As many others have stated, thank you for making this very easy to understand. It's fascinating how many bad profs there are out there attempting to teach this. If you think about it, it's not that hard but for some reason, many people struggle to explain this properly because they do not spend the time like you did to make it accessible. Again, thank you for doing this.
You turned convolution from a dreaded enemy to an important ally which springs up to rescue while performing inverse laplace of evil looking functions. You sir, are a hero.
Starting from 10:06 when you starting evaluating the integral & on the second line, the last part should have read: -0.5*TAU*cost t, because your're integrating w.r.t. TAU. Anyways, thanks v. much for all your efforts. God bless!
at 10:00 I think you made a mistake in trigo identity, it should be (a-b) also (a+b) to prevent confusion. This identity is product to sum formula if I recall correctly
Just yesterday I was searching for a vid on convolution for my ODE class. Today this new vid popped up in my feed. I'm using it to replace the one I found yesterday, I suppose I should watch this one first, but that's not really necessary. If it is a Trefor Bazett vid, it is good.
Little known fact: the verb for convolution is "to convolve," which means to roll something together. Although it absolutely also "convoluted" the two functions - meaning making something more difficult to understand, it is not what it intend to do :-D
Believe it or not, probability brought me here. I was looking for a more rigorous definition of a convolution. I never studied the Laplace transform. Interestingly enough, two nonnegative RVs that have the same Laplace transform have the same distribution.
I know what you meant fam, I saw the mistake in the video too. If you check the trigo identity he posted at 10:00 its (b-a) it should be (a-b) you'll arrive at 2T-t
I don't know. The definition of convolution is integral from 0 to t, or from -inf to +inf? In different sources, it's defined differently. Can someone explain?
@@tjk581 But the Laplace transform only cares about the values of f(x) for positive x, so you can define f piecewise so that it is sin(x) only for x > 0, giving the result in the video.
If limit has between negative infinity to t in the convolution formula instead of negative infinite to positive infinite, should we call LTI system? Please reply.
Thank you for the explanation. There is just one thing which is bother me. Sometimes speak rate is very fast then it becomes slow suddenly. Sometimes I couldn't understand that I needed to slow the video and it can be distructor.
How can we solve linear differential equations of first order derivative like - dy/dx - y/x = (2x) whole cube by Laplace transform. Please sir, plzz reply
Sajad in this video, the value of f(x) and g(x) is 0 when x < 0. This is the normal approach to evaluate system’s response since we assume the input function is applied to system at t = 0 and before t = 0, we do not do anything to the system.
This is a great series. Stats question. Could you do a video on using the Laplace transform to get a characteristic function of a pdf? If possible, example 1 compares the moment generating function to the characteristic function of a pdf. Example 2 does a pdf with an undefined moment generating function to show how the characteristic function is more broadly defined.
As many others have stated, thank you for making this very easy to understand. It's fascinating how many bad profs there are out there attempting to teach this. If you think about it, it's not that hard but for some reason, many people struggle to explain this properly because they do not spend the time like you did to make it accessible. Again, thank you for doing this.
You turned convolution from a dreaded enemy to an important ally which springs up to rescue while performing inverse laplace of evil looking functions. You sir, are a hero.
😭😭😭
I like your t-shirt haha
You just explained convolution 100 times better than my textbook and my professor! Thanks!!
Haha thanks!
Wonderfully explained. Time to do my final exam. Thank you once again.
Good luck!
Starting from 10:06 when you starting evaluating the integral & on the second line, the last part should have read: -0.5*TAU*cost t, because your're integrating w.r.t. TAU. Anyways, thanks v. much for all your efforts. God bless!
This playlist and the ODE playlist have been getting me through this 5 week summer class
I hope you grow in popularity. Not that it should be needed, but I think many people would benefit from your insight. Thank you for your videos.
this came in clutch, you made it so simple while my professor made it super confusing so thank you Trefor
Haha thanks!
Best video on UA-cam till date
You are single-handedly carrying all my math related subjects throughout my degree.
A quite difficult (but so essential!) concept very well explained! Thanks!
Glad you enjoyed!
*Over
You cleared up all my confusion. Thanks a lot. ❤️❤️❤️
You’re welcome 😊
at 10:00 I think you made a mistake in trigo identity, it should be (a-b) also (a+b) to prevent confusion. This identity is product to sum formula if I recall correctly
Dr Trefor, as usual excellent videos, If there are any math/engineering students that don't "Ace" their exams it is THERE fault...Great JOB !
