Causal System - Mathematical Definitions

Mathematical Definitions

Definition 1: A system mapping to is causal if and only if, for any pair of input signals and such that

the corresponding outputs satisfy

Definition 2: Suppose is the impulse response of the system . (only fully accurate for a system described by linear constant coefficient differential equation)

then the system is causal, otherwise it is non-causal.

Read more about this topic:  Causal System

Famous quotes containing the words mathematical and/or definitions:

    As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.
    Blaise Pascal (1623–1662)

    What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.
    —G.C. (Georg Christoph)