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...
Great example! He made simple the scary notation and held my hand through all the calculations. Now I’m ready for anything he throws at me in the next video.😊❤.
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!
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
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 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.
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) ..:)
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
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!!!
"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.
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.
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.
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.
Great example!! He explains the purpose of the video at the beginning. He goes through the mechanics of the notation. This fixes in my mind the simplicity of the scary notation. Now I’m ready for anything!❤
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
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 ;)
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.
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.
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.
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.
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.
@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!
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
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!!!
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.
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.
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.
@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.
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😂
@@Oldschukcomedy whoo-hoo thanks 😁
@@Oldschukcomedyand again lol
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...
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
a better idea is to use the product to sum formulas:
sin A cos B = ( 1 / 2 ) * [ sin ( A + B ) + sin ( A - B ) ]
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.
Great example! He made simple the scary notation and held my hand through all the calculations. Now I’m ready for anything he throws at me in the next video.😊❤.
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.
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!
wow. best video on intro to convolution that I could find! amazing!
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
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.
A bit long winded but brilliantly explained. A true master of teaching.
your ''t'' looks like a ''+" . Apart from that, it's a very good explanation.
Hahahahaha guys press 7 a couple of times on your keyboard when you're on the video. TOOTYTOOTYTOOTY
thank me later
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.
who ever you are ...i just want to say that you're awesome!!!!! love you man thanks for the vids!!
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 .
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!
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) ..:)
Sal you the real MVP
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
What you did was some simple maths, can you explain more what the meaning of Convolution is?
i scrolled down to write exactly what you've written here.. i kept waiting for him to explain what convolution is..
Sal,
As a DSP EE this is the most important concept ever.
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!!!
I can not believe how helpful this would have been if I had youtube when I was at uni.
Using this in my Digital Signal Processing (Electrical Engineering) class
Very nice video and please do make a video on Convolution intuition.
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 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.
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.
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.
Great tutorial - and thank you for the small refreshers in the middle - its been a while since I had used them
Much better than my University Engineering Prof lol. Good Gravy, university standards are terrible nowadays.
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.
omg u just helped me so much n my web hw, this is why i love youtude seriously
Thank you very much for this video! It was a great example-driven tutorial and I learnt a lot from it!
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.
Great example!! He explains the purpose of the video at the beginning. He goes through the mechanics of the notation. This fixes in my mind the simplicity of the scary notation. Now I’m ready for anything!❤
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
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...
Thanks Sal. This helped me understand convolution
...in Electrical Engineering...used to combine two signals...works in conjunction with Fourier analysis...in signal processing...
Thanks a lot, found it really helpful! (got to admit, I'm digging the color scheme, very easy going)
thank you! This video helped me so much in understanding convolution
thank you Khan !!
I love this guy.
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 ;)
very good- concepts cleared - thank u
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.
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.
By means of Werner formulas, the integral for the convolution would require way fewer steps in order to be calculated!
Well explained... Thankuu..m fully satisfied
helped me a lot. thanks 😊
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.
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.
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.
lol i have a test tomorrow, your 20 minute video saved me a lot of time
@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!
Thank you very much. GREAT Tutoring.
Good explanation, thanks!
So am I... and it is essential for us engineers to use the correct terminology.
BUT other definitions use different limits for the integration (-INF to +INF). What is the difference?
In Signal and System theory when finding the zero-state response also
very nice , i want also ask the same , please , make a video on Convolution Intuition , thx
we are witing for it :)
towards the very end.. sal turned a sum of two trig functions into a product of two functions.. because he can.
superb...made me convoluted....1/2sint..
Anand Krishnan Come on... Didn't you pay attention? It's 1/2*t*sin(t)!
thaaaaaaaaaaaanks man , you are the best !
Yeah, this lesson taught nothing about what convolution is or what it's used for. This was just an integration exercise.
In this definition of convolution, the range for integration may vary. It does not have to be from 0 to t.
there is generally more than one identity per trig expression
Thankyou so much
good thanks
Can't agree more with ya. The lecture should focus more on, like, what is convolution, what is its application...
this is the best! thank you
@redougulas You wouldn't have been able to hear Khans voice in this video if it were not for the convolution.
T and Tau - maybe choosing different letters would have helped.
Is this a video about convolution or a video about how to integrate the example function?
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??
Thanks for the video
it is much better to use product to sum formula for trig : 2sinAcosB= sin(A+B)+sin(A-B)
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!!!
THANKYOU!! sooo much
Hello Khan! I would´ve liked to see some examples on text exercises within this subject. Love your videos.
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.
engineers=oompa loompa of science
Actually, convolute is a legitimate synonym of convolve.
Source: wolframalpha, and using google searching "define: convolute"
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.
RunItsTheCat i agree with you.
You're my hero Sal.
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.
and look for bryan douglas Laplace, very good!
We will do the integration ourselves, tell us the idea of fooking convolution?
Nice video!
muy bueno gracias
at the very end, when writing out the answer, in the orange, you forget to write g(tau) as cos(tau).
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?
Thanks.....
mind... blown
@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.