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Basic System Properties (ECE301)
Memoryless System
A system is memoryless if for any $ t \in \mathbb{R} $ the output at $ t_0 \, $ depends only on the input at $ t_0 \, $
In other words it doesn't depend on past or future events or information.
System With Memory
A system has memory it's output at any given time depends somehow on either a past and/or future event or piece of information.
Causal System
A system is causal if it's output at any time doesn't depend on a future event/piece of information. In other words it's output at any given time only depends on past or present events/information.
Non-Causal System
Any system thats output at any given time depends on a future event or piece of information isn't a causal system.
Linear System
A system is linear if it upholds both additivity and multiplicity.
In mathematical terms the following must be satisfied:
$ y[a+b]=y[a]+y[b] \, $
$ y[ka]=ky[a] \, $
Non-Linear System
A system is called non-linear if it doesn't uphold BOTH the additive and multiplicity properties.
Time-Invariant System
A system is called time-invariant if for any input $ x(t)\, $ at time $ t \in \mathbb{R} $ the shifted input $ x(t-t_0)\, $ yields response $ y(t-t_0) \, $
Time-Variant System
A system is called time-variant if for any input $ x(t)\, $ at time $ t \in \mathbb{R} $ the shifted input $ x(t-t_0)\, $ response ISN'T equal to $ y(t-t_0) \, $
Stable System
A system is stable if in CT it's impulse is absolutely integrable. That is:
$ \int_{-\infty}^{\infty} \begin{vmatrix} h(\tau)\end{vmatrix}\, d\tau \ll \infty $
