Initial conditions for the LTI systems described as a difference equations

1. What are the conditions for a system to be LTI system?
2. Do LTI systems have initial conditions?
3. Why are initial conditions zero for a LTI system?
4. What is a difference equation in signals and systems?

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.

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 ) .

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.

What is a difference equation in signals and systems?

An equation that shows the relationship between consecutive values of a sequence and the differences among them. They are often rearranged as a recursive formula so that a systems output can be computed from the input signal and past outputs.