Howtosignalprocessing
- Do LTI systems have initial conditions?
- What are the conditions for a system to be LTI system?
- Why are initial conditions zero for a LTI system?
- Which response of LTI system does not depend on initial conditions?
Do LTI systems have initial conditions?
A causal LTI system has zero initial conditions and impulse response ℎ(𝑡). Its input (𝑡) and output (𝑡) are related through the linear constant-coefficient differential equation. d 2 y ( t ) d t 2 + α d y ( t ) d t + α 2 y ( t ) = x ( 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.
Why are initial conditions zero for a LTI system?
We use LTI systems in practice. That means the system should be LINEAR. Zero initial conditions ensure Linearity. That is why, Initial Conditions are assumed to be Zero in transfer function model.
Which response of LTI system does not depend on initial conditions?
Explanation: A LTI system is said to be memoryless only if it does not depend on any previous value of the input.
