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

• oujea
In summary, the conversation discusses the concepts of non-causal and causal systems, as well as the integral of x(T)dT. The definition of derivative is also mentioned, and there is confusion about whether it is causal or not. The definitions of memoryless and causal systems are provided, but there are conflicting explanations and references. The conversation ends with a request for clarification on the differences between the two definitions of derivative and whether anyone can provide further explanation.

#### 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.

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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

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.

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

## 1. What is a non-causal system?

A non-causal system is a system in which the output depends on future inputs, rather than just past and present inputs. This means that the output at any given time is affected by inputs that have not yet occurred.

## 2. Why is a non-causal system problematic?

A non-causal system can be problematic because it goes against the fundamental principle of causality, which states that the cause must occur before the effect. This can lead to issues with predictability and stability of the system.

## 3. How is dx(t)/dt system non-causal?

The dx(t)/dt system is non-causal because the output at any given time is dependent on the derivative of the input, which includes future values of the input. This means that the output is not solely determined by past and present inputs, violating the principle of causality.

## 4. What are some examples of non-causal systems?

Some examples of non-causal systems include predictive models, such as weather forecasting or stock market prediction. These systems use future inputs to make predictions about the output, making them non-causal.

## 5. Can a non-causal system be made causal?

In some cases, a non-causal system can be made causal by introducing additional information or variables that can account for the future inputs. However, this may not always be possible and can result in a more complex system. It is generally preferred to design systems that are inherently causal to avoid potential issues.