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

  • Thread starter oujea
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  • #1
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Hello

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

EDIT:

I found this:
ogkt8n.png


and this:
6hht0y.jpg


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:

Answers and Replies

  • #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
 
  • #3
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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.
 
  • #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
http://perso.univ-rennes1.fr/ian.sims/pdfs/L3%20SSP%2010-11%20Model%20Exam%20Solution%20Guide.pdf
b. The system y(t) = dx/dt

Is not memoryless as derivative cannot be determined from a single point

Is causal: output does not anticipate future values of input
thats a french university



two conflicting answers, can anyone shed light on this?
 
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  • #5
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i found it too, but it did not explain it well...
 

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