Thank you!!
Wow. Only if the classes were this good.
You and Dr Peyam have best explanation of Convolution!
if a = tau and b = t - tau, then how did you get b - a = 2tau - t? shouldnt it be t - 2tau?
Just got yourself a new sub :) thank you for the concise way you explain things
Thanks for subbing!
Everybody : let us revise for tomorrow's exam
Me at 12.am :
Dr. Trefor....
First of all, I like your T-Shirt.
Thank you very much for sharing the knowledge.
Thanks so much. The example my teacher gived is so complicated and confusing. Your example helped me totally understand it.
Just yesterday I was searching for a vid on convolution for my ODE class. Today this new vid popped up in my feed. I'm using it to replace the one I found yesterday, I suppose I should watch this one first, but that's not really necessary. If it is a Trefor Bazett vid, it is good.
Great video. Thank you for sharing. Regards from Panama 🇵🇦
So good, so far. Awesome!!!😄😄
What a concise explantation? Thank you Dr.
love from India sir !
Great explanation! and also I liked the t-shirt..
Professor Trefor your T shirt is fantastic. Can you please tell me where I can buy one?
Same haha, I was looking more at his shirt than listening to his explanation
Dr you really doing a good job...appreciate ur work.
..
As usual outstanding...❤❤👏👏
Good stuff for my signals and systems class.
Clear and concise.
Little known fact: the verb for convolution is "to convolve," which means to roll something together. Although it absolutely also "convoluted" the two functions - meaning making something more difficult to understand, it is not what it intend to do :-D
Your videos are so helpful doc ❤️🙏
You are of great help. Thanks
Believe it or not, probability brought me here. I was looking for a more rigorous definition of a convolution. I never studied the Laplace transform. Interestingly enough, two nonnegative RVs that have the same Laplace transform have the same distribution.
Nice T shirt sir, covered all functions 😊
this is what i was looking for! thank you for the amazing video.
This was very helpful.
I love ur T-Shirt!
Great explanations!
Well explained. Thank you!
Whoah T shirt 👚 contains summary of one year of Mathematics.
6:25 but why is L[f(t) * g(t)] = F(s) . G(s) ? Is there a different derivation for this property??
Great video. 👍👍👍
spent more time looking at the shirt than actually paying attention XD
Thank you for your great work. Probably missing a little comment about the Domain of *.
Simply brilliant.
At 4:00, how does dtau turn into negative du? Where did the t go?
Thank you very much!!!!!
I'm sure I can't be the only one with this question. Where can we get that t-shirt? As always great video, thanks for helping those in need!!
I looked at your T-shirt more times than I used in the class.
Dr, in your example, how can you get (2T - t) instead of (t - 2T) ? Help me out 🥺😭
Use trigo. Identities
from sin(T)sin(t-T)
let A=T & B=t-T
Then Subtract to get sinAsinB:
cos(A-B) = cosAcosB + sinAsinB
cos(A+B) = cosAcosB - sinAsinB
cos(A-B) - cos(A+B) = 2sin(A)sin(B)
sin(A)sin(B) = 1/2[cos(A-B) - cos(A+B)]
Then Substitute: (A = T ; B = t-T)
sin(T)sin(t-T) = 1/2{cos[(T) - (t - T)] - cos[(T) + (t - T)]}
Then you get:
sin(T)sin(t-T) = 1/2[cos(2T - t) - cos(t)]
Cos is an even function therfore cos(x) = cos(-x) for every x in R.
I know what you meant fam, I saw the mistake in the video too. If you check the trigo identity he posted at 10:00 its (b-a) it should be (a-b) you'll arrive at 2T-t
Great video as usual
so what is the difference between multiplication and convolution
Nicely done
Please bring a video on generalized convolution ( reference t. M Apostol)
the only thing wrong with this video is we still don't know where to get the epic t-shirt.
Clear and Great
I subbed for the shirt, stayed for the video
I don't know. The definition of convolution is integral from 0 to t, or from -inf to +inf? In different sources, it's defined differently. Can someone explain?
If f and g are zero for negative values, then they are the same and the int from negative infinity to infinity is the same as 0 to t
@@DrTrefor But for evaluating convolution of f(x)=g(x)=sin(x) you used integral form 0 to t , when sin(x) isn't 0 for negative x.
