Hello Everyone,
My name is Dr. Saurabh Mani Tripathi and you
are watching my YouTube channel “EE-Lectures”.
The topic of this short-lecture is “Continuous-time
vs. Discrete-time Signals and Analog vs. Digital
Signals”.
In my preceding short-video lecture, I have
described various terms namely ‘signal’,
‘system’, ‘system behavior’, ‘system
analysis’ and ‘mathematical model of the
system’.
In this short-video lecture, I will first
describe the ‘Continuous-time and Discrete-time
Signals’ and thereafter the ‘Analog and
Digital Signals’.
I will also highlight why the terms ‘analog’
and ‘digital’ should not be confused with
the terms ‘continuous-time’ and ‘discrete-time’.
So, let us now understand the continuous and
discrete-time classifications of the signals.
Actually, a signal which is defined at every
instant along the time-axis is known as a
‘Continuous-time signal’.
For example, look at this illustration.
You may see, at every instant along the time-axis,
the signal does assume some value.
So, this is a continuous-time signal.
On the other hand, look at this illustration.
In this illustration, you may notice that
the signal is assuming values only at equally-spaced
discrete-instants along the time-axis.
This is nothing but a ‘discrete-time signal’
since this signal is defined only at discrete
instants of time.
So, one may now state– “A signal which
is defined only at discrete instants along
the time-axis is known as the discrete-time
signal”.
Now, look at this figure.
This figure illustrates a relationship between
a continuous-time signal and a discrete-time
signal.
Actually, by sampling the continuous-time
signal at a uniform rate, one may derive the
discrete version of the signal.
Here, the symbol t has been used to denote
‘time’ in case of the continuous-time
signal.
On the other hand, the symbol k has been used
to denote ‘time instants’ in case of the
discrete-time signal.
Now, the question is – What are the analog
and digital classifications of the signals?
Very often, the terms ‘analog’ and ‘digital’
are confused with that of ‘continuous-time’
and ‘discrete-time’.
If you presume likewise, then you are also
making a big mistake.
As I have already described, the terms ‘continuous-time’
and ‘discrete-time’ qualify the nature
of a signal along the time-axis or you may
say along the horizontal-axis.
On the other hand, the terms ‘analog’
and ‘digital’ qualify the nature of the
signal along the amplitude-axis or you may
say along the vertical-axis.
Keeping this key difference in view, we may
describe the analog and digital classifications
of the signals.
Now, look at this illustration.
You may observe that the signal is taking
on an infinite number of values along the
amplitude or you may say along the vertical-axis.
Actually, a signal whose amplitude can take
on any value in a continuous-range along the
vertical-axis is known as an ‘analog signal’.
So, this figure illustrates nothing but an
analog signal.
Now, look at this illustration.
You may observe that the signal amplitude
is taking on only a finite number of values
along the vertical-axis.
Actually, a signal whose amplitude can take
on only a finite number of values along the
vertical-axis is known as a ‘digital signal’.
So, this figure illustrates a digital signal.
Another example of ‘digital signal’ is
the signal interacting in a digital computer
whose amplitude takes on only two binary values,
i.e. 0 and 1.
However, it is worth mentioning here, in order
to qualify a signal as digital one, the number
of values which the signal amplitude takes
on need not be restricted to two.
It can be any number but finite.
Now see the illustration of the analog signal
once more.
It is worth noted that the ‘analog signal’
illustrated in this figure qualifies to be
a ‘continuous-time signal’ also since
at every instant along the time-axis, the
signal does assume some value.
Since, this signal is defined at every instant
along the time-axis and the amplitude of the
signal is taking on an infinite number of
values along the vertical-axis; so we must
call this signal a “Continuous-time, Analog
Signal”.
Similarly, the ‘digital signal’ illustrated
in this figure also qualifies to be a ‘continuous-time
signal’.
Since, this signal is defined at every instant
along the time-axis and the amplitude of the
signal is taking on only a finite number of
values along the vertical-axis; so we must
call this signal a “Continuous-time, Digital
Signal”.
As I have already stated, one may derive the
discrete version of a continuous-time signal
just by sampling the signal at a uniform rate.
Therefore, the discrete versions of these
two continuous-time signals can be represented
as shown now on your screen.
Notice that, this signal is defined only at
discrete instants along the time-axis.
Also, the amplitude of the signal is taking
on an infinite number of values along the
vertical-axis.
So, we must call this particular signal a
“Discrete-time, Analog Signal”.
Furthermore, when we look at this particular
signal, it is defined only at discrete instants
along the time-axis.
However, the amplitude of the signal is taking
on only a finite number of values along the
vertical-axis.
So, we must call this signal a “Discrete-time,
Digital Signal”.
While summarizing in one sentence what I have
discussed in this short video lecture, I may
state–
“Analog signal is not necessarily be continuous-time
and digital signal need not be discrete-time”.
I hope, you are now able to explain others,
why the terms ‘analog’ and ‘digital’
should not be confused with the terms ‘continuous-time’
and ‘discrete-time’.
That's it for now.
Thanks for watching.
Good bye.
