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 its 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 its output at any time doesn't depend on a future event/piece of information. In other words its output at any given time only depends on past or present events/information.

Non-Causal System

Any system whose 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 its impulse is absolutely integrable. That is:

$ \int_{-\infty}^{\infty} \begin{vmatrix} h(\tau)\end{vmatrix}\, d\tau \ll \infty $



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Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett