into to signal and systems

1. Principles of Signals and Systems
Prof. Aditya K. Jagannatham
Department of Electrical Engineering
Indian Institute of Technology, Kanpur
Lecture- 01
Introduction to Signals and Systems, Signal Classification – Continuous and
Discrete Time Signals
Keywords: Introduction to Signals and Systems, Signal Classification,Continuous and
Discrete Time Signals
Hello, welcome to this module in this massive open online course alright. So in this
module we are going to look at signals and systems, the properties of signals and
systems.
(Refer Slide Time: 00:30)
So this course concerns itself with, as the title implies, signals and systems, two of the
fundamental quantities which are relevant in all of electrical, electronics and
communication engineering and relevant in a very profound sense. Their knowledge is
fundamental to understanding the various concepts or aspects of different applications in
electrical electronics and communication engineering.

2. (Refer Slide Time: 01:32)
So what we are interested in this massive open online course is to understand the
fundamental concepts in the properties of signals and systems and more importantly we
are interested in this interplay between signals and systems.
(Refer Slide Time: 02:43)
Now consider the case of a system which I am representing it schematically over here
and if I transmit a signal x(t) through this system, I have an output y(t). Now these are
the signals, x(t) is the input signal and y(t) is the output signal. So we would like to
characterize and better understand what happens when I take a signal, transmit it through

3. a system, what is this interaction, how the system acts upon this signal to generate the
output, because we are going to use systems to process these signals suitably. So we
would like to understand the interplay between signals and some of the impact systems
have on signals and also designing appropriate systems to extract certain behavior from
the signals.
So this interaction between signals and systems is of fundamental importance and these
are used in several branches of electrical engineering, for instance in the design of power
systems where they are monitored and efficiently controlled using the smart grid and you
can have applications in communication systems, such as 3G wireless systems or Wi-Fi
such as a 802.11x systems. So this course aims to look at the properties of both
continuous as well as discrete signals along with systems.
(Refer Slide Time: 06:09)

4. (Refer Slide Time: 08:15)
Let us start with a definition of a signal.
(Refer Slide Time: 09:38)
A signal can be defined as basically, it is a physical quantity that conveys information
about some physical phenomena, for instance such as a voltage signal, an
electromagnetic wave which is a signal that is transmitted over the air from the base
station to the mobile station which is carrying information about the communication
between two individuals or let us say it is a data signal carrying information about either
a video or an image that has been transmitted. So a signal is a bearer of information.

5. (Refer Slide Time: 12:20)
An image can also be thought of as a signal in space and we have signals in both space
and time, for instance a video signal which is 2 dimensional, each frame of the video can
be thought of as an image. So it has variation in space as well as time because it
comprises of a sequence of frames in time.
(Refer Slide Time: 13:48)
Now when we consider time signals we represent them using x(t), y(t) etc., and many
principles that we develop for the analysis of such signals which vary in time in a single
dimension can also be extended for 2D, 3D signals or a separate set of techniques can be

6. developed for them, but based on the fundamental principles that we learn for this time
signal. So in this course we are going to consider the analysis of such simple signals
which are varying with time and these can be suitably extended to other scenarios for
instance images which are 2D space signals or video which is a 3 dimensional both space
and time varying signals.
So a signal represents some physical quantity which conveys information about some
phenomenon that we are interested and naturally to understand more about that
phenomenon, we need to process that signal suitably. So we are going to consider time
varying signals or signals which are functions of time and these are known as time
signals.
(Refer Slide Time: 17:35)
So consider the classification of signals. Signals can be continuous time signals for
instance, ( ) sin(2 )x t t , that is a continuous time signal, it is also known as a sinusoid
or a sinusoidal signal eithercos(2 )t orsin(2 )t both are known as sinusoids. It is defined
continuously over time.

7. (Refer Slide Time: 17:29)
So it is defined continuously at all time instants either from minus infinity to infinity or
over a continuous time interval not at a specific set of time instants.
(Refer Slide Time: 19:23)
Now we have discrete time signals which are defined at discrete set of time instants. For
instance, you have a discrete time signal which can be defined at discrete set of time
instants, this is known as a stem plot and these discrete set of time instants can either be
positive or negative.

8. (Refer Slide Time: 20:27)
So these are only defined at a set of discrete time instants. So it can be identified as a
series or sequence of numbers, for instance we have x(0) at time instant 0, x (1) at time
instant 1, x(2) at time instant 2 and so on.
(Refer Slide Time: 21:33)
So these can be defined as a sequence or series of numbers and so also known as a time
series, for instance if the signal is in time, it is a discrete time signal. So naturally similar
to discrete time signals, you can also have discrete space signals. For instance, if you
take an image signal and if you sample it at appropriate instants in space, this is a

9. discrete space signal. In fact, if you look at modern images which are represented as a
collection of pixels its nothing but a discrete space signal. The discrete time signals can
also be obtained by sampling continuous time signals. So I can go from a continuous
time signal to a discrete time signal and I can obtain a continuous time signal from a
discrete time signal through a suitable filtering operation.
(Refer Slide Time: 24:02)
So a discrete time signal can be obtained can be obtained by suitably sampling a
continuous time signal. There are certain properties of the sampling process. If you take
a continuous time signal and if you sample it at suitable points over a time grid, you get
points that are equal spaced in time, which are the samples.

10. (Refer Slide Time: 25:15)
These are samples and these are the sampling time instants. So by sampling continuous
time signal I am able to obtain a discrete signal. These discrete time signals are more
convenient to process, for instance in a digital communication systems such as most of
our mobile phones are based on such as for instance 3G, 4G, wireless communication
systems, it is convenient to handle digital signals which can be obtained again from
discrete time signals.
So discrete time signals give rise to digital signals and such signals can be processed
much more readily in comparison to the conventional systems which were analog in
nature, for instance the amplitude modulation, FM radio and so on. The examples of
discrete time signals would be the modern communication systems such as 3G, 4G or
your GSM which is a 2G communication system or for instance all your modern
communication systems such as Wi-Fi, etc., even your modern landline probably uses
digital communication systems your set top boxes in TV that is a very good example
which are alternative to your analog cable. So basically that concludes the basic
classification of signals as both continuous and discrete time signals.

11. (Refer Slide Time: 30:10)
(Refer Slide Time: 30:30)
Consider an exponential kind of signal, for instance
1
( )
2
n
x n
 
  
 
for 0n  and 0
otherwise. If you can look at this signal, since half is basically less than 1, it is going to
be a decreasing signal. So this is a discrete time signal defined only at discrete time
instants. So basically let us conclude this module with that.
So we have seen signals as physical quantities that convey some information about a
certain phenomenon. We are interested in studying the signals, behavior of these signals,

12. the properties of these signals and we begin with the characterization or classification of
these signals first as two basic classes that is continuous time and discrete time signals.
So we will stop here and continue with other aspects in subsequent modules. Thank you
very much.