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How is dx(t)/dt system non-causal

  1. Mar 28, 2012 #1

    Can someone please explain me how is system

    y(t)=dx(t)/dt non-causal and system with memory? I tried it using derivation definition, but I did not understand it.

    Also I'm interested in integral of x(T)dT (from -inf to to) - is it always causal and how? Do you have any literature or links where it is well explained.

    Thank you in advance


    I found this:

    and this:

    How can I know from this definition of derivative that it is not causal? And on those two pictures, dx(t)/dt definition is different, so what's correct? I have before seen second one, but never the first one.
    Last edited: Mar 28, 2012
  2. jcsd
  3. Mar 28, 2012 #2
    the definitions are equivalent at the limit δt → 0. both expressions give the change in x(t) when you vary t by Δt, devided by Δt. one of them considers a posative Δt from the point of interest, while the other is negative.

    unfortunately i dont know what memoryless or casual means
  4. Mar 28, 2012 #3
    A system is memoryless if the output at each time depends only on the input
    at the same time.

    A system is causal if the output at each time depends only on the input at
    the same time or on the prior inputs.
  5. Mar 28, 2012 #4
    ok, well in that case its a bit more complicated.
    the internet seems to suggest a system is causal if y(t) depends on x(t), dx/dt, x(t-T) for T>0
    ie, things in the past and present only.

    ... which explains why the first dx/dt definition you post lists it as non causal, since x(t+δt) is in the future. but that now highlights a difference between the definitions.

    that info came from "personalpages.manchester.ac.uk/staff/martin.brown/signals/Lecture17.ppt" [Broken] (its a presentation *.ppt)

    another reference gives
    thats a french university

    two conflicting answers, can anyone shed light on this?
    Last edited by a moderator: May 5, 2017
  6. Mar 28, 2012 #5
    i found it too, but it did not explain it well...
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