A system is memoryless if its output at a given time is dependent only on the input at that same time, i.e., at time depends only on at time ; at time depends only on at time . A memoryless system does not have memory to store any input values because it just operates on the current input.

How do I know if my LTI is memoryless?

An LTI system is called memoryless if the output signal value at any time t depends only on the input signal value at that same time. Again from the convolution integral, if h(t) = 0 for all nonzero values of t, the system is memoryless.

What is a memoryless signal?

This example defines a simple system, where the output signal at each time depends only on the input at that time. Such systems are said to be memoryless because you do not have to remember previous values (or future values, for that matter) of the input in order to determine the current value of the output.