Hey all!. I have a simple question. why do we analyze a system's ROC in s-domain and how does it impact our time signal.
I don't know what ROC stands for. The general answer to your question about Laplace transforms is that they transform an Ordinary Differential Equation in the time domain into an algebraic equation in the frequency domain. It is established that there is a 1:1 correspondence between time domain solutions and frequency domain solutions. In practice this means that you can find all possible solutions by either method and they are unique. That is, there are no other solutions that can be found.Hey all!. I have a simple question. why do we analyze a system's ROC in s-domain and how does it impact our time signal.
In Complex Analysis there is the concept of an "analytic function". The following explanation is from wikipedia:Yes u got my point. Pole and zero analysis is enough to obtain stability information, then why do we use a concept called Region of Convergence.
Hello there,Hey all!. I have a simple question. why do we analyze a system's ROC in s-domain and how does it impact our time signal.
Hi, i want you to elucidate more on this particular point of yours inside the quote, "Poles and zeros tell you something about the response too but that is a somewhat different view because it is more specific which tells you something about just one specific system". From your point what i conclude is, poles and zeroes are specific to a system, then what does ROC do?Hello there,
The ROC is a general statement which refers to a range of values where a function can provide reasonable results. If you go outside that range that function will provide unrealistic results unless maybe at least part of the response is inside that range and i think it has to be the dominant part.
Poles and zeros tell you something about the response too but that is a somewhat different view because it is more specific which tells you something about just one specific system.
For example, if the ROC is the unit circle, then anything inside that circle is both stable and causal. We are able to state that even without referring to any specific system.
You should really look around the web and look for some examples.
I also recommend looking at the root locus procedure if you are interested in stability.
It tells you that you have a first order linear system with an exponential decay. As you move along the jω-axis from very small frequencies to very large frequencies the system response as a function of frequency is monotonically decreasing and approaches 0 at the point 0 + j∞what does it say about the system, about its inputs and outputs?
Here is a graphic of the time domain responses based on the pole positions in the complex plane.Or for a better convenience take a system whose transfer functions is H(s)=1/(s+3), its ROC is s>-3. ok, fine now how does that information reflect into the time domain.
Oh yes math is the root to all engineering and in general science. The math just goes on and the more you know the better understanding of electrical engineering you will gain.The more I learn EE, the more I realize I like to learn math 1st, in general, because otherwise I'm banging my head wondering where stuff comes from, and it's too close to cheating. It's like standing on a bridge that I'm afraid is about to collapse.
I've been shagging around with LT's again, and trying to figure out some of equations, calculus-wise in R it's no problem (for common functions), so I'm another few steps closer to doing something useful with freq-domain functions in EE. So far I'm mainly using phasors and single frequencies sill tho. But I can find basic pole's/zero's, but only of the most basic circuits.
My current ODE textbook must have all this tho, so I just have to keep plowing through it all.
I was the same way. Some students prefer to learn the math along with the engineering concepts because it grounds the math with something tangible or at least relevant to them. But to me the equations were pure sorcery until I understood the math behind them. The Laplace transform, in particular, was a bewildering beast until I took the effort to lear where it came from and what it actually does. Then it all made perfect sense.The more I learn EE, the more I realize I like to learn math 1st, in general, because otherwise I'm banging my head wondering where stuff comes from, and it's too close to cheating. It's like standing on a bridge that I'm afraid is about to collapse.
I don't believe this is historically accurate. Statistical correlation wasn't developed until the late 19th century, many decades after Laplace's death.actually Laplace transform formula comes from the correlation formula in statistics...
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by Jake Hertz
by Jake Hertz
by Jake Hertz