@@tjk581 But the Laplace transform only cares about the values of f(x) for positive x, so you can define f piecewise so that it is sin(x) only for x > 0, giving the result in the video.
That was very helpful Dr. Bazzet, thank you. Can you please send me the link of the shirt you’re wearing? It’s amazing.
Why do convolutions need to be so convoluted?
10:15 what happened to the tau in the interation
If limit has between negative infinity to t in the convolution formula instead of negative infinite to positive infinite, should we call LTI system? Please reply.
Where did you get that your shirt from? I love it. I was hoping to see it in your store. Would definitely buy it if you're selling it
My wife actually gave it as a present years ago and I've never been able to find the exact one again!
@@DrTrefor Oh no! 😭
Although I might not understand much of this yet, I'm beginning to grasp how to do the calculations
very nice video.
I heard another term called polynomial mutiplication used exchangable with the convulution.Are they the same or different?How do they relate?
I like your T shirt!
Hello, thanks for the video, I appreciate it!
Btw, where did you get your t-shirt from? I like it, haha.
6:20 Can we also say that this is an isomorphism?
@@DrTrefor Got it. Thank you!
Oh thanks I'm taking electricity course and I'm using it very much
@@DrTrefor yeah of course it's almost all EM based on laplace transform for signals....
really well explained :)
I need to solved this integral and it really confuses me. I don't understand that t-tau part being in the argument.
How did the sign of integral change? I did not get that part. What of we are integrating from -inf to inf??
Thank you Marc Gasol
nice shirt btw, where can I get it?
I'm wondering the same thing
Thank you for the explanation. There is just one thing which is bother me. Sometimes speak rate is very fast then it becomes slow suddenly. Sometimes I couldn't understand that I needed to slow the video and it can be distructor.
I like your shirt!
How can we solve linear differential equations of first order derivative like - dy/dx - y/x = (2x) whole cube by Laplace transform. Please sir, plzz reply
@@DrTrefor Thanks sir, i love ur channel. You are doing a great job.
Thanks so much.
what about differential property? time shift and fourier ? halpp ;u;
Hi, how is this related to a convolution in a Convolutional Neural Network?
Where can we buy the T-shirt you wear ☺️?
Where can l get that T shirt ?
May I know where can I buy your t-shirt? It's so cute! (That blue one with many common math functions. )
this was great
How we get 2j-t, shouldnot be t-2j ?? 10:01
Use trigo. Identities
from sin(T)sin(t-T)
let A=T & B=t-T
Then Subtract to get sinAsinB:
cos(A-B) = cosAcosB + sinAsinB
cos(A+B) = cosAcosB - sinAsinB
cos(A-B) - cos(A+B) = 2sin(A)sin(B)
sin(A)sin(B) = 1/2[cos(A-B) - cos(A+B)]
Then Substitute: (A = T ; B = t-T)
sin(T)sin(t-T) = 1/2{cos[(T) - (t - T)] - cos[(T) + (t - T)]}
Then you get:
sin(T)sin(t-T) = 1/2[cos(2T - t) - cos(t)]
How did you get -(1/2)tcost?
Hi.
in fourier analysis instead of 0 and t, we write -∞ and +∞ for bounds.
why there is a difference between these two?
Sajad in this video, the value of f(x) and g(x) is 0 when x < 0. This is the normal approach to evaluate system’s response since we assume the input function is applied to system at t = 0 and before t = 0, we do not do anything to the system.
@@rezhaadriantanuharja3389 what about the upper bound?
Sajad If tau > t, then (t - tau) < 0 and g(t-tau) = 0
@@rezhaadriantanuharja3389 Thank you
where did you get this Tshirt, professor?
your shirt but y is the indicator function on a dense set :)
I need a bigger numpad... dot product, cross product, scalar multiplication, convolution, holy crap.
This is a great series. Stats question. Could you do a video on using the Laplace transform to get a characteristic function of a pdf?
If possible, example 1 compares the moment generating function to the characteristic function of a pdf.
Example 2 does a pdf with an undefined moment generating function to show how the characteristic function is more broadly defined.
1.59 i guess it is not a function of t but tau. the way you wrote it down.
Fun question: A(f,g)=Lf*Lg
What is A?
the tshirt for me🤣🤣🤣🤣🤣🤣
where can i get this shirt?