Convolution and Unit Impulse Response
ฝัง
- เผยแพร่เมื่อ 12 ต.ค. 2024
- The Dirac delta function, the Unit Impulse Response, and Convolution explained intuitively. Also discusses the relationship to the transfer function and the Laplace Transform. Signal Analysis for Linear Systems. My Patreon page is at / eugenek
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Great job 👏🏻 keep going
You are the best ❤️❤️
Hi Eugene! I'm an undergrad EEE student from Bangladesh. I found your videos very useful in understanding things intuitively. Particularly for this video, I translated the subtitles into Bengali. I'll email you the transcript with timestamps included. Can you add this for my Bangladeshi students? Thanks for your effort.
@KaziNazmulYT, Thanks! I just uploaded your translated subtitles. Thank you very much!
@@EugeneKhutoryansky Thanks to you.
And thus we have the very foundation of digital signal processing.
You have mastered the art of using animations to explain concepts. I wanted to let you know whatever you are doing is helping students like us big time. I hope you will make more videos in the future. Stay safe out there.
Thanks and I an glad that my videos are helpful.
This metal track slaps so hard
it was a nice transition after Chopin
Sound like dream theater to me, do you know the name of the song ?
@@charllsquarra1677 Beethoven 😅
This channel and this video is spectacular
yeah the guitar tone is real juicy.
@@adoniz99 we finally know which group of people listen to dream theater
I was waiting for this topic from your channel for past 2 years. Amazing Videos as always. I will always suggest my students to watch your videos. You are giving life to the unimaginable stuffs. You are awesome. You will be always remembered by all Engineering Students.
Waiting for z Transform, Stability of System etc.
Thanks for the compliment. I already have a video on stability at th-cam.com/video/p9qrHdPEe28/w-d-xo.html
Beautiful. I needed this video last semester. Make more of these.
Thanks for the compliment. More videos are on their way.
don't you know how to say please how rude
also, you can contribute to www.patreon.com/EugeneK/posts ... I do
Give me ur ak i will shout you moron
Eugene. When I was taking my signals and systems class I had the hardest time understanding convolution and I remember searching your uploads hoping you had a video. It’s been some time since that happened but I’m so glad you made this. Although now I’m graduated and a professional who uses this, I’m still amazed at what there is to learn from your videos. Thank you so much for taking the time to make these.
Thanks. I am glad that you like my videos.
This is one of the most, if not, by far the most amazing Physics channel on TH-cam. I am planning in double majoring and receive a B.S. in Mechanical Engineering and Chemical Physics.
Thanks for the compliment.
U planning to WHAT !?
1) Für Elise
2) Rock n' Roll
3) More Für Elise
2) heavy metal*
Rock and roll would be led zeppelin.
Amazing graphical explaination.. lot many students ppl dont undertsand in a class room.. this video clear all doubts..very detail..
Please add more like these videos on signals nd systems..
Thanks for the compliment about my video. More videos on all topics are on their way.
It’s funny how much better students learn when you use computer graphics to teach them. I don’t know how people learned math and math. science before TH-cam!
We've been waiting for you for quite a long time!!!! Good to see you again!!
He's back! These videos are gems. I showed them to my students for demos on electricity.
Every time watching your videos i have that awesome enlightment moment. As a mechanical engineer who pursue into mastering control theory and systems,sometimes i find its math difficult to grasp intuitively but you make it so easy keep uploading man you best
Thanks for the compliments. I am glad that my videos are helpful.
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Thanks.
Then I will start to translate into French. Thx for the script, it's much harder without it.
Edit : easier than I tought.
Sir i love you
Adrien, thanks. I have approved your French subtitles for this video on Convolution. I very much appreciate it. By the way, three weeks ago, someone submitted French subtitles for the video "Boost Converts and Buck Converters" which I was not able to approve because of a mistake I noticed in the very first sentence. The submission had the word "decrease" instead of "increase." Anyone who speaks French can review, edit, and resubmit their translation. If you are interested, the link for adding / reviewing translations for the "Boost Converts and Buck Converters" video is at th-cam.com/users/timedtext_video?v=vwJYIorz_Aw&ref=share
Thanks.
Any heroes who translate it into Spanish? My English isn't very good :/
P.D. awesome video
@@EugeneKhutoryansky Thank you sir. I see how much you try to help human being out there the tears on my eyes now. I don't believe in God but if you do? God bless you.
I don't know what is crazier, that someone was able to graphically and simply explain convolution without "flipping" the function, or that this is literally the simplest anyone will ever come to explaining convolution.
Honestly im kinda hating on Eugene rn cause in all the ways i visualized convolution not once did i put it in this 3 dimensional form like he did. My way works too tho.
