systems theory Systems theory is the Transdisciplinarity, transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, de ...

, an anticausal system is a hypothetical

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...

with outputs and internal states that depend ''solely'' on future input values. Some textbooks and published research literature might define an anticausal system to be one that does not depend on past input values, allowing also for the dependence on present input values. An acausal system is a system that is not a

causal system In control theory, a causal system (also known as a physical or nonanticipative system) is a system where the output depends on past and current inputs but not future inputs—i.e., the output y(t_) depends only on the input x(t) for values of t ...

, that is one that depends on some future input values and possibly on some input values from the past or present. This is in contrast to a causal system which depends only on current and/or past input values.Distinguishing Causal and Acausal Temporal Relations, Kamran Karimi and Howard J. Hamilton, The seventh Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), 2003. This is often a topic of

control theory Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applic ...

and

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a ...

(DSP). Anticausal systems are also acausal, but the converse is not always true. An acausal system that has any dependence on past input values is not anticausal. An example of acausal signal processing is the production of an output signal that is processed from an input signal that was recorded by looking at input values both forward and backward in time (from a predefined time arbitrarily denoted as the "present" time). In reality, that "present" time input, as well as the "future" time input values, have been recorded at some time in the past, but conceptually it can be called the "present" or "future" input values in this acausal process. This type of processing cannot be done in real time as future input values are not yet known, but is done after the input signal has been recorded and is post-processed. Digital room correction in some sound reproduction systems rely on acausal filters.

References

See also