029. Laplace Transform Summary: Definition, Properties
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- Опубликовано: 21 окт 2024
- Introductory Circuits and Systems, Professor Ali Hajimiri
California Institute of Technology (Caltech)
chic.caltech.ed...
029. Laplace Transform Summary: Definition, Properties, differentiation and integration, Laplace transform of elementary functions.
© Copyright, Ali Hajimiri
20161115111706EE44
Professor, you are the only source who I have come across to introduce operational calculus for problem solving. This makes things a lot more intuitive and that's how engineers should be taught things.
Actually you make my day when i see the new update And always i'm looking forward to the new one with Passion.thank you so much dear respected professor.thank you ..
You're welcome.
You're an awesome instructor! Do you plan on posting more videos soon?
Hi, professor at 9:24 when you do laplace transform of P(x(t)) are you assuming that s is positive? If not, e^(-st) won't be zero in infinity, right?
Hi, Professor
0:29, Does the equation mean y(t)=H(s)x(t) when x(t)=e^(st)? But in lecture of system function, you said that only forced response is H(s)x(t). Where does this discrepancy com from?
6:14, the upper bound of laplace should be negative infinity while the lower bound should be t, for input x(t)=e^(st)u(t). Because we have x(t-tau) in the convolution which leads to u(t-tau). u(t-tau) is non-zero from negative to t. Otherwise it won't even converge
Sir, can you please state (and prove if possible) the initial and final value theorems for the operator method.
6:14, the upper bound of laplace should be negative infinity while the lower bound should be t, for input x(t)=e^(st)u(t). Because we have x(t-tau) in the convolution which leads to u(t-tau). u(t-tau) is non-zero from negative to t. Otherwise it won't even converge
@50:22 Sir , Why did you say s- is a complex frequency ?
Because, in general s is a complex number. See the lecture on poles and zeros and the impulse response of systems with different pole locations.
First of all, thank you very much for recording these gorgeous lectures, I've never felt so comfortable, while attending an online course. I've a doubt, What does taking Laplace transform on both sides of a differential equation mean? Please take a look at this question, math.stackexchange.com/questions/3431062/how-is-laplace-transform-more-efficient
In the operator method, we wrote the input and output in terms of Dirac-Delta function, therefore we essentially created two ways of arriving at y(t), one by applying X(P) and H(P) in succession or by applying Y(P) only, so we were able to equate these two processes. According to the results that we arrived at in this lecture, the final H(D) for a system when the input is e^st is equal to the Laplace Transform. *What are we essentially doing while we "apply" Laplace transform on both sides?*
On plain sight, while we take LT on both sides, we are assuming that the LHS and the RHS of a ODE are the impulse responses of a system and we are calculating the response of this system when the input is e^st and after applying the transform the e^st in the responses cancel out on both sides leaving us two functions of 's' on the LHS and RHS of the equation and finally this gives Y(s). But why do all this(I don't understand why all these works though, it was pretty clear when we did the former, that is, writing x(t) and y(t) in terms of operators acting over delta)? Why not form H(P) as we did before and substitute 's' instead of 'P'. What actual advantage did Laplace transform bring with it, when compared to the previous operator-method?
i came across LT in my math, circuits, control engineering and signals and system.so there is no way to runaway from this transform .but most of the time we only need unilateral L.T. except for signals and system where i had to study both of them .
Which book would you recommend for signals and systems ,control systems and communication engineering ? Thanks for telling me about Artice Davis book on circuits.
Oppenheim is a classic book on Signals and Systems. I like Zimmer for communications.
Hello, do you have a pdf copy of Artice Davis book, I couldn't find it anywhere.
6:33 - Basic Laplace Transform Properties