In signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, an anti-causal system is one whose output depends only on present and future inputs. An anti-causal system that is also linear and time-invariant

LTI system theory

Linear time-invariant system theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas. It investigates the response of a linear and time-invariant...

 is an anti-causal filter. By contrast, a filter whose output depends only on past and present inputs is called a causal filter

Causal filter

In signal processing, a causal filter is a linear and time-invariant causal system. The word causal indicates that the filter output depends only on past and present inputs. A filter whose output also depends on future inputs is non-causal. A filter whose output depends only on future inputs is...

.

An example of an anti-causal filter is a maximum phase filter, which can be defined as a stable

BIBO stability

In electrical engineering, specifically signal processing and control theory, BIBO stability is a form of stability for linear signals and systems that take inputs. BIBO stands for Bounded-Input Bounded-Output...

, anti-causal filter whose inverse is also stable and anti-causal.