Memoryless Systems
A memoryless system is one that produces an output Y(t) that is purely dependent on the input at that specific time t.
Memoryless System: y(t) = 2x(t) + 7t
System with Memory: y(t) = 2x(t) +7(t-5)
The first example above is memoryless since it only depends on the time 't'. The second example has memory since it depends on both the time 't' and the time 't-5'.
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'.
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'.
