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

[oujea]

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:

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.

 

[earlofwessex]

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 don't know what memoryless or casual means

 

[oujea]

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.

 

[earlofwessex]

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?

 

[oujea]

i found it too, but it did not explain it well...