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Memory and Memory-less System
A system is said to be memory-less, if and only if its output to a corresponding input depends only on the value of the input at that current time.
A system is said to have memory when, for a given input the output does not only depend on the value of the input at that current time.
Causal and Non-Causal Systems
A system is said to be causal if for any input, the output has no dependence on the value of the input at any time in the future. A system is said to be non-causal if for any input, the output has any dependence on the value of the input at any time in the future.
Linear and Non-Linear Systems
A system is said to be linear if it obeys the principle of superposition and is closed under scalar multiplication. That is for set of given inputs, each with their respective outputs, any linear combination of the inputs will produce a corresponding linear combination of their outputs.
A system is said to be non-linear if it does not obey the principle of superposition and is not closed under scalar addition. That is for a set of given inputs, each with their respective outputs, any linear combination of the inputs will not produce a corresponding linear combination of their outputs.
Time Invariant and Non-Time Invariant Systems
A system is said to be time invariant if for a given input and corresponding output, when the input is shifted by some t0 in time its corresponding output is the output shifted by that same t0 in time.
A system is said not to be time invariant if for a given input and corresponding output, when the input is shifted by some t0 in time its corresponding output is not shifted by that same t0 in time.
Stable and Unstable Systems
A system is said to be stable if for a given input bounded by some value B, the corresponding output is also bounded by some value B'. That is the output converges to to some finite value.
A system is said to be unstable if for a given input bounded by some value B, the corresponding output is not bounded by any value. That is the output diverges (either to negative or positive infinity).
