The Convolution of Two Functions | Definition & Properties

[@nice4hat]

I like your t-shirt haha

[@vaibhavdlxit1050]

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.

[@ejkitchen]

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.

[@bromarskiii]

You just explained convolution 100 times better than my textbook and my professor! Thanks!!

[@DrTrefor]

Haha thanks!

[@ricardobautista-garcia8492]

Wonderfully explained. Time to do my final exam. Thank you once again.

[@DrTrefor]

Good luck!

[@DrDerivative]

if a = tau and b = t - tau, then how did you get b - a = 2tau - t? shouldnt it be t - 2tau?

[@josiahkolar4209]

This playlist and the ODE playlist have been getting me through this 5 week summer class

[@migo77]

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!

[@RubALamp]

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.

[@sobhanboss3935]

this came in clutch, you made it so simple while my professor made it super confusing so thank you Trefor

[@DrTrefor]

Haha thanks!

[@RanbirSingh-no3mc]

Best video on KZbin till date

[@sarveshchandak]

You cleared up all my confusion. Thanks a lot. ❤️❤️❤️

[@DrTrefor]

You’re welcome 😊

[@PiyushPastor]

Wow. Only if the classes were this good.

[@BentHestad]

A quite difficult (but so essential!) concept very well explained! Thanks!

[@DrTrefor]

Glad you enjoyed!

[@1qaz1qaz15]

*Over

[@NPCNo-xm2li]

You are single-handedly carrying all my math related subjects throughout my degree.

[@eggxecution]

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

[@eric_welch]

Just got yourself a new sub :) thank you for the concise way you explain things

[@DrTrefor]

Thanks for subbing!

[@hsotnicam]

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

[@TUCSKIRTHIKR]

Everybody : let us revise for tomorrow's exam Me at 12.am :

[@uchiha_kakashi6716]

so what is the difference between multiplication and convolution

[@ConceptualCalculus]

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.

[@visualgebra]

You and Dr Peyam have best explanation of Convolution!

[@BoZhaoengineering]

Professor Trefor your T shirt is fantastic. Can you please tell me where I can buy one?

[@Tosti_bakker]

Same haha, I was looking more at his shirt than listening to his explanation

[@jaydean5243]

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 !

[@DrTrefor]

Thank you!!

[@ProfeARios]

Great video. Thank you for sharing. Regards from Panama 🇵🇦

[@Ayrmodros]

Thanks so much. The example my teacher gived is so complicated and confusing. Your example helped me totally understand it.

[@m7mdarwani964]

Clear and concise.

[@rmb706]

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.

[@zulhishamtan4308]

Dr. Trefor.... First of all, I like your T-Shirt. Thank you very much for sharing the knowledge.

[@fernandogallardo3477]

Good stuff for my signals and systems class.

[@johanfrancis2001]

Dr you really doing a good job...appreciate ur work. ..

[@ase1362]

You are of great help. Thanks

[@manrajmann4732]

love from India sir !

[@farukdemirel903]

Great explanation! and also I liked the t-shirt..

[@SHAHHUSSAIN]

As usual outstanding...❤❤👏👏

[@paulkanucawec9489]

What a concise explantation? Thank you Dr.

[@codyfan1097]

Your videos are so helpful doc ❤️🙏

[@universalalgorithm3263]

Why do convolutions need to be so convoluted?

[@joaomattos9271]

Thank you very much!!!!!

[@hectorgalva7495]

So good, so far. Awesome!!!😄😄

[@abang571]

Dr, in your example, how can you get (2T - t) instead of (t - 2T) ? Help me out 🥺😭

[@edilmarlulab7079]

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)]

[@thejohncenafan100]

Cos is an even function therfore cos(x) = cos(-x) for every x in R.

[@eggxecution]

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

[@yuzou2008]

I love ur T-Shirt!

[@beophobic9653]

Great explanations!

[@twillkickers]

At 4:00, how does dtau turn into negative du? Where did the t go?

[@prashantjoshi5389]

6:25 but why is L[f(t) * g(t)] = F(s) . G(s) ? Is there a different derivation for this property??

[@master_zenrade]

Whoah T shirt 👚 contains summary of one year of Mathematics.

[@SuperHovik]

How did you get -(1/2)tcost?

[@philcooper279]

Simply brilliant.

[@JohnAbreu17]

Thank you for your great work. Probably missing a little comment about the Domain of *.

[@chinnamuniyandi2023jrf]

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.

[@raghuveerdani4046]

How did the sign of integral change? I did not get that part. What of we are integrating from -inf to inf??

