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CHAPTER-1
Fundamental Concepts
Author: Dr. Manoj Duhan
1.1
Vetter : Mr. Sandeep Arya
ANALOG SIGNALS
We are very familiar with analog signals. The reading of a moving coil or moving
iron voltmeter and ammeter, dynamometer wattmeter etc., are all analog quantities. The trace
on a CRO screen is also analog. Analog methods for communication system have long been
in use. Frequency division multiplexing is the means of analog communication. An electronic
amplifier is an analog circuit. The low level analog signal (audio, video, etc.) is amplified to
provide strength to the signal. Analog circuit systems (position control, process control) have
been in use for the past many decades. Analog Computers use voltages, resistances and
potentiometric rotations to represent the numbers and perform arithmetic operations. Analog
differentiation, integration, etc., is also done. Operational amplifier is a very versatile analog
electronic circuit used to perform a variety of operations (addition, subtraction, multiplication,
division, exponentiation, differentiation, integration etc.).
Analog integrated circuits are
widely used in electronic industry.
1.2
DIGITAL SIGNALS
The term digital is derived from digits. Any device or system which works on digits
is a digital device or system. A digital voltmeter indicates the value of voltage in the form of
digits, e.g., 230.25. Reading an analog instrument introduces human error and also requires
more time. A digital reading is more accurate, eliminates human error and can be read
quickly.
Communication systems have also gone digital.
The initial signal waveform is
always analog. To use digital transmission, the signal waveform is sampled and the digital
representation transmitted. The process of converting analog signal to digital form is also
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known as digitizing. For multiple channels of transmission, Time Division Multiplexing is
used.
Digital control systems are fast replacing analog control systems. In digital control
systems the error is in the form of digital pulses.
Digital computers have revolutionalized the concept of computers. Their capability
ranges from simple calculations to complex calculations using numerical techniques. Many
computing tasks which required hours and days take only a few minutes on digital computers.
Digital signal processing is concerned with the representation of continuous time
(analog) signals in digital form. It is based on Claude Shannon’s∗ sampling theorem which
states that “A band limited continuous time signal can be reconstructed in its entirety from a
sequence of samples taken at intervals of less than
1
where fN is the highest frequency
2f N
present in the signal.” It is essential that the analog signal is band limited which limits how
much it can change between samples. The sampling rate has to high to be ensure accuracy.
Since the initial signal is always analog and the final required signal is also mostly
analog, a digital system requires three essential aspects (1) conversion of analog signal to
digital form (2) transmission of digital signal (3) reconstruction of analog signal from the
received digital signal as shown in Fig. 1.1
A continuous time function x(t) is converted into a digital signal x(n) by an analog to
digital (A/D) converter. The output of discrete time system is y(n) and is converted to
continuous time function by digital to analog (D/A) converter. The discrete time system, in
digital communications, is a digital communication channel. To achieve high fidelity, the
sampling rate may have to be very high say 50000 samples per second. Each sample may be
encoded by (say) 18 bits. The frequency fs (in Fig. 1.1) must be more than twice fN the
highest frequency in the analog signal. Very large scale integration (VLSI) digital circuits
have capability to sample at very fast rate so that high fidelity is achieved.
∗
Sampling is done to convert analog signal to digital signal.
214
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x(t)
A/D
Converter
x(n)
Discrete
Time system
y(n)
D/A
converter
y(t)
Clock
(Period T = 1/fs)
Clock
(Period T = 1/fs)
Fig. 1.1 Digital system
A DSP (digital signal processing) chip is the core of digital system used in cellular
phones, modems, disk drives, digital automotive systems etc. It was invented only about 15
years ago but its applications have grown tremendously.
Digital methods have the following advantages over analog methods :
1.
Digital devices work only in two states (say on and off). Thus their operation is
very simple and reliable.
2.
Digital display is very accurate and can be read at a fast speed. Human error is
eliminated.
3.
Electronic components exhibit change in behaviour due to ageing, change of
ambient temperature etc. Therefore, the behaviour of analog circuits tends to be
somewhat unpredictable. However, digital circuits are free from these defects.
4.
Digital ICs are very cheap and compact in size.
5.
Variety of digital ICs are available.
6.
Power requirement of digital circuits is very low.
7.
Digital systems have the characteristic advantage of memory. Thus information
can be stored over a period of time. The space required for this stage is very
small. One compact disc∗ can store information contained in many books.
8.
Digital systems have high fidelity and provide noise free operations.
9.
By integrating system peripheral functions on a DSP chip, the reliability can be
enhanced and cost reduced.
10.
When volumes are high, they can be manufactured at low cost.
11.
The same digital system can be used with a variety of software for a number of
tasks.
12.
∗
Standardisation & Repeatability.
A compact disc is known s CD.
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1.3
BASIC DIGITAL CIRCUITS
In a digital system there are only a few basic operations performed, irrespective of the
complexities of the system. These operations may be required to be performed a number of
times in a large digital system like digital computer or a digital control system, etc. The basic
operations are AND, OR, NOT, and FLIP-FLOP. The AND, OR, and NOT operations are
discussed here and the FLIP-FLOP, which is a basic memory element used to store binary
information (one bit is stored in one FLIP-FLOP).
1.3.1
The And Operation
A circuit which performs an AND operation is shown in Fig. 1.2. It has N inputs (N
≥ 2) and one output. Digital signals are applied at the input terminals marked A, B, …, N, the
other terminal being ground, which is not shown in the diagram. The output is obtained at the
output terminal marked Y (the other terminal being ground) and it is also a digital signal. The
AND operation is defined as : the output is 1 if and only if all the inputs are 1.
Mathematically, it is written as
Y = A AND B AND C … AND N
=A⋅B⋅C⋅… ⋅N
= ABC …N
…(1.1)
Ao
Bo
oY
No
Fig. 1.2 The standard symbol for an AND gate
where A, B, C, … N are the input variables and Y is the output variable. The variables are
binary, i.e. each variable can assume only one of the two possible values, 0 or 1. The binary
variables are also referred to as logical variables.
Equation (1.1) is known as the Boolean equation or the logical equation of the AND gate.
The term gate is used because of the similarity between the operation of a digital circuit and a
gate. For example, for an AND operation the gate opens (Y = 1) only when all the inputs are
present, i.e. at logic 1 level.
Truth Table Since a logical variable can assume only two possible values (0 and 1),
therefore, any logical operation can also be defined in the form of a table containing all
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