Memoryless System & System with Memory
- A system is memoryless if for any t0, the output y(t0) only depends on the present input, x(t0).The output doesn't depend on past or future input, x(t0 + k) for any integer k.
- A system is a system with memory if for any t0, the output y(t0) depends on not only the present input, x(t0) but also the past or future, x(t0 + k) for any integer k.
Example
$ y(t) = x(t) + x(t^2)\, $
If t equals to 2, $ y(2) = x(2) + x(4)\, $.
Then the output depends on the present and future inputs. So the system is memory.
