I have read when studying this subject that a system is LTI and causal if and only if it can be expressed as a difference equation (if it is in continuos time, as a differential one). I don't know if this is true, mayne I'm remembering it wrong.
The problem is that today I thought of the case of an IIR filter. It is not causal and it can be written as a difference equation.
So I have two questions about this:
1) Why does an LTI system have to accomplish the initial rest condition (causality?) in order to be expressed as a difference equation?
2) What about the IIR filters? They are not causal and they can be expressed as a difference equation. Why is that? What am I thinking wrong?