Introduction to the convolution | Laplace transform | Differential Equations | Khan Academy

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Introduction to the Convolution
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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6 окт 2009

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Комментарии : 222

@neilsmith4159 8 лет назад

Khanvolution

@ashishkesharwani1559 6 лет назад

hahaha, true...:)

@nocturnalvisionmusic 2 года назад

@@ashishkesharwani1559 only one response in five years and 532 likes... decided to fix :D Great pun though :)

@Ojzesports Год назад

@@nocturnalvisionmusica year later I add another comment to keep the tradition you started😂

@nocturnalvisionmusic Год назад

@@Ojzesports whoo-hoo thanks 😁

@changyuanlin2233 8 лет назад

This is the introduction to the integration rather than convolution!

@zc4612 3 года назад

Newbie to convolution here. Is this not the convolution of f and g?

@devanshsharma2106 2 года назад

@@zc4612 he is joking bro. he meant definiton is just one line. rest video is about integrating.

@someonetoogoodforyou 11 лет назад

For those who are interested: Convolution is used frequently in vibration analysis of second order systems.

@existentialrap521 2 года назад

Which is why I'm prolly learning it in diff equations rn xD

@OlisserGomez 11 лет назад

i just watched this video on a Saturday night and thoroughly enjoyed it, especially the ending where he was able to cancel and simplify, it's an odd sense of satisfaction. I need to start drinking and going out again...

@michaelempeigne3519 7 лет назад

a better idea is to use the product to sum formulas: sin A cos B = ( 1 / 2 ) * [ sin ( A + B ) + sin ( A - B ) ]

@thefinitejoke 10 лет назад

Great introduction to convolution. My professor tends to go off on random tangents and this exercise finally gave me an idea of the nuts and bolts.

@tymothylim6550 3 года назад

Thank you very much for this video! It was a great example-driven tutorial and I learnt a lot from it!

@KanitaKhaled5 11 лет назад

wow. best video on intro to convolution that I could find! amazing!

@redshot17 14 лет назад

Finally I understood how a Convolution is done. Thank you very much.

@sizzlingal 14 лет назад

Thank you so much! like everyone else, i did not understand what my Professor has been talking about all semester! If i didnt watch these videos, id have no understanding of Diffeq's. May you be blessed for posting these videos!

@marcalanstreeter 12 лет назад

Great tutorial - and thank you for the small refreshers in the middle - its been a while since I had used them

@09seaner 9 лет назад

Sal you the real MVP

@6ZYX6 11 лет назад

Thanks a lot, found it really helpful! (got to admit, I'm digging the color scheme, very easy going)

@rend_neu 6 лет назад

Thanks a lot Sir, Btw, you can just multiply and divide by 2 to Sin(tau)Cos(tau) that would convert it into sin(2tau) /2 Now that's more easy to integrate, just write = -Cos(2tau)/(2*2) ..:)

@clovisfritzen 10 лет назад

Good explanation, thanks!

@Ronaldoh1 14 лет назад

who ever you are ...i just want to say that you're awesome!!!!! love you man thanks for the vids!!

@perala123 10 лет назад

your ''t'' looks like a ''+" . Apart from that, it's a very good explanation.

@rafaelsevilla432 11 лет назад

con·vo·lut·ed /ˈkänvəˌlo͞otid/ Adjective (esp. of an argument, story, or sentence) Extremely complex and difficult to follow. Intricately folded, twisted, or coiled. Synonyms convolute - intricate

@DrFlox 13 лет назад

For a future video it would be great to see a visual explanation of convolution, what is actually happening with the functions?

@mohamedhaamuth5921 2 года назад

Ýeah you were write that ten years ago am now watching it. Did you live or not drflox .

@thomaszweef 13 лет назад

thank you! This video helped me so much in understanding convolution

@Captain_Rhodes 9 лет назад

yea but its just simple integration. what does it actually mean?

@bakothegreat 7 лет назад

It is not a simple integral. Often times it is many integrals with many integrations by parts.

@philcooper279 2 года назад

A bit long winded but brilliantly explained. A true master of teaching.

@espionn 7 лет назад

Hahahahaha guys press 7 a couple of times on your keyboard when you're on the video. TOOTYTOOTYTOOTY thank me later

@philipotterberg4408 6 лет назад

Hello Khan! I would´ve liked to see some examples on text exercises within this subject. Love your videos.

@Mossi420 10 лет назад

What you did was some simple maths, can you explain more what the meaning of Convolution is?

@jsal7666 4 года назад

i'm currently 17 as of now, ill see u in 3-4 years when i actually learn about this

@loganunger2405 3 года назад

I'm 17 rn and learning about this in class 😎

@theromancobra 10 лет назад

I am a ME major taking differential equations and before I started watching your lessons, I was barely passing. I now have an A+ thanks to your videos. Thanks for the help!!!

