Continuous and Discrete Time Signals Video Lecture - Electrical Engineering (EE)

in this video we are going to discuss
continuous-time and discrete-time
signals so in the last class we observe
the classification of signals in that
the first classification is
continuous-time and discrete-time
signals I already told you a
continuous-time signal we can define the
signal at any interval of time for
discrete-time signal we can determine
that signal we can determine the
amplitude of the signal at a particular
instant ervil's of time that means at
continuous interval some time we can
determine the signal only at a discreet
intervals of time we can define the
signal of discrete so here you can see
the definition and example waveforms of
both continuous and discrete time signal
if you go for continuous time signal a
signal which is defined for all values
of P P I considered as time if a signal
which is defined for all values of time
is called as continuous time signal so
here these are the examples related to
continuous time signal if you consider
this signal this is a sine wave so here
if you consider this signal so for
example I mentioned only continuous
intervals or discrete intervals so here
for example if you want the value at 0.1
or 0.2 by taking the reference line and
mapping with this voltage you can say
what is the signal at a particular
instant of time that means so like this
we can we can say what is the reference
amplitude that a signal is having at all
instants of time so for example if you
are having signal like this this is a
square wave so this square wave for this
square wave also for example if you want
at 2.5 so at a 2.5 you can map this
voltage and you can see the reference
voltage so you can draw a line here and
you can see the voltage corresponding to
this height of that peak so you can see
a particular voltage at any instant of
time so coming to this
so here also we can say what is the
amplitude at any instant of time from
minus infinity to infinity if you're
triangular wave is there by just drawing
a line from x-axis to that wave and by
taking the reference from this y-axis
voltage then we can say what is the
corresponding voltage at particular
instant of time in all these waveforms
not only these three we are having so
many continuous waveforms
so just like in the nature we are having
a continuous wave so there is no cuts in
between the wave from minus infinity to
infinity or in a given time period we
can we can have a continuous wave that
is called as continuous signal so here
we can determine the signal value at any
instant of time that is the only point
we need to say about continuous time
signal so coming to discrete time signal
so here we can't see values at some
intervals of time that means so only at
discrete intervals of time we can define
the signal if they ask it for any
decimal points like curves at zero point
one what is the value of the in this
signal if they are asking we can't say
that signal so that means so this is
zero one two three four only at a
discreet intervals these signals are
defined so that's why if they ask for
any not discrete intervals that means
for example zero point one two point
five six point five like that if they
are asking we can't determine that
signal so this signal nature will be
like this it's having samples with it
with a different voltage at particular
instant of time for example the sample
at one may have one volt
sample at two how two volts and three
volts like that so coming to discrete
signals one important point is for
discrete time signal time is discrete
but amplitude is always continuous so
please keep in mind for a discrete
signals only time is discrete but the
amplitude is continuous that means you
can say
Richard at anytime for any sample for
example if you considered a digital
signal so digital signal is next version
of discrete signal
so after Quantrill quantization of a
discrete signal we are going to get
digital signal that digital signal you
know that's having only once and zeros
by watching by observing that ones and
zeros you can't say what is the
amplitude of that signal instantly so
that's why for a digital signal both the
amplitude and time are discreet we can't
say well what is the time and what is
the amplitude particular time period we
can't solitude particular amplitude is
not there for a digital signal so for a
digital signal both the amplitude and
time or discrete coming to the equations
for example I want to consider time
period as two for example peak to peak
you can consider from here to here all
one complete cycle you can consider as
time period if I want to make any
definition for this waveform I want to
consider a particular time period I am
considering like two this is the time
period that means capital T value I am
considering like two so now if you want
to make any waveform equation we know
that this is in the form of sine wave so
we need to consider the definition of
sine wave X of P equal to why I am
writing X of T means as this is
continuous if we need to consider the
signal in the function of continuous
time so continuous time always can be
represented with T and this great time
always will represent with so yeah so
here also you need to mention X of here
so here for example if you are
considering T equal to 2 means so you
need to compare with the equation a sine
Omega T plus 5 so you need to substitute
the values in this then you are going to
get this wave equation but you know you
don't know the value of amplitude for
example
say you are having two volts here peak
voltage so you are having a highest peak
as to so amplitude can be noted by this
waveform is 2 volts so then a value is 2
and P value you know as 2 so you know
the relation between angular frequency
Omega and this time period so always so
T is equal to 2 pi by Omega naught by
this you can say Omega R Omega naught e
you can consider Omega naught is equal
into 2 pi by T as you know the value of
T is equivalent to you are going to get
PI Omega is equal into PI say there is
no phase shift that means consider Phi
is equal into 0 say we are not having
any phase shift consider Phi is
equivalent to 0 so here you can see if
the waveform is like this we are not
having a phase shift like that I am
considering Phi is equivalent to 0 so
here I am substituting everything here
so now any sign in a place I am writing
just to sign so Omega naught T that
means Omega naught value is PI so sine
PI T 2 sine PI T is the description or
wave equation for this particular wave
like that we can define that way the
only difference between this and this is
we can define only at discrete intervals
of time the definition won't worry that
means here X Ophion is equivalent to for
example here also if you are considering
2 here also if you are considering your
time period as 2 then you are going to
write the equation like X of n is equal
to 2 sine Phi n so 2 sides PI n or 2
sine n pi you can write so this is the
wave equation for this wave so like this
you are going to get the equations also
when you are representing continuous
times
you need to represent in terms of T when
you are representing your discrete
signal you need to represent in terms of
discrete time n now coming to a
conversion of continuous time to
discrete time how we can convert this
continuous time signal into discrete
time signal so that can be done by
sampling process sampling process is
nothing but multiplication with a pulse
train for example if you are having this
signal if you want to convert into this
signal so just you need to multiply with
a pulse time so here you can see if you
multiplied with a pulse trying then you
are going to get this so you can see if
you multiply with a pulse train of
amplitude 1 I'm multiplying so like
there's some multiplying so this is the
pulse train with impulse train this is
also called as impulse train trying out
Finn pulses so I'm just considering as
amplitude of 1 why because I don't want
to change my amplitude from 2 so if you
want to change your amplitude if you
want to amplify then you can change the
amplitude of pulse right then these two
will be multiplied with any other value
then you will get some bigger amplitude
when I consider the amplitude of 1 for
pulse train whatever the amplitude
maintained in the continuous wave will
follow in the discrete signal so now
consider here if this sample is
multiplied here it will come here so if
this sample is multiplied here it will
come here whatever the values we are
having in between so here that are going
to vanish why because I from this sample
to this sample so you can notice a value
0 in the pulse train if 0 is multiplied
here this part of your continuous wave
is going to vanish that's why this this
wave is going to cut as discrete but on
discrete sine wave so like this we can
convert any continuous time
signaling to discrete some time signal
after converting into this trail if you
done quantization and the encoding then
if you done encoding then you are going
to get your digital signal how we are
getting digital signal from continuous
signal means first we need to convert
into discrete and then digital that
means of the converting like this you
need to encode the signal according to
the step sizes according to the step
voltages so that means you need to put
your reference voltage as five or six or
seven like that so in process you you
just put a reference voltage according
to that reference voltage you are going
to encode these values so if the sample
voltage exceeds that then you just put
one if the sample value not exceeding
that you are going to put zero so like
that one zero one zero one zero time
will come so that is called as digital
signal so whatever we are having here in
signals and systems is only continuous
and discrete time signals so this is the
description about continuous and
discrete time signals