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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Khanvolution
hahaha, true...:)
@@ashishkesharwani1559 only one response in five years and 532 likes... decided to fix :D
Great pun though :)
@@nocturnalvisionmusica year later I add another comment to keep the tradition you started😂
@@Ojzesports whoo-hoo thanks 😁
For those who are interested: Convolution is used frequently in vibration analysis of second order systems.
Which is why I'm prolly learning it in diff equations rn xD
This is the introduction to the integration rather than convolution!
Newbie to convolution here. Is this not the convolution of f and g?
@@zc4612 he is joking bro. he meant definiton is just one line. rest video is about integrating.
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...
a better idea is to use the product to sum formulas:
sin A cos B = ( 1 / 2 ) * [ sin ( A + B ) + sin ( A - B ) ]
your ''t'' looks like a ''+" . Apart from that, it's a very good explanation.
Finally I understood how a Convolution is done.
Thank you very much.
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.
Sal you the real MVP
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) ..:)
i'm currently 17 as of now, ill see u in 3-4 years when i actually learn about this
I'm 17 rn and learning about this in class 😎
For a future video it would be great to see a visual explanation of convolution, what is actually happening with the functions?
Ýeah you were write that ten years ago am now watching it.
Did you live or not drflox .
A bit long winded but brilliantly explained. A true master of teaching.
wow. best video on intro to convolution that I could find! amazing!
yea but its just simple integration. what does it actually mean?
It is not a simple integral. Often times it is many integrals with many integrations by parts.
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
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.
BUT other definitions use different limits for the integration (-INF to +INF). What is the difference?
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!
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
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.
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.
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.
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.
good luck for you university!
What you did was some simple maths, can you explain more what the meaning of Convolution is?
who ever you are ...i just want to say that you're awesome!!!!! love you man thanks for the vids!!
...in Electrical Engineering...used to combine two signals...works in conjunction with Fourier analysis...in signal processing...
Very nice video and please do make a video on Convolution intuition.
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!!!
Sal,
As a DSP EE this is the most important concept ever.
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.
By means of Werner formulas, the integral for the convolution would require way fewer steps in order to be calculated!
I can not believe how helpful this would have been if I had youtube when I was at uni.
Thank you very much for this video! It was a great example-driven tutorial and I learnt a lot from it!
Using this in my Digital Signal Processing (Electrical Engineering) class
people should just stop whining..one reason why youtube may be better for learning is that if the tutor is going too slow for you, just hit the fast forward!!!
You should have skipped all the algebra and trig. It is completely beside the point of convolution.
"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.
tohopes not agree with you
It is 100% much easier if done via integration by parts. No need to memorise all that trig identities
i scrolled down to write exactly what you've written here.. i kept waiting for him to explain what convolution is..
I love this guy.
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.
As others have stated I would have appreciated learning what a convolution is, how it was invented, why it is useful and some sample real-world uses cases without spending any time whatsoever on simplistic calculus mechanics.
Much better than my University Engineering Prof lol. Good Gravy, university standards are terrible nowadays.
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 ;)
omg u just helped me so much n my web hw, this is why i love youtude seriously
thank you Khan !!
Great tutorial - and thank you for the small refreshers in the middle - its been a while since I had used them
towards the very end.. sal turned a sum of two trig functions into a product of two functions.. because he can.
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.
Ridiculously overcomplicated example with no intuition as to what convolution is/does/is useful etc.. Not up to your usual standards by a long shot.
very good- concepts cleared - thank u
helped me a lot. thanks 😊
Well explained... Thankuu..m fully satisfied
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.
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
Hahahahaha guys press 7 a couple of times on your keyboard when you're on the video. TOOTYTOOTYTOOTY
thank me later
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.
thank you! This video helped me so much in understanding convolution
Yeah, this lesson taught nothing about what convolution is or what it's used for. This was just an integration exercise.
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.
@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!
All your videos are great. Let me say that first. But I've a big critic to give you that hopefully will help make your videos even better.
You share this issue with the vast majority of math teachers.
You focus a lot on the mechanical procedures and algebra, you stress even too much all the little steps. But you completely fail to give the big picture of what you are actually doing and why.
Convolution here: one can learn to compute the convolution and you gave the definition. But you did not explain at all what it is, what it does.
It's a moving average between 2 functions. The resulting function is a new function of course.
Some of the most easy to grasp applications of this is in computer graphics for blurring an image you take a convolution of the image with itself on 2 dimensions.
It's like teaching a derivative without explaining what it means. Sure you can mechanically follow the procedure but it's kind of important to give an intuition of what math operation is doing.
Thanks Sal. This helped me understand convolution
In Signal and System theory when finding the zero-state response also
Can't agree more with ya. The lecture should focus more on, like, what is convolution, what is its application...
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...
Both 'convolve' and 'convolute' are right. Google both the definations.
good thanks
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.
Thankyou so much
So am I... and it is essential for us engineers to use the correct terminology.
there is generally more than one identity per trig expression
Thanks a lot, found it really helpful! (got to admit, I'm digging the color scheme, very easy going)
T and Tau - maybe choosing different letters would have helped.
muy bueno gracias
We will do the integration ourselves, tell us the idea of fooking convolution?
Good explanation, thanks!
Thanks for the video
Thank you very much. GREAT Tutoring.
In this definition of convolution, the range for integration may vary. It does not have to be from 0 to t.
@redougulas You wouldn't have been able to hear Khans voice in this video if it were not for the convolution.
When you were multiplying (1/2) sin t by (1/2) sin 2t when you were distributing you inserted + where it should have been multiplication. Result should have been (1/4)(sin t)(sin 2t) but you got (1/4)sint + sin 2t
+David Battle you fixed it in the next step by ignoring the + lol. Two wrongs make a right?
I find that strange as well... a fair mistake perhaps??
superb...made me convoluted....1/2sint..
Anand Krishnan Come on... Didn't you pay attention? It's 1/2*t*sin(t)!
Do you have an example for a fixed signal for a given time, and a signal affected by t. Eg, f(t) = 1, g(t) = t/2
@postigaceltic Insulting people giving you constructive criticism is not generally advised. I too am enthusiastic about calculus and have taught it to myself for the last two years from videos online. One of the first (and most difficult) things is to establish a general order in which to learn the topics, now I have no idea why you would want to know about convolution (trig integrals should certainly be learned first), but criticizing the makers of free videos is fairly ungrateful act.
What kind of tool do you use for the presentation? is it a tab ?
Thanks
if L [ f ( t ) ] = F ( s ), then L [ t f ( t ) ] = - d / ds [ F ( s ) ]
Example : L ( sin at ) = a / ( s^2 + a^2 )
so L ( t sin at ) = - d / ds [ a / ( s^2 + a^2 ) ]
L ( t sin at ) = - [ - a * 2s * ( s^2 + a^2 )^( - 2 ) ] = 2as / ( s^2 + a^2 )^2
it is much better to use product to sum formula for trig : 2sinAcosB= sin(A+B)+sin(A-B)
Is this a video about convolution or a video about how to integrate the example function?
engineers=oompa loompa of science
this is the best! thank you
thaaaaaaaaaaaanks man , you are the best !
very nice , i want also ask the same , please , make a video on Convolution Intuition , thx
we are witing for it :)
Hello Khan! I would´ve liked to see some examples on text exercises within this subject. Love your videos.
mind... blown
Nice video!
Actually, convolute is a legitimate synonym of convolve.
Source: wolframalpha, and using google searching "define: convolute"
THANKYOU!! sooo much
You're my hero Sal.
Thank you so much :)