LTI system $y(t)=x(t-T)$ with or without memory

1. Is LTI system memoryless?
2. How do you know if a system is memoryless?
3. What are the conditions for a system to be LTI system?
4. How do you calculate the output of an LTI system?

Is LTI system memoryless?

An LTI system is called memoryless if the output signal value at any time t depends only on the input signal value at that same time.

How do you know if a system is memoryless?

A system is memoryless if its output at a given time is dependent only on the input at that same time, i.e., at time depends only on at time ; at time depends only on at time . A memoryless system does not have memory to store any input values because it just operates on the current input.

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.

How do you calculate the output of an LTI system?

The output of any LTI system can be calculated using the input and the impulse function for that system. Convolution has many important properties: Commutativity: x ( t ) ∗ h ( t ) = h ( t ) ∗ x ( t ) x(t) \ast h(t) = h(t) \ast x(t) x(t)∗h(t)=h(t)∗x(t)