Howtosignalprocessing
- Is the inverse of a causal system causal?
- What is inverse of a system?
- What is causality of a system?
- What is an example of causal system?
Is the inverse of a causal system causal?
(b) The inverse of a causal LTI system is always causal.
What is inverse of a system?
In words, the inverse system can be described as follows. The original system transforms an input signal u into an output signal y. This transformation depends on the initial state vector x(0) of the system at time 0. The inverse system retrieves u from y if a suitable initial state (0) is chosen.
What is causality of a system?
A system is said to be causal if it does not respond before the input is applied. In other words, in a causal system, the output at any time depends only on the values of the input signal up to and including that time and does not depend on the future values of the input.
What is an example of causal system?
a) y(t)=x(t)
Here, the signal is only dependent on the present values of x. For example if we substitute t = 3, the result will show for that instant of time only. Therefore, as it has no dependence on future value, we can call it a Causal system.
