The six basic properties of Systems_OldKiwi

Memory_OldKiwi

A system with memory has outputs that depend on previous (or future) inputs.

• Example of a system with memory:

$ y(t) = x(t - \pi) $

• Example of a system without memory:

$ y(t) = x(t) $

Invertibility_OldKiwi

An invertible system is one in which there is a one-to-one correlation between inputs and outputs.

• Example of an invertible system:

$ y(t) = x(t) $

• Example of a non-invertible system:

$ y(t) = |x(t)| $

In the second example, both x(t) = -3 and x(t) = 3 yield the same result.

Causality_OldKiwi

A causal system has outputs that only depend on current and/or previous inputs.

• Example of a causal system:

$ y(t) = x(t) + x(t - 1) $

• Example of a non-causal system:

$ y(t) = x(t) + x(t + 1) $

Stability_OldKiwi

Time Invariance_OldKiwi

Linearity_OldKiwi