EECS20N: Signals and Systems


A system is causal if the output value at a particular time depends only on the input values at that time or before. For LTI systems, if we examine the convolution sum,


then it must be true that h(m) = 0 for all m < 0. Were this not true, then there would be non-zero terms in the summation above where m < 0, and those terms would involve a future sample of the input, x(n − m). Conversely, it is easy to see that if h(m) = 0 for all m < 0, then the system is causal.

Causality is an important practical property of a system that receives its data in real time (physical time). Such systems cannot possibly look ahead in time, at least not until someone invents a time machine. However, there are many situations where causality is irrelevant. A system that processes stored data, such as digital audio off a compact disk or audio files in a computer, has no difficulty looking ahead in "time".