[@JOAE23]

Well explained. Thank you!

[@RAMKUMAR-rh4um]

Nice T shirt sir, covered all functions 😊

[@tjk581]

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?

[@DrTrefor]

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

[@tjk581]

@@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.

[@angelmendez-rivera351]

@@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.

[@ahmedesamamer]

Where can l get that T shirt ?

[@deyardeyar8163]

10:15 what happened to the tau in the interation

[@sogol2261]

Great video. 👍👍👍

[@sergiopallas4567]

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!!

[@nnamdiYT]

I heard another term called polynomial mutiplication used exchangable with the convulution.Are they the same or different?How do they relate?

[@MisterBinx]

I need to solved this integral and it really confuses me. I don't understand that t-tau part being in the argument.

[@Acesushii]

what about differential property? time shift and fourier ? halpp ;u;

[@procerpat9223]

Nicely done

[@thepie-phitalks07]

Please bring a video on generalized convolution ( reference t. M Apostol)

[@muhammadfaizan2232]

Clear and Great

[@matteodare1706]

this is what i was looking for! thank you for the amazing video.

[@blackspitit]

Hi, how is this related to a convolution in a Convolutional Neural Network?

[@amroalatasi2415]

That was very helpful Dr. Bazzet, thank you. Can you please send me the link of the shirt you’re wearing? It’s amazing.

[@leixiao169]

Where can we buy the T-shirt you wear ☺️?

[@liheather2367]

where did you get this Tshirt, professor?

[@NimbusAbi]

where can i get this shirt?

[@sujanban686]

I looked at your T-shirt more times than I used in the class.

[@sergiomanzetti1021]

Where can I get that t-shirt?

[@kenny44871]

Great video as usual

[@tesset8828]

your shirt but y is the indicator function on a dense set :)

[@vicadegboye684]

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

[@DrTrefor]

My wife actually gave it as a present years ago and I've never been able to find the exact one again!

[@vicadegboye684]

@@DrTrefor Oh no! 😭

[@michaelholland5424]

very nice video.

[@AS-bg9lg]

Hello, thanks for the video, I appreciate it! Btw, where did you get your t-shirt from? I like it, haha.

[@hezhou2062]

Link of your t-shirt plz

[@JuntaoChu]

May I know where can I buy your t-shirt? It's so cute! (That blue one with many common math functions. )

[@ChristianBilankov]

Where do I get that shirt?

[@asadshamsiev2462]

Thank you Marc Gasol

[@MrMobi007]

the only thing wrong with this video is we still don't know where to get the epic t-shirt.

[@rajkumarray2907]

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

[@rajkumarray2907]

@@DrTrefor Thanks sir, i love ur channel. You are doing a great job.

[@noureldinechaker131]

spent more time looking at the shirt than actually paying attention XD

[@jacobanderson5693]

Thanks so much.

[@MachoMandem]

I subbed for the shirt, stayed for the video

[@neptune8422]

I like your T shirt!

[@joesmith8288]

6:20 Can we also say that this is an isomorphism?

[@joesmith8288]

@@DrTrefor Got it. Thank you!

[@superdahoho]

nice shirt btw, where can I get it?

[@rtusiime]

I'm wondering the same thing

[@sajjad213]

Hi. in fourier analysis instead of 0 and t, we write -∞ and +∞ for bounds. why there is a difference between these two?

[@rezhaadriantanuharja3389]

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.

[@sajjad213]

@@rezhaadriantanuharja3389 what about the upper bound?

[@rezhaadriantanuharja3389]

Sajad If tau > t, then (t - tau) < 0 and g(t-tau) = 0

[@sajjad213]

@@rezhaadriantanuharja3389 Thank you

[@kexinsaw7092]

I like your shirt!

[@j.o.5957]

Although I might not understand much of this yet, I'm beginning to grasp how to do the calculations

[@gulsumsecilsermet8583]

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.

[@theblitz1687]

this was great

[@josephhajj1570]

Oh thanks I'm taking electricity course and I'm using it very much

[@josephhajj1570]

@@DrTrefor yeah of course it's almost all EM based on laplace transform for signals....

[@KhinThazin-nx8xd]

Thank you

[@aoqu8349]

How we get 2j-t, shouldnot be t-2j ?? 10:01

[@edilmarlulab7079]

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)]

[@stringsam]

really well explained :)

[@brandonklevans7473]

Awesome shirt

[@epicmorphism2240]

Fun question: A(f,g)=Lf*Lg What is A?