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:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (18171862)
“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)