@aureliotambiga1049 7 лет назад

helped me a lot. thanks 😊

@1carlento 15 лет назад

I'm doing my second year mechanical engineering at university and this is helping me a lot thank you very much for posting this amazing clips.

@hulk8889 2 года назад

good luck for you university!

@Via.Dolorosa 10 лет назад

thank you Khan !!

@evil-robot 13 лет назад

Excellently set out. It especially highlights the need to check your workings. Lol. Do you have any videos showing how to convolve 2 non-periodic functions, such as a triangular pulse and a gating function, please? I get confused where different limits of integration apply to different areas of the process.

@nadineblackrose 9 лет назад

Thankyou so much

@111Prince111 13 лет назад

omg u just helped me so much n my web hw, this is why i love youtude seriously

@amak1131 12 лет назад

An old video but THANK YOU. Instructor never did explain things very well. Was also unsure where to plug the 0 and t into. Simple looking back, but the confirmation was great.

@BlackBile666 13 лет назад

I can not believe how helpful this would have been if I had youtube when I was at uni.

@Ayplus 11 лет назад

In Signal and System theory when finding the zero-state response also

@karimkhan1312 11 лет назад

very good- concepts cleared - thank u

@leew089 12 лет назад

I found it was immensely easier to use product to sum formulas for the trig convolutions. It cut the work in half and there were a lot of nice cancellations. In fact I think it was the only sub I did.

@horcrux65 12 лет назад

he said he was about to define what convolution is at the beginning, but he ended up solving a made up a convolution problem without even defining.

@antzikal 12 лет назад

Yep,I agree. What you said is correct in modern Greek. Not sure if that was the pronunciation in ancient Greek though, there is a belief that you would pronounce a (α) and u (υ) separately. It's really annoying hearing it as "tao". τ should sound line "tough" , as you may say "tough guy" ,taf may be misleading

@sisip123 14 лет назад

this is the best! thank you

@toridvoice 12 лет назад

This is extremely helpful. Next video of high level math could you not go over U substitution... or explaining the other math... I mean I assume all of the people that come here are engineers... or at least have other sources of calc 1 or 2.

@Bearkiller777 13 лет назад

Thanks Sal. This helped me understand convolution

@AmitKumar-um9bt 6 лет назад

Well explained... Thankuu..m fully satisfied

@binvid 13 лет назад

Thank you very much. GREAT Tutoring.

@zamamohammed9092 11 лет назад

i scrolled down to write exactly what you've written here.. i kept waiting for him to explain what convolution is..

@kirtankoro 7 лет назад

8:03 Isn't it easier to use the formula of double sin instead of the replacement method? Like sin(tau)cos(tau)=sin(2tau)/2...

@ad2181 15 лет назад

Sal, As a DSP EE this is the most important concept ever.

@deemdoubleu 4 года назад

BUT other definitions use different limits for the integration (-INF to +INF). What is the difference?

@abuhajara 14 лет назад

yes, because if you have real time problem. For example, if you using real time microprocessor, you may get around FFTs by using convolution, specially if you are using FIR filter.

@danielgibbons301 4 года назад

Using this in my Digital Signal Processing (Electrical Engineering) class

@adjsmith 8 лет назад

Is there any chance of expanding on this series with some applications? I'm about to finish my DE course and have found that the applications are the most difficult part.

@baxtermason6909 Год назад

...in Electrical Engineering...used to combine two signals...works in conjunction with Fourier analysis...in signal processing...

12 лет назад

THANKYOU!! sooo much

@anshumanSrivastavaHere_I_COME 8 лет назад

lol i have a test tomorrow, your 20 minute video saved me a lot of time

@shazaduh 15 лет назад

Very nice video and please do make a video on Convolution intuition.

@shakesbeer00 7 лет назад

In this definition of convolution, the range for integration may vary. It does not have to be from 0 to t.

@chinthakashehan7172 8 лет назад

Thanks for the video

@einsteinino 14 лет назад

By means of Werner formulas, the integral for the convolution would require way fewer steps in order to be calculated!

@camilo7456777777 14 лет назад

muy bueno gracias

@BluesMan2 14 лет назад

Thank you so much :)

@mzeki99 3 года назад

I love this guy.

@caseyalanjones Год назад

This video explains how to evaluate a convolution, but not the what or the why. First I would like to know what a convolution is, why I would want one, and what t and tau are meant to represent.

@Integrelle 4 года назад

Much better than my University Engineering Prof lol. Good Gravy, university standards are terrible nowadays.

