Recent content by Tasos51

Regarding @Vanadium 50 riddle, what time period does 15% refer to ; It is not clear.

I think the question is on how to interpret this probability, not on how it is arrived at. So my view is that there is only one way to interpret this probability, since it is not a recurring event (like tossing a coin): the notion of subjective probability based on games of chance. This is...

I agree with all of the above, but not the last statement. I cannot "believe" in a mathematical statement: it is either proved or disproved. I believe though that the answer is difficult and invloves distribution theory. Another fact, as I mentioned, is that improper systems cannot be put in...

I refer to the solution, not the impulse response. If it contains singularities at 0 (deltas and its derivatives), it means y(0) is not 0, which contradicts the requirement that a causal LTI system should be initially at rest. It is like having an instantaneous input a t=0, when there should be...

Could that mean that the system is not at initial rest, since at 0 it has some non-zero value ? I mean, if the solution to the differential equation contains singularity terms concentrated at zero, this can be viewed as non-zero initial conditions, thus the system is not at initial rest.

So, what is the support of the unit doublet ?

In control systems, the definition of causality is taken as (in words): "the output does not depend on future inputs". For this definition, there exists a test: a system is causal if its impulse response h(t) is 0 for t<0. This is well documented. In parallel, and with no documentation, it is...

I think you are confusing causality with differentiability or realizability. I am not sure how they are connected.

It doesn't. The derivative is not defined at the peak.

Well actually, I started looking at this while writing a textbook on Control (in Greek). Since I did not want to rely on past books, I started searching for a proof which I could not find anywhere. I agree it is of academic importance, but we academics are eager to get to the bottom of things...

(Almost) every textbook on Control Systems contains this assertion-theorem. That's why PID is non-causal. Stability is another matter. And note that we are talking about Linear, Time Invariant (LTI) systems, initially at rest (in order to get the transfer function). In books for distributions...

I was not sure this is the only approach (e.g. derivatives of deltas), and still am not. If this is the case, it looks quite complicated. Some texts do refer to impulse responses that include derivatives of deltas (e.g. Willsky, Signals & Systems), but I would not say "discuss". Maybe, because...

No they are not considered non-causal. This is to be proved, this is the whole idea. Non-causal are systems whose impule response is NOT 0 for t<0.

"The impulse response (just the inverse transform) then has derivatives of delta functions so would be non-causal": Well, this is not obvious to me. Am I missing something trivial ?

I think looking at the differentiator is a correct approach. So, its impulse response is the unit doublet. Causality requires it to be 0 for t<0. Is it ? Furtermore, causality does not make sense for signals, only systems.