027. System Function: Forced and Natural Response, Poles and Zeros, Time Domain View, Laplace Xform

[@ehsanderakhshanniya7881]

Saying thank you hardly seems enough after all you have done for us.thank you so muchthank youu sooo much dear proffesor.

[@AliHajimiriChannel]

You are welcome.

[@pyrokinetikrlz]

Holy shit! This is the most elegant way of presenting the Laplace transform I ve seen. Usually, teachers just introduce it by defining it and listing is properties, but in this lecture is a natural followup of the previous concepts. great job!

[@AliHajimiriChannel]

I am glad that it fit well. Thanks for your kind comments.

[@isacdaimary9908]

I wish I came across these lecture few years ago. Thank you Dear professor

[@TheWarBleed]

I'm in love your videos. How come they have these low amount of views?!? Thanks for your efforts. we need more professors like you :)

[@phzhao5132]

When we talk about the definition of transfer/system function. What does making p=s mean? p is an operator while s is a complex number.

[@aryamick]

Sir can you please confirm that (47:16) we have not discussed the impulse response of terms like 1/(s^2+a*s+b)^3. For these we have to break into monomials with complex roots? Thank you so much for making these (& analog circuit design) lectures available online, just can't express my gratitude.

[@coolwinder]

10:48 - An Example - ______ - Hitting the system with zero frequency to produce only natural frequencies at the output ______ - Hitting the system with pole frequency to produce it's natural frequencies and a spike/dip with input frequency 23:00 - Non-validity of H(s) for Pole Frequencies 26:23 - Concept of Poles and Zeros, Low-Pass Form 31:48 - S-Plane 48:05 - Laplace Transform Derived from Two-Sided Input Signal

[@aravindhvasu195]

Thank you very much for this beautiful playlist. But how did you conclude that the other part was the natural response? I mean, why should it be the natural response ?

[@AliHajimiriChannel]

The forced response is captured by the first part, so whatever is not forced and we call that the natural response.

[@aravindhvasu195]

@@AliHajimiriChannel Alright, thank you very much for your time. If you have time, can you please take a look at math.stackexchange.com/q/3431062/525644 This question is based on your gorgeous lectures :) I've added a comment on the Laplace transform video too :)

[@coolwinder]

Is H(s) amplification factor for forced or stedy-state response? So forced (or stady-state) response for the pole frequencies would be actually zero as they asymptotically approach zero with it's negative exponential value?

[@coolwinder]

So are we saying that if we excite the system with pure never ending sinusoid (two complex frequencies with conjugate pure imaginary parts), and if our system is stable, after natural response has subsided, we would only get that excitation frequency at the output? So that's the reason we can discard Yn(p)? Is Yn(p) changing for different e^st inputs or is it constant, that is, its system impulse response operator? 18:30 i suppose it changes with input.

[@coolwinder]

Do all zeros need to be real or have a complex-conjugate pair, for a real system? 51:25 So having a two-sided input would give as immediately the amplification factor of the input complex frequency without a need to wait (as we have been waiting from -inf) for the output signal to enter steady-state (which for periodic sinusoidal input signal would be something like >> duration of impulse response + period of input signal

[@coolwinder]

8:50 - What happens with natural response part? Does it decay?

[@Jhonatan31415]

What is the book used on this class ?

[@AliHajimiriChannel]

Linear Circuit Analysis by Artice Davis. However, there are parts of the class not covered by the book.

[@enelysionfields2376]

isnt laplace evaluated from zero to infinity?

[@AliHajimiriChannel]

Two-sided Laplace transform is from -inf to +inf. Now if you deal with one sized signals (for example, step, ramp, ...) which would happen if you are dealing with the impulse response of causal systems, then the integral value is zero for negative times, hence you can evaluate it from 0 to +inf and you get the one-sided Laplace. Watch video 029 kzbin.info/www/bejne/jF6nfJalnbZ4rMk , staring around the 4th minute.

[@companymen42]

Why do you need to have pairs of poles for the system to be a real system?

[@AliHajimiriChannel]

That is not necessarily true. If you have complex poles in your system, they should come in complex conjugate pairs for the transfer function to be real. You obviously can have a first order system with a single real pole.