@awarahajilatif6432 9 лет назад

good thanks

@bla7091 14 лет назад

It was more of an integral and geometry lesson, things I learned way before the concept of convolution came up. If the title changes, this will be a great example though

@maxmuller590 6 лет назад

At 12.37 it is faster if you know that the integral of f(x)×d/dx f(x) dx is equal to 1/2f(x)^2. You can Prove that with Integration by parts.with best regards ;)

@sharikamesba 14 лет назад

excellent video! Thank you =]

@linuxuser5 13 лет назад

thaaaaaaaaaaaanks man , you are the best !

@CrispyCyclicCenk 10 лет назад

thank you

@lindseyxiao5366 7 лет назад

Nice video!

@FrenzyLi 12 лет назад

The integral simplification step is a bit complicated. A simpler approach is applying this: Sin[A] Cos[B] = 1/2 ((Sin[A - B] + Sin[A + B])) So you get: Sin[t - τ] Cos[τ] = 1/2 (Sin[t] + Sin[t - 2τ]) Now the INT is made easier for Sin[t] can be lifted out of the integration and the Sin[t - 2τ] is easy. The whole integration leaves: 1/2 t Sin[t] I guess this introduction to convolution is a introduction to the calculation of the convolution! The characteristics of convolution is not shown though.

@MortazaHussein 14 лет назад

very nice , i want also ask the same , please , make a video on Convolution Intuition , thx we are witing for it :)

@TerresEndormies 12 лет назад

@sadiqtronics: Careful. Your notation is confusing. The integral of cos(at) dt is (1/a)sin(at). I think that is what you mean, and you are correct. However, that is exactly the integral Sal uses in the video. Here, a = 2. Anyway, hope you got it worked out!

@0869614876 5 лет назад

Thank you

@ronijun888 14 лет назад

Thanks.....

@sadiqtronics 12 лет назад

Nice explanation. Am however confused at how you got the integral of cos2t as u indicated. Isn't the integral of cos(ab)=1/asin2b?

@janitarjanitar 13 лет назад

towards the very end.. sal turned a sum of two trig functions into a product of two functions.. because he can.

@zarghamrazajatoibaloch8147 5 лет назад

Thanks

@sathasiva1885 11 лет назад

Mathematics or engineering is not about calculation but about ideas represented with mathematical symbols.This video failed itntroduce the concept in the first place as well as with simple examples..

@akamzaki6247 12 лет назад

Thanks for the video, however - I think a conceptual explanation would have been more useful... most of this lecture was just an integration. Beyond the first formula you stated I learnt nothing of convolutions in this video.

@kevinshaughnessy5032 8 лет назад

You're my hero Sal.

@KansasFashion 6 лет назад

So man, First question, I wonder can we do convolution to more than two functions? Second, I have a project, for now, I want to put a chirp inside of a song and detect this chirp in the song in the matlab. Should I use anything involved with convolution? Or should I use Fourier format? Please let me know!

@fpseli117 11 лет назад

engineers=oompa loompa of science

@Arminpars2 13 лет назад

the "whole hairy problem" that lasts 19 minutes would be done in 3 minutes if you were to rewrite the integral "sin(t-tau).cos(tau)" as integral: "1/2*[sin(t) + sin(t-2*tau)]" and integrate them separately i.e. : "1/2 int(sint * dtau)" + "1/2 int(sin(t-2*tau)*dtau)" where "int" stands for integral.

@DiggOlive 12 лет назад

@redougulas You wouldn't have been able to hear Khans voice in this video if it were not for the convolution.

@keddaoui 9 лет назад

What kind of tool do you use for the presentation? is it a tab ?

@kimrunic5874 7 лет назад

Wow. This is pie and custard to me. I thought I was clicking on a music tech video.

@RunItsTheCat 9 лет назад

I feel like this video didn't serve well as an introduction to a new concept. I think if you began the video with the proof leading up to convolution's definition, the concept will make much more sense thereafter, rather than the viewer attempting to piece together what or why you are doing what you are doing through the example.

@rj-nj3uk 7 лет назад

RunItsTheCat i agree with you.

@holymasteric 12 лет назад

So am I... and it is essential for us engineers to use the correct terminology.

@tohopes 8 лет назад

You should have skipped all the algebra and trig. It is completely beside the point of convolution.

@seinfan9 7 лет назад

"In this video, I'm not going to dive into the intuition of the convolution..." My guess is that it was on point, but definitely something 99% of people don't need or care for.

@TheStrelok7 6 лет назад

tohopes not agree with you

@josemendez9919 5 лет назад

It is 100% much easier if done via integration by parts. No need to memorise all that trig identities

@photon2724 4 года назад

I don't know what this does to the two waves though...Are we just combining them together? feels like Im just following a series of steps without knowing what I'm trying to achieve.