Does a causal system have to be non-recursive?

  1. I have been trying to search for a clear definition of "discrete causal systems". The thing I want to know, which I've not been able to find, is whether non-recursiveness of the difference equation is part of the requirement for a causal discrete system?

    Thanks!

    BiP
     
  2. jcsd
  3. AlephZero

    AlephZero 7,298
    Science Advisor
    Homework Helper

    A causal system is just one where the output at time ##T## only depends on the input at times ##t \le T##. In other words, the filter doesn't know anything about the future. That is a requirement for any filter that operates in real time (unless you want to change the laws of physics!) . If you are filtering data that has been acquired in the past, the filter doesn't have to be causal.

    Recursiveness is irrelevant. That just says the output at time ##T## also depends on the output at times ##t \le T##, but those outputs ultimately depend on the inputs.

    Recursiveness is useful in practice because you can design a filter that does a finite number of "operations" (either analog or digital) but the output depends on all the input from times ##-\infty < t \le T##. A simple example would be an digital "exponential smoothing" filter where the output at time ##T## is a weighted average of the input at time ##T##, and the output at the previous time ##T-\delta t##.
     
    Last edited: Mar 13, 2014
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