Sufficient condition for a system to have memory

1. When a system is said to have memory?
2. How do you know if a system has memory?
3. Can a non causal system be memoryless?
4. How do I know if my system is memoryless?

When a system is said to have memory?

A system is defined as Non-Memoryless (with Memory) if its output at any time depends on current and previous values of the input and of previous values of the output; causal systems are under consideration. For physical systems to have memory, they must have energy/information storing element(s).

How do you know if a system has memory?

Systems with memory

In other words, a system y(t₀) has memory if its output at time t₀ depends on the input x(t) for t > t₀ or t < t₀, i.e. it depends on values of the input other than x(t₀). Example of a memoryless system: Resistor v(t₀) = R i(t₀); the voltage at time t₀ depends only on the current at time t₀.

Can a non causal system be memoryless?

In contrast, the output signal of a noncausal system depends on one or more future values of the input signal. All physically realizable systems are causal. Note that all memoryless systems are causal, but not vice versa.

How do I know if my system is memoryless?

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.