Causal system
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A causal system (also known as a physical or nonanticipative system) is a system where the output y(t) at some specific instant t0 only depends on the input x(t) for values of t less than or equal to t0. Therefore these kinds of systems have outputs and internal states that depends only on the current and previous input values.
The idea that the output of a function at any time depends only on past and present values of input is defined by the property commonly referred to as causality. A system that has some dependence on input values from the future (in addition to possible dependence on past or current input values) is termed an acausal system, and a system that depends solely on future input values is an anticausal system. However, some authors have defined an anticausal system as one that depends solely on future and present input values or, more simply, as a system that does not depend on past input values.
Classically, nature or physical reality has been considered to be a causal system. Though causality is still thought to be found in nature, discoveries in modern physics have challenged the view that nature is strictly causal. For an in-depth discussion, see causality (physics).
[edit] Mathematical Definition
Given two input signals x1(t) and x2(t) that have the relation:
then it follows that:
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