The Convolution of Two Functions | Definition & Properties

[@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.

[@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.

[@nice4hat]

I like your t-shirt haha

[@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!

[@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!

[@sarveshchandak]

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

[@DrTrefor]

You’re welcome 😊

[@DrDerivative]

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

[@RanbirSingh-no3mc]

Best video on KZbin till date

[@NPCNo-xm2li]

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

[@Ayrmodros]

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

[@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!!

[@BentHestad]

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

[@DrTrefor]

Glad you enjoyed!

[@1qaz1qaz15]

*Over

[@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.

[@PiyushPastor]

Wow. Only if the classes were this good.

[@visualgebra]

You and Dr Peyam have best explanation of Convolution!

[@m7mdarwani964]

Clear and concise.

[@zulhishamtan4308]

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

[@eric_welch]

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

[@DrTrefor]

Thanks for subbing!

[@ase1362]

You are of great help. Thanks

[@ProfeARios]

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

[@fernandogallardo3477]

Good stuff for my signals and systems class.

[@joaomattos9271]

Thank you very much!!!!!

[@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

[@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.

[@JOAE23]

Well explained. Thank you!

[@manrajmann4732]

love from India sir !

[@paulkanucawec9489]

What a concise explantation? Thank you Dr.

[@beophobic9653]

Great explanations!

[@TUCSKIRTHIKR]

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

[@johanfrancis2001]

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

[@codyfan1097]

Your videos are so helpful doc ❤️🙏

[@farukdemirel903]

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

[@JohnAbreu17]

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

[@master_zenrade]

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

[@SHAHHUSSAIN]

As usual outstanding...❤❤👏👏

[@RAMKUMAR-rh4um]

Nice T shirt sir, covered all functions 😊

[@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!!

[@philcooper279]

Simply brilliant.

[@hectorgalva7495]

So good, so far. Awesome!!!😄😄

[@matteodare1706]

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

[@yuzou2008]

I love ur T-Shirt!

[@asadshamsiev2462]

Thank you Marc Gasol

[@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

[@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

[@sujanban686]

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

[@muhammadfaizan2232]

Clear and Great

[@uchiha_kakashi6716]

so what is the difference between multiplication and convolution

[@procerpat9223]

Nicely done

[@sogol2261]

Great video. 👍👍👍

[@michaelholland5424]

very nice video.

[@KhinThazin-nx8xd]

Thank you

[@MachoMandem]

I subbed for the shirt, stayed for the video

[@thepie-phitalks07]

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

[@j.o.5957]

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

[@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.

[@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.

[@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! 😭

[@kenny44871]

Great video as usual

[@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.

[@neptune8422]

I like your T shirt!

[@raghuveerdani4046]

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

[@AS-bg9lg]

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

[@theblitz1687]

this was great

[@jacobanderson5693]

Thanks so much.

[@noureldinechaker131]

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

[@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

[@universalalgorithm3263]

Why do convolutions need to be so convoluted?

[@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....

[@SuperHovik]

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

[@kexinsaw7092]

I like your shirt!

[@twillkickers]

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

[@MrMobi007]

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

[@prashantjoshi5389]

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

[@MisterBinx]

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

[@ahmedesamamer]

Where can l get that T shirt ?

[@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.

[@brandonklevans7473]

Awesome shirt

[@liheather2367]

where did you get this Tshirt, professor?

[@stringsam]

really well explained :)

[@JuntaoChu]

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

[@NimbusAbi]

where can i get this shirt?

[@x_ma_ryu_x]

life saver

[@youreverydaytutor278]

nice T-shirt

[@felixgomez5085]

Nice !

[@nnamdiYT]

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

[@leixiao169]

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

[@deyardeyar8163]

10:15 what happened to the tau in the interation

[@sergiomanzetti1021]

Where can I get that t-shirt?

[@armanfahradyan6207]

Great video, but actually I think sin function on your T-shirt is flipped, it is -sin ))

[@blackspitit]

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

[@Acesushii]

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

[@hezhou2062]

Link of your t-shirt plz

[@sukshithshetty4847]

I fell in live with ur tshirt

[@tesset8828]

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

[@accuset]

I need a bigger numpad... dot product, cross product, scalar multiplication, convolution, holy crap.

[@ChristianBilankov]

Where do I get that shirt?