You're right this video IS the simplest mathematical explanation for this topic EVER (at least on YT)
Still a difficult topic to digest though😅
Nevertheless I think it's magnificent
The basic idea of convolution isn't too hard. It's just made harder because engineers and mathematicians are generally kind of bad at explaining things.
Please do some videos for control systems like, open-loop, closed-loop, feedback...etc...thank you
I may do more in depth videos on control systems and feedback, but I already have a few videos that talk about it. For example, feedback is discussed in my video on Op Amps, and I already have a video on State Space Stability Analysis.
Eugene said no bro
Taking convolution for years, this is the first time to understand what it is all about, Thnx
I am glad my video was helpful. Thanks.
Extremely good explanation of convolution. Yours is a precious gem.
Glad you liked my explanation. Thanks.
Been in grad school 6 years and this is by far the best this has ever been explained
Thanks for the compliment about my explanation.
This is the most educational channel on youtube. Hands down.
Thanks for the compliment.
I rarely leave a comment, I’m a Engineering student from Australia studying in Germany. I appreciate these and the people who took the time to explain this so well ❤️
Thanks. I am glad you liked my video.
I had never found such an great intuition of convolution before .... greetings and regard from INDIA!!
Thanks. I am glad you liked my video.
Hi Eugene, can you explain why the total output is the sum of the area of red rectangles and not the sum of the height of each rectangle? I mean, the output at certain time is the sum of each individual unit impulse response at that time isn't it?
We have to account that these are not real unit impulse functions in that they do not have infinite height. Therefore, we have to multiply each unit impulse response function by a very small number (d tau) to compensate for this.
Very good explanation! The visuals make it so much easier to understand how unit impulse works for solving linear systems. Maybe you can do a video on linear differential equations and Green functions since the technique is very similar. Cheers
Fantastic video. Helps us actually visualize the formula.
For what it's worth, I am not in college or studying this for my degree, I just have an innate fascination with convolution and digital signal processing. This was throughly explained.
Thank you!
Glad you liked my video. Thanks.
Epic. The first CLEAR unambiguous explanation of the difference between t and tau.
Thanks.
me on exam after watching this:
** You fool! I have been trained in your Jedi arts by Eugene Khutoryansky **
Sir your work is really exellent. I get a excellent visual understanding through your videos . I have got many concepts cleared. Keeping myself away by demanding more content from you(I know its a lot of work). I would love to see your videos on control systems(Root locus, Nyquist criterion, Bode plot)
Thanks for the compliments. I may do videos on those topics in the future.
Lol naw if he do videos on any of them topics ima be PISSED ! Lol yall go have to struggle like i did no help from Eugene for Nyquist theorems and all that nope.
Thank you so much for this video. I had never understood convolution, just used it without comprehension. Now i think I know the basic principle behind it. Thanks again, I love your videos and so much appreciate the effort put on making them as explanatory as possible with the aid of graphical illustrations.
Thanks for the compliment about my videos.
Ohhh this is just presented so well. Finally, a graphical intuition for the convolution integral (or sum in discrete time) that is derived from the more general superposition sum (add up the unit impulse responses -- like a bell rung at each time step), rather than from what I've always thought is a counter-intuitive reading of the formula: fold, shift, element-wise multiply, sum.
Thanks. I am glad you liked my explanation.
Half a semester in 10 minutes. Thank you again Mr. Khutoryansky!
I am glad you liked my video. Thanks.
Really got awestruck by the clear explanantion...This helped me a lot!!! Thanks a lot
Thanks. I am glad that my explanation helped.
I am soo sooo happy that u starts uploading videos 🙏
this video made me understand this, it made me relax and it made me sleepy.. thank you and goodnight
Learned this stuff in school, had no idea how any of it worked, I just followed the patterns in the math. This video actually allowed me to understand what the hell I was even doing!
Thanks. Glad my video was helpful.
this is without a doubt one of the best STEM youtube channels ever.
Please don't stop and keep up the good work 😉
Thanks for the compliment. More videos are on their way.
Thank you so muchhhhhhh, this is the first time I really understand why the order of terms are opposite in convolution dot product!!!!
I am glad my video was helpful.
about 5:53, the result is not failed, but most people know as the action of the input form the video that the unit impulse delta(t-tau) (running sum) effect the output, so I think based on the additivity and homegeneity , the out result may better change to [y(t) = integral(0, t) input_function(tau).unit impulse_response( t - tau).d tau], in other words, Height = input_function(tau).unit impulse_response(t - tau), I want to iterate that because of the commutativity is one of the properties of convolution, the result "input_function(t -tau).unit impulse_response(tau) catching from the video is also right.
I was confused by the same thing, wondering how no one pointed it out! Thought I'm the only one who is still confused even after such great visualisation.
thank you very much, that's what I'm looking for ,for a long time. it's genuinely done. ALL MY SUPPORT
ثاني عربي هنا
Great video. This makes a lot more sense to me than than "flip and slide" explanation which changes with t instead of tau (the actual variable). Thank you for effort.
