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# convolution and LTI systems

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#### purnapragna

Hi i want to know :
Is the convolution integral is applicable only to LTI systems? I mean what is the condition that has to be imposed on the system so that to find the impulse response of it we can use convolution integral. To be more eloborate, should the system has to satisfy both the properties or any one is enough to find its impulse response using the convolution integral?

thnx

purna!

I dont think convolution is applicable only to LTI system. See adaptive filters theory for instance: The output signal, is the convolution in time of the input signal with the adaptive filters coeficient, in spite of the fact that the filters coeficient varies with time, obviously an adaptive filters is not invariant in time, and convolution operation remain applicable. It is just an oppinion, I wouldn't tell you that it is 100% right, counteroppinions are wellcome.

in an instance ur adaptive filter is Time-Invariant (TI) so u can use convolution.
but in the system like :
y = t.x(t)
ur sys. all the time is T-Variant.
and I think that convolution is only applicable to LTI systems.
bye

purnapragna said:
Hi i want to know :
Is the convolution integral is applicable only to LTI systems? I mean what is the condition that has to be imposed on the system so that to find the impulse response of it we can use convolution integral. To be more eloborate, should the system has to satisfy both the properties or any one is enough to find its impulse response using the convolution integral?

thnx

purna!

LTI systems as you know are Linear Time Invariant systems. There are 2 types of signals-discrete and continuous signals. Convolution Integral is applicable to continuous signals and convolution sum is applicable to discrete signals. To know more about these refer Signals and Systems by Simon Haykins and Barry Van Veen.

thnx

purna!

yes, it is impossible.
we directly use both of the linearity and time-invariency properties of LTI systems to prove the theorem. (remember The Sifting Property of the Impulse function that help us to build other signals,based on integral of impulses...)
so, it is impossible to use convoloution integral for non-LTI systems.
take a look: https://cnx.org/content/m10085/latest/

I feel that convolution integral is valied only for LTI systems and not for all systems.

conv int is only for LTI

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