This document discusses pulse code modulation (PCM) and its key elements. It describes how PCM works by sampling an analog signal, quantizing the sample values to discrete levels, and encoding the quantized levels into a digital signal. The key elements of a PCM system include a transmitter that performs sampling, quantization, and encoding using an analog-to-digital converter, and a receiver that performs decoding, demodulation, and digital-to-analog conversion. Regenerators along the transmission path help reconstruct the signal and combat noise and distortion. The document then discusses sampling, quantization, and coding in more detail.

1. RCC Institute of Information Technology
Canal South Road, Beliaghata
Kolkata - 700 015, West Bengal, India
Topic: Pulse Code Modulation (PCM) Uniform
Quantisation
Name: Saumalya Ghosh
University Roll No.: 11700320011
Paper Name: Digital Communication & Stochastic
Process
Paper Code: EC503
Department: Electronics & Communication Engineering

2. PULSE MODULATION
It may be recalled that Pulse modulation can be classified under two
heads e.g., Pulse analog modulation and Pulse digital modulation In
the analog forms of pulse modulation the time is only expressed in
the digital form and any one of the pulse parameters (pulse
amplitude, duration or position) is varied in a continuous manner in
accordance with the message signa Pulse Amplitude Modulation
(PAM), Pulse Duration (Width) Modulation (PDM/PWM) and Pulse
Position Modulation (PPM) are examples of pulse analog
modulation.) Thus, in these modulation schemes information
transmission is accomplished in an analog form at discrete times. 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
that converts the analog signal to its corresponding digital form. It is
for this reason the analog-to digital conversion is some times called
Pulse digital modulation. The simplest form of pulse digital
modulation is known as Pulse Code Modulation (PCM).

3. (In this system the message signal is first sampled and then amplitude of each
sample is 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. The allowed quantization levels are finally
coded to obtain the analog signal in the digital form. The process allows the
message to be transmitted by means of coded electrical signals thereby
distinguishing PCM from all other methods of pulse modulation. In addition to
Pulse Code modulation, a number of other pulse digital modulation techniques
are existing. However, PCM acts as a benchmark against which performances of
other schemes are compared. In the next section we discuss the PCM system in
detail.
Fig. 1: Elements of a PCM system

4. ELEMENTS OF PULSE CODE MODULATION
(PCM)
The basic elements of a PCM system are shown in Fig.1. Pulse code
Modulation (PCM) system is much more complex than any other pulse
modulation system because it involves a number of message processing
operations. The essential operations accomplished in the transmitter of a
PCM system are sampling, quantizing and encoding. The sampling,
quantizing and encoding operations are usually done by a single device
which is known as analog-to-digital (A/D) converter. The essential
operations in the receiver are the regeneration of the impaired signal,
decoding and demodulation of the train of quantized samples Regeneration
of the signal is also done at intermediate points along the transmission route
from the transmitter to the receiver. This regeneration is done with the help
of regeneration repeaters shown in Fig.1 which reconstruct the transmitted
sequence of coded pulses at intermediate points enroute to combat
accumulated effects of signal distortion and noise. The other two functions
of the receiver are usually accomplished by a converter called a digital-to-
analog (D/4) converter.

5. Sampling refers to the process of taking instantaneous values of the
message signal at regular intervals in the case of uniform sampling and
thereby discretizing the time frame of the same analog signal. Quantizing
refers to the use of a finite set of amplitude levels called quantization levels
so that the instantaneous value of the message signal amplitude can be
rounded off and approximated to the nearest available level. The process of
sampling and quantizing converts an analog signal into a quantized discrete-
time signal. By assigning digital code to the quantized levels the analog
signal is finally converted into a true digital signal. It may be pointed out that
the quantization and coding operation used in the PCM system makes it
distinctively different from analog modulation techniques. Although We
model the A/D converter as a sampler followed by a quantizer and coder, in
he practice the A/D converter is performed by a single device that takes the
analog signal g(t) as the input and produces a binary coded number. The
operation of sampling and quantization can be performed in either order.
However, in practice sampling is usually performed before quantization. It
may be pointed out here that sampling of a signal does not result in
any loss of information nor does it introduce any distortion if the signal
bandwidth is finite.

6. Fig. 2: Elements of an analog-to-digital (A/D) converter
In principle, any bandlimited analog signal can be
reconstructed from samples, provided that the sampling rate is
sufficiently high to avoid the problem commonly known as aliasing. On
the other hand quantization introduces distortion in the signal which is an
irreversible process. The basic building block of an A/D converter is
shown in Fig.2. The amount of distortion introduced is determined by the
number of bits, in the A/D conversion process which is directly related to
the number of quantization levels used for approximating the sample
values. In the next three sections we discuss in detail the basic three
process e.g. sampling, quantizing and coding involved in PCM.

8. Department: Electronics & Communication Engineering
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