Thanks.
Absolutely the best video on convolutions on the internet
Thanks for the compliment about my video.
This is one of my favorite videos of all time.
I am glad you liked my video.
Finally! A video on convolution that I understand.
This is brilliant, so well explained, you just saved my life sir
Thanks for the compliment and I am glad my video was helpful.
This video made impulse response very clear. I needed it when I learnt this idea in signal processing. it is spectacular.
Thanks.
I can't believe I missed this awesome video before!!!
Very good video. The animations help decipher a challenging topic!
Thanks!
I loved this video. ..great work
Thanks for the compliment. I am glad you liked my video.
absolutely love your videos do you make the graphics as well? As I think these graphics transform a physic class or electronics class into somethign that is easily understood...
Thanks for the compliment. Yes, I make all the animations for my videos myself. Thanks.
I am unable to comprehend why we went in 3rd dimension for tau? please help me in understanding the crux of it.
idk why but this video completely overcomplicates it, convolution is better understood by flipping the kernel over the y axis and expressing the point-wise product of the areas overlapped as a function of the shifted position of the kernel; this only works for linear time invariant systems though
this is a great video. i started off understanding impulse responses from discrete impulse responses where each unit is one sample. i now know where my knowledge sat within a wider context. and understanding right where the laplace tranform sits and that its to do with le frequencies is awesome. thank you sir.
Dear Eugene all of your science works are always great... thank you so much.. we're love you
Thanks for the compliment. I am glad you like my videos.
Amazing. Don't know why i pay for college where no one matches this level of explanation
btw, can you elaborate the part where you said "The total output at this moment in time is the sum of the areas of all the red rectangles" - why
thanks and plz don't stop making such great content
because impulse input is at instant but output can vary according to system so lets say you apply an impulse input at 2 and 5 sec and the linear system is decaying function with time constant 10 sec...
at t =0 both input and output will be 0,
at t =2 input = impulse, output = decaying function starts
at t= 3 input =0, output = decaying function with less amplitude
at t=5 input = impulse, output = output due to impulse + decayed output given by 2 sec impulse, hence sum of both area
literally
i am searching every where to get this concept
you killed it
great work 💝
keep it up
1 like + 1 subscribe
Thanks for the compliment. I am glad to have you as a subscriber.
Thanks for the clever and crystal clear explanation! I was having difficulties to digest this concept.
Thanks for the compliment. Glad my video was helpful.
Very nicely explained. Found it at the right time. Thanks
Thanks.
your explanation was like listening to a poem, thank you
Thanks. I am glad you liked my explanation.
Simply awesome as always
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Gold, Thank you so much for making it easier to understand such concept. I have already send this to my students.
Thanks. I hope your students like my video.
Incredibly well animated Visualization
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these videos deserve all my semester money
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This is one of the better things in internet
Не знаю, как на английском, но в русском языке описываемая на 1:57 называется импульсной или дельта функцией. Единичной называется ступенька у(t)=0 при t=t0.
The Russian translation has now been updated as you suggested. Thanks.
Another Master piece 😍😍😍
Thanks !
Wow, I sure wish I had this video when way back in the day I was learning this in school!
Only someone who really masters the subject can explain it so well
Thanks for the compliment.
this is fantastic. Amusing. Amazing. I'm at a loss for words.
Thanks. I am glad you liked my video that much.
The dank metal track outta nowhere. Sounds like BTBAM.
AYYYY
Hands down the best convolution tutorial I have seen. After watching this you feel like Keanu Reeves in Matrix saying "I know kung fu".
Thanks for the compliment about my video.
Absolutely crazy, beautiful, amazing video. Thank you very much!
Thanks for the compliment about my video. I am glad you liked it.
I've said it before, I'm saying it again - the best sh*t on TH-cam is on this channel. Period.
Still no idea how people in the past studied without the access to things like that......
Thanks for the compliment.
Thanks! Suddenly I understand the output is nothing but the summation of current and several previous impulse responses as well as that's what the convo equation wants to present for us.
Glad my video was helpful. Thanks.
Square wave frequency drive systems have these types of issues in hydraulics. Many heavy equipment machines use this .
There is often a lag of output beginning and ending.
As usual, genius and again another black hole turned to be bright star 👏
Thanks for the compliment.
We have been waiting for your videos...... And one more thing, please Organize videos in our(your) channel topic wise.. Some videos are present in many playlists
Really helped be understand convolution, thank you!
Thanks. I am glad you liked my video.
Very good, basic concept behind DSP
one of the best vid of convolution explanation !!
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It's a huge loss to have found these videos so late
How can you be beyond genius 👏👏👏👏
Thank you so much
It was beautiful😢
Thanks for the compliment. Glad you liked my video.
