SYSTEMS - DEFINITIONS

System

For the purpose of this website, a system is a transformation between signals.

Input, excitation or stimulus

Any signal that is transformed by a system. If several signals are transformed simultaneously, the system is said to have several inputs.

Output or response

Any signal that is produced as a consequence of the transformation of the inputs to a system.

Reference state

A reference set of simultaneous inputs to a system, and their corresponding outputs.

Asymptotic state

A set of functions to which the inputs and outputs of a system tend at long times.

Steady state

An asymptotic state for which all inputs and outputs have a final value.

Perturbation

A deviation from a reference state caused by a variation of one excitation.

Linear system

A system with the following properties:

a) Homogeneity.

Let an input/ouput pair be

(1)

where the arrow represents the action of the system. Then, if is a constant,

(2)

b) Additivity.

Let two input/ouput pairs be

	(3)
	(4)

Then the output of the sum is the sum of the outputs:

(5)

Nonlinear system

A system that is not linear.

Causal system

A system for which no response occurs (i.e. it is zero) before the pertubation time of the first excitation.

Time-invariant system

A system for which the only effect of a shift in time of the inputs is the same shift of the outputs. That is, for any input/ouput pair, eq. (1),

(6)

for any constant .

Copyright © 2003-2013 Antonio Sánchez Torralba
Last modified:
Monday, 04-Mar-2013 11:58:25 CET