Howtosignalprocessing
- Why convolution is applicable on LTI systems only?
- What is the convolution sum representation of LTI systems?
- Is convolution only for LTI systems?
- What are the conditions for a system to be LTI system?
Why convolution is applicable on LTI systems only?
Convolution is an incredibly useful operation because it can be used to predict the output of an LTI system to any input.
What is the convolution sum representation of LTI systems?
x[i]h[n − i], where h[n] is the unit pulse response of S. This is known as the convolution representation of a discrete-time LTI system. This name comes from the fact that a summation of the above form is known as the convolution of two signals, in this case x[n] and h[n] = Sδ[n].
Is convolution only for LTI systems?
Convolution is a mathematical operation, it is not used to "define" an LTI system. It can be used to easily find an LTI system's output to any input, but you can define an LTI system in multiple ways, for example y(t)=3x(t).
What are the conditions for a system to be LTI system?
Also, the causality condition of an LTI system reduces to h(t) = 0 ∀t < 0 for the continuous time case and h(n) = 0 ∈n ≤ 0 for the discrete time case. Similarly, the strictly causality condition of an LTI system reduces to h(t) = 0 ∀t ≤ 0 for the continuous time case and h(n) = 0 ∀n ≤ 0 for the discrete time case.
