waveforms. PCM is the most applied of all the digital coding systems in use today. PCM is therefore widely accepted as the standard against which the other digital coder systems are calibrated. Here, we can note one more point that PCM belongs to a class of signal coders
known as waveform coders. In this chapter, we shall present a detailed discussion of different digital pulse modulation techniques.
4.2       DISCRETIZATION IN TIME AND AMPLITUDE
            As discussed earlier, pulse modulation may be classified under two heads i.e., pulse analog modulation and pulse digital modulation. In case of pulse analog modulation, only time is expressed in the digital form and any one of the pulse parameters (i.e., pulse amplitude, duration or position) is varied in a continuous manner in accordance with the message signal. Pulse amplitude modulation (PAM), Pulse duration (width) modulation (PWM) and Pulse position modulation (PPM) are the examples of pulse analog modulation. In these modulation schemes, information transmission is accomplished in an analog form at discrete times. On the other hand, in the pulse digital modulation, the time and the pulse parameter (usually the amplitude) occur in discrete form and digital coded form respectively. Pulse digital modulation is therefore basically a scheme which converts the analog signal to its corresponding digital form. It is for this reason that the analog-to-digital conversion is sometimes known as pulse digital modulation.
The simplest form of pulse digital modulation is called pulse code modulation (PCM). In this system (i.e., PCM), the message signal is first sampled and then amplitude of each sample is s  rounded off to the nearest one of a finite set of allowable values known as quantization levels, so that both time and amplitude are in the discrete form. This means that in pulse code modulation both parameters i.e., time and amplitude are expressed in discrete form. This process is called discretization in time and amplitude.
4.3 CONCEPT OF QUANTIZATION (U.P. Tech, Sem. Exam., 2005-2006) (05 marks)
In communication systems, sometimes it happens that we are available with analog signal, however, we have to transmit a digital signal for a particular application. In such cases, we have to convert an analog signal into digital signal. This means that we have to convert a continuous time signal in the form of digits. To see how a signal can be converted from analog to digital form, let us consider an analog signal as shown in figure 4.1(a). First of all, we get samples of this signal according to sampling theorem. For this purpose, we mark the time-instants t0, t1, t2 and so on, at equal time-intevals along the time axis. At each of the time-instants, the magnitude of the signal is measured and thus samples of the signal are taken. Figure 4.1(b) shows a representation of the signal of figure 4.1(a) in terms of its samples.
Now, we can say that the signal in figure 4.1(b) is defined only at the sampling instants. This means that it no longer is a continuous function of time, but rather, it is a discrete-time,but rather, it is a descrete-time signal. However, since the magnitude of each smaple can take any value in a continuous range, the signal in figure 4.1(b) is still an analog signal.

DO YOU KNOW?
Modern communication systems are often a mixture of analog and digital sources and transmission techniques. The trend is toward digital systems.

This difficulty is neatly resolved by a process known as quantization. In quantization, the total amplitude range which the signal may occupy is divided into a number of standard levels.
As shown in figure 4.1(c) , amplitudes of the signal x(t) lie in the range
(-mpmp) which is partitioned into L intervals, each of magnitude . Now, each sample is approximated or rounded off to the nearest quantized level as shown in figure. Since each sample is now approximated to one of the L numbers therefore the information is digitized.
DIAGRAM
FIGURE 4.1 (a) An analog signal, (b) Samples of analog siagnal, (c) Quantization
NOTE: The quantized signal is an approximation of the original one. We can improve the accuracy of the quantized signal to any desired degree simply by increasing the number of levels L.
4.4 PULSE CODE MODULATION (PCM)   (U.P. Tech-Semester Exam. 2002-2003)
Pulse-code modulation is known as a digital pulse modulation technique. In fact, the pulse-code modulation (PCM) is quite complex compared to the analog pulse modulation techniques (i.e., PAM, PWM and PPM) in the sense that the message signal is subjected to a great number of operations. Figure 4.2 shows the basic elements of a PCM system. It consists of three main parts i.e., transmitter, transmission path and receiver. The essential operations in the transmitter of a PCM system are sampling, quantizing and encoding as shown in figure
4.2. As discussed earlier, sampling is the operation in which an analog (i.e., continuous-time) signal is sampled according to the sampling theorem resulting in a discrete-time signal. The quantizing and encoding operations are usually performed in the same circuit which is known as an analog-to-digital converter (ADC).
Also, the essential operations in the receiver are regeneration of impaired signals, decoding and demodulation of the train of quantized samples. These operations are usually performed in the same cirucit which is known as a digital-to-analog converter (DAC).
DIAGRAM
FIGURE 4.2 The basic elements of a PCM system (a) Transmitter
(b) Transmission path (c) Receiver.
Further, at intermediate points, along the transmission route from the transmitter to the receiver, regenerative repeaters are used to reconstruct (i.e., regenerate) the transmitted sequence of coded pulses in order to combat the accumulated effects of signal distortion and noise.
As discussed in article 4.3, the quantization refers to the use of a finite set of amplitude levels and the selection of a level nearest to a particular sample value of the message signal as the representation for it. In fact, this operation combined with sampling, permits the use of coded pulses for representing the message signal. Thus, it is the combined use of quantizing and coding that distinguishes pulse code modulation form analog modulation techniques.
Few Important Points
            Now, let us summarize PCM in the form of few points as under:
(i)         PCM is a type of pulse modulation like PAM, PWM or PPM but there is an important difference between them PAM, PWM or PPM are “analog” pulse modulation systems whereas PCM is a “digital” pulse modulation system.
(ii)        This means that the PCM output is in the coded digital form. It is in the form of digital pulses of constant amplitude, width and position.
(iii)       The information is transmitted in the form of code words. A PCM system consists of a PCM encoder (transmitter) and a PCM decoder (receiver).
(iv)       The essential operations in the PCM transmitter are sampling, quantizing and encoding.
(v)        All the operations are usually performed in the same circuit called as analog-to-digital converter.
(vi)       It should be understood that the PCM is not modulation in the conventional sense.
(vii)      Because in modulation, one of the characteristics of the carrier is varied in proportion with the amplitude of the modulating signal. Nothing of that sort happen in PCM.

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