Causal System
A causal system (non-anticipative system) is one that produces an output that is dependent on either present or past values of 't'. Therefore, a causal system does not produce an output x(t) based on any future value of 't'. Furthermore, we can conclude that all memoryless systems are causal because they only depend on a present value of 't'.
Non-Causal System
A non-causal system is exactly what you would expect, the opposite of a causal system. A non-causal system is one that produces an output that IS dependent on some future value of 't'. In addition to being dependent on a future value of 't', the system's output may also be dependent on a present or past value of t.
Causal System:
y(t) = x(t-9) + 6
Non-Causal System: y(t) = x(t+9) +6
The first system is causal since it is dependent on a past value of 't'. However, the second system is non-causal because it depends on a future value of 't'.
