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:
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)
“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)