@@EugeneKhutoryansky
Before seeing your awesome video I never actually understood what was going on when we actually meant convolution.
I just memorized the formula and solved all solutions related to that.
Now I actually understood what it all meant.
So from the bottom of my heart with utmost sincerity I thank you.
Thanks you🙏, God bless you.
You really made my day.
I hope you have a good day as well my great teacher!
Glad my video was helpful. Thanks.
@@EugeneKhutoryansky
It will be helping many many generations of students..
All of them will be grateful to you just like me.
The work you did is a master piece.
Thanks.
this is the best video i have ever seen
I am glad you liked my video. Thanks for the compliment.
I needed this about 2 years ago Eugene -_- u always do this
Still rock wit u heavy tho. No love lost.
Awesome Explanation! Splendid. Love from India.
Thanks.
1:26 I got lost here. Why with only the unit impulse response we can determine the response to the rest of inputs? Is it because any input can be described as a combination of impulses?
EDIT: Hahaha, nevermind, @ 2:33 you read my mind. It was what I thought.
By the way I loved this video. Convolution has always been something strange to me. I'd love to watch more videos related to this branch of engineering (signals, systems, controls.)
Indeed my friend... th-cam.com/video/3eDDTFcSC_Y/w-d-xo.html
What a coincidence I am studying total response of impulse function right now and I got this video 😮😮😮
it's inevitable.
Nice! Very nicely explains things intuitively and visually. I've encountered the convolution integral while reading textbooks, but I haven't gotten around to understanding it or having an idea what it means :)
Thanks. I am glad you liked my explanation.
this actually made a lot of sense this time. I've certainly tried to understand before but I really followed what was going on woo!
I am glad my video was helpful. Thanks.
Best video I’ve seen on the topic
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Amazing! What a great explanation. Love it.
Thanks. I am glad you like my explanation.
Wonderful video and explanation as always 😉. Could you also make video about Duhamel’s Integral and explain what is it and where it uses ? I’m sure, it would be very interesting and useful for many of us
Thanks for the compliment. I will add Duhamel’s Integral to my list of topics for future videos. Thanks.
Amazing animation
Thanks for the compliment about my animation.
Unbelievable, somebody would do this. Amazing explanation! More videos for controls please.
Glad you liked my video. More are on the way. By the way, I have a video on State Space Stability Analysis at th-cam.com/video/p9qrHdPEe28/w-d-xo.html
Fucking beautiful. Thank you so much. I may actually pass my first signals and systems exam thanks to this video.
Please also explain why did you go into third dimension perpendicular to regular height and width of input and output functions. I assume there might be something which i can't comprehend but please explain.
This was absolutely fantastic! Thank you very much for this amazing explanation!
I have subscribed to your channel now :)
Keep up the good work!
Thanks for the compliment and I am glad to have you as a subscriber.
Awesome art!! Keep on doing these videos!!
Thanks for the great videos. I'm an engineering student in South Korea. Could you explain why the output is the sum of red rectangles. I think that the output must be the sum of heights? What does the area of each red rectangle mean physically or intuitively?
As delta tau approaches zero, the number of rectangles approaches infinity. Therefore, if we take the sum of all the heights, we will get an infinite number. We need to multiply by delta tau to get a finite number. Another way to think about it is that the height represents the output of a true unit impulse input. But, we do not have true unit impulse inputs, which must have an area of 1 (on the time axis). Instead, each of our inputs have an area which is multiplied by delta tau (on the time axis). Therefore, each of the outputs also needs to be multiplied by delta tau (on the tau axis).
@@EugeneKhutoryansky what was the need to go in Tau axis.
What kind of Black Magic do you use to make complicated things so clear ? Thank you so much
I am glad you liked my video. Thanks.
That is awesome! Can I use a screenshot of that video for a presentation? How should I cite you?
Yes, you can use a screen shot. You can site me by providing a link to my video and mentioning my channel name: "Physics Videos by Eugene Khutoryansky"
Thanks.
On 7:42, after saying contributions of each of the output functions(h(t), unit impulse response) approaches to zero, you said its reason is because unit impulse input functions shown here have finite height whereas a true unit impulse input function should have a height which approaches infinity. By "contribution" of output functions, we refer to their area right(this is just a clarification question)? And my actual question is, do their area approach to zero because unit impulse input functions' height goes to infinity, or unit impulse input functions' width and thus unit impulse responses' width goes to zero? Thanks in advance.
A true unit impulse would have a width that approaches zero and a height that approaches infinite. In our case, the so called unit impulse has width (dτ) that approaches zero and a finite height. But, we compensate for the finite height with the fact that we have an infinite number of these so called unit pulses.
... where the heck were you?!? THIS WAS THE BANE OF MY EXISTENCE
Lol