Memoryless Systems
Definition: 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 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'.
