Causal systems - Paradox? Confusion of definition?

1. What is an example of causal system?
2. How do you determine if a system is causal or not?
3. What is the another name for causal system *?
4. Are all memory systems causal?

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.

How do you determine if a system is causal or not?

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 the another name for causal system *?

This is why, a causal system is also called a non-anticipated system. Where, y(t) or y(n) and x(t) or x(n) are the output and input of the system respectively.

Are all memory systems causal?

A memoryless system is always causal (as it doesn't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values). is memoryless (and necessarily causal) because it only needs the current input sample x[n] to compute the output.