Systems with Memory and without Memory

A system is said to be memoryless if the output at any time depends on only the input
at that same time. Otherwise, the system is said to have memory. An example of a
memoryless system is a resistor R with the input x ( t ) taken as the current and the voltage
taken as the output y ( t ) .
The input-output relationship (Ohm's law) of a resistor is
An example of a system with memory is a capacitor C with the current as the input x( t )
and the voltage as the output y ( 0 ; then

y (t)

A second example of a system with memory is a discrete-time system whose input and
output sequences are related by


y (n)