A system is said to be memoryless, if its output for each value of the independent variable is dependent only on the value of the input signal at that value of the independent variable.
The principle of linearity is equivalent to the principle of superposition, i.e. a system can be said to be linear if, for any two input signals, their linear combination yields as output the same linear combination of the corresponding output signals.
To say a system is linear is equivalent to saying that the system obeys both additivity and homogeneity.
Say, for a system, the input signal x(t) gives rise to an output signal y(t), and it is said to be shift invariant if the input signal x(t - t 0 ) gives rise to the output y(t - t 0 ), for every t 0, and every possible input signal.
A system in which a bounded input leads to a bounded output is said to be BIBO stable.
In a causal system, the value of the output signal at any instant depends only on the "past" and "present" values of the input signal and/or "past" values of the output signal.
If a system is additive or homogeneous, then x(t)=0 implies that y(t)=0.
If a causal system is either additive or homogeneous ,then y(t) can not be non zero before x(t) is non-zero.
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