Basic System Properties Video Lecture - Signal & Systems - Electrical Engineering

today we will be discussing about the
properties of the systems now if all
this while we have come to know about
the different inputs basically XSP in
case of continuous-time signal and X F n
in terms of in discrete-time signal now
system as a whole can be represented
like this you have a system you have
inputs it may be continuous-time or
discrete-time and some transformation
takes place on the input and you get Y
of T corresponding to X of T if you give
cutting this time
input to the system the transformation
is the transformed signal is Y of T if
we give X of n the transformed signal is
very often that can be represented here
like Y of T is equal to transformation
on X of T and Y of n as transformational
except n now we have different
properties of the system based on input
and output relationship the first one
happens to be linearity
now if I take this in this case there
was a single input and you got a single
output if I take more than one input say
I'll take weighted sum or more than one
input if there is a one input X of T I
would get Y of T if there is more than
one in this case it is precisely two so
if this is an input to the system and
then the transformation happens the
output what you get must be a into y1 of
T corresponding to transformation on X F
of x1 of T plus B into y 2 of T
corresponding to the transformation
which happens on x2 of T so if this
condition is satisfied then the system
is said to be linear now to put it in
words if the input to the system is a
weighted sum of weighted sum means you
multiply by a factor weighted sum sum
you have a positive sign here
so it is weighted sum of two or more
signals that is in this case have taken
two signals so its input is more a
weighted sum of two or more signal then
signals then the output should be the
weighted sum of responses to individual
signals what is a response to x1 of T it
is by 1 of T the response who gives the
system gives a response that is a
transformation happens on x1 of T you
get wipin of T and transformation
happens on x2 of T you get Y 2 of T now
this is in the case for the case of
continuous-time signal so if you have a
discrete-time signal then the condition
is a x1 of T plus B it's one of n B x2
of n the transformation happens and you
get Y a y1 of n plus b y2 of n if this
condition is satisfied for a discrete
system then the system is said to be
linear in nature so the next property is
time invariance so from the first
property we have come to know that X of
T undergoes transformation and you get Y
of P through the C through the system
now if there is a shift in the input by
an amount T naught that means you have
the input X of T and transformation
occurs on it so you get Y of T if there
is a shift in the input then there
should be corresponding shift in the
output if this condition is satisfied
then the system is said to be time
invariant time invariant and the
properties and invariance property now
this is in the case of continuous-time
see similar thing hood will hold good
for discrete-time signal that
X of n if you give us input the
transformation occurs and you get Y of M
then if there is a shift in the input of
discrete-time signal that is X of n
minus n not then there should be
transponding shift shift in the output
as well so if this condition is
satisfied the system the discrete-time
system is said to be time invariant
system so the third property is
causality now a system is said to be
causing if output at any instant will
depend on the input at the same instant
or the previous instant so you have the
input output relationship that is Y of T
is transformation on X of T now the
system as from the definition the system
is system is said to be causal if output
at any instant say for example I will
take instant Y of one output at any
instant if it depends upon the input at
the same instant or output at one
instant depends on the input at the
previous instance say Y of X of minus 1
Y of 1 is equal to X of minus 2y or 1 is
equal to X of minus 3 and so on that
means output at any instant will depend
on the input at the same instant or the
previous instance but not the future
instant that is why one should not a
viable ez is dependent upon input at 3 C
this is the current instant present
instead and this is a future instant so
if output at present in strength depends
upon the input at future instant that
this is said to be non Gaussian system
and for all these conditions this
stem is said to be causal in nature that
is output at present instant will depend
upon the input at the same instant or
the previous instance but not the future
instance now the fourth property is
memory now from the definition the
system is said to have memory if output
at any instant depends upon the input at
the previous instant or the future
instant but not the current instant
so if taking an example if I of T is
transformation on H of T now if output
at one instant as have taken the instant
to be one in the previous case I will
take the same output at one instant
depends upon the input in the past
incident or a passing sin that is X of
-1 or Y everyone is equal to X of minus
two Y everyone is equal to X of minus 3
or future instance that is Y of 1 is
equal to X of 2 Y of 1 is equal to X of
3 Y of 1 is equal to X of 5 if these
conditions are satisfied then the system
is said to have memory now when will the
system be called as memory lists if
input at one instant depends upon output
at one instant depends upon the input at
the same instant if this condition is
satisfied then the system is said to be
memoryless here if this cut these
conditions are satisfied the system is
said to have memory memory system here
the system is said to be mammal
memoryless that is if output at one
instant depends upon input at the same
instant then it is said to be memoryless
system if output at one instant is the
upon inputted the past instance or the
future instance then the system is said
to have mammoths the final property
which we'll be discussing is stability
you have improved but relationship if by
of T is output it is got by
transformation on X of T now this
stability is also named as PIB was
definitely our BIOS ability or whatever
you want to call it as this be IB was
transferred be I stands for bounded
input and B was transferred bounded
output now the definition is definition
for stability is if you give a bounded
input to the system the output and if
you get the output which is bounded then
the system is said to be stable now what
do you mean by bounded input and bounded
output see if I have an input if input
is X of M which is equal to some value B
your face which is less than infinity
than the system then the input is said
to be bounded that means any value which
is less than infinity if you provide it
to the system as an input then that
signal is said to be a bounded signal or
if you give a bounded input and if you
get a bounded output Y of n which is
some valued be your one which is again
less than infinity for a bounded input
if you get a bounded output then the
system is said to be stable in nature or
it reset said to be having Bible
stability now for a bounded input if you
get output to be approaching infinity
then the system is said to be unstable
in nature
so we have studied these many properties
under the properties of system health
I'll be solving problems related to this
properties in the upcoming videos now
for different types of signals like even
an art and the operations done on
independent variable T and n please have
a look into my previous videos thank you