Convolution and Unit Impulse Response

[@EugeneKhutoryansky]

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

[@bibibiti1098]

Great job 👏🏻 keep going You are the best ❤️❤️

[@KaziNazmulYT]

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.

[@EugeneKhutoryansky]

@KaziNazmulYT, Thanks! I just uploaded your translated subtitles. Thank you very much!

[@KaziNazmulYT]

​@@EugeneKhutoryansky Thanks to you.

[@aneupan]

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.

[@EugeneKhutoryansky]

Thanks and I an glad that my videos are helpful.

[@johnopalko5223]

And thus we have the very foundation of digital signal processing.

[@nzuckman]

This metal track slaps so hard

[@charllsquarra1677]

it was a nice transition after Chopin

[@adoniz99]

Sound like dream theater to me, do you know the name of the song ?

[@shaunsmith8184]

@@charllsquarra1677 Beethoven 😅 This channel and this video is spectacular

[@pepe6666]

yeah the guitar tone is real juicy.

[@wodddj]

@@adoniz99 we finally know which group of people listen to dream theater

[@772storminorman]

Beautiful. I needed this video last semester. Make more of these.

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@mohamedel-shafey1912]

don't you know how to say please how rude

[@physiqueDrummond]

also, you can contribute to www.patreon.com/EugeneK/posts ... I do

[@soccerbels7947]

Give me ur ak i will shout you moron

[@itach1freak]

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.

[@EugeneKhutoryansky]

Thanks. I am glad that you like my videos.

[@SAJAN_ECE]

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.

[@EugeneKhutoryansky]

Thanks for the compliment. I already have a video on stability at kzbin.info/www/bejne/pmrUo3uahaqYaJo

[@ubaldogonzalez4252]

This is one of the most, if not, by far the most amazing Physics channel on KZbin. I am planning in double majoring and receive a B.S. in Mechanical Engineering and Chemical Physics.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@seandafny]

U planning to WHAT !?

[@dhk1126]

We've been waiting for you for quite a long time!!!! Good to see you again!!

[@MN-sc9qs]

He's back! These videos are gems. I showed them to my students for demos on electricity.

[@tymofei8586]

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

[@EugeneKhutoryansky]

Thanks for the compliments. I am glad that my videos are helpful.

[@viahttp]

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..

[@EugeneKhutoryansky]

Thanks for the compliment about my video. More videos on all topics are on their way.

[@XxfishpastexX]

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 KZbin!

[@hibby2264]

This is the most educational channel on youtube. Hands down.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@marinamaher8211]

Taking convolution for years, this is the first time to understand what it is all about, Thnx

[@EugeneKhutoryansky]

I am glad my video was helpful. Thanks.

[@2livenoob]

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.

[@seandafny]

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.

[@Z-eng0]

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

[@briefcasemanx]

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.

[@RahulSharma-oc2qd]

I am unable to comprehend why we went in 3rd dimension for tau? please help me in understanding the crux of it.

[@jimmea6317]

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

[@4.0.4]

1) Für Elise 2) Rock n' Roll 3) More Für Elise

[@shayanmoosavi9139]

2) heavy metal* Rock and roll would be led zeppelin.

[@leosmi1]

Please do some videos for control systems like, open-loop, closed-loop, feedback...etc...thank you

[@EugeneKhutoryansky]

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.

[@seandafny]

Eugene said no bro

[@justforwork4310]

Been in grad school 6 years and this is by far the best this has ever been explained

[@EugeneKhutoryansky]

Thanks for the compliment about my explanation.

[@priyanshukumawat4142]

I had never found such an great intuition of convolution before .... greetings and regard from INDIA!!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@davidbabic6121]

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 ❤️

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@solewalk]

Extremely good explanation of convolution. Yours is a precious gem.

[@EugeneKhutoryansky]

Glad you liked my explanation. Thanks.

[@marcosdelgado3305]

One of the best visual depictions of a convolution that I've seen

[@EugeneKhutoryansky]

Thanks.

[@chologonzalo999]

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?

[@EugeneKhutoryansky]

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.

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?v=acAw5WGtzuk&ref=share You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit buttons for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@adrien5568]

Then I will start to translate into French. Thx for the script, it's much harder without it. Edit : easier than I tought.

[@sec_g_69shreyashsrivastava72]

Sir i love you

[@EugeneKhutoryansky]

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 kzbin.info_video?v=vwJYIorz_Aw&ref=share Thanks.

[@oscarleonrodriguez2005]

Any heroes who translate it into Spanish? My English isn't very good :/ P.D. awesome video

[@ZinuBatul]

@@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.

[@DaveThaBossDTB]

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!

[@EugeneKhutoryansky]

Glad you liked my video. Thanks.

[@misugijun]

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.

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@JohnDoe-fg9ng]

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!

[@EugeneKhutoryansky]

Thanks. Glad my video was helpful.

[@mikkliish]

Absolutely the best video on convolutions on the internet

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@mohamededbey]

this is without a doubt one of the best STEM youtube channels ever. Please don't stop and keep up the good work 😉

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@Amine-gz7gq]

among the best

[@faisonsensemble3379]

thank you very much, that's what I'm looking for ,for a long time. it's genuinely done. ALL MY SUPPORT

[@QUBY-101]

ثاني عربي هنا

[@samuelbarham8483]

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.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@alanchuangi]

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.

[@preethilakshminarasimhan7094]

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.

[@lakshmanannatarajan9831]

Really got awestruck by the clear explanantion...This helped me a lot!!! Thanks a lot

[@EugeneKhutoryansky]

Thanks. I am glad that my explanation helped.

[@area51xi]

Epic. The first CLEAR unambiguous explanation of the difference between t and tau.

[@EugeneKhutoryansky]

Thanks.

[@TheMuhammedtaha1]

this video made me understand this, it made me relax and it made me sleepy.. thank you and goodnight

[@AutoFirePad]

Half a semester in 10 minutes. Thank you again Mr. Khutoryansky!

[@EugeneKhutoryansky]

I am glad you liked my video. Thanks.

[@elijahsmith7552]

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.

[@EugeneKhutoryansky]

Thanks.

[@NicheNi]

I am soo sooo happy that u starts uploading videos 🙏

[@apophenic_]

This is one of my favorite videos of all time.

[@EugeneKhutoryansky]

I am glad you liked my video.

[@russellguo7572]

Thank you so muchhhhhhh, this is the first time I really understand why the order of terms are opposite in convolution dot product!!!!

[@EugeneKhutoryansky]

I am glad my video was helpful.

[@BoZhaoengineering]

This video made impulse response very clear. I needed it when I learnt this idea in signal processing. it is spectacular.

[@EugeneKhutoryansky]

Thanks.

[@lijia2595]

This is brilliant, so well explained, you just saved my life sir

[@EugeneKhutoryansky]

Thanks for the compliment and I am glad my video was helpful.

[@pushpendubiswas3439]

Finally! A video on convolution that I understand.

[@masaamri1172]

Dear Eugene all of your science works are always great... thank you so much.. we're love you

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you like my videos.

[@pepe6666]

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.

[@harshchikorde9495]

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)

[@EugeneKhutoryansky]

Thanks for the compliments. I may do videos on those topics in the future.

[@seandafny]

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.

[@TheJaniable]

me on exam after watching this: ** You fool! I have been trained in your Jedi arts by Eugene Khutoryansky **

[@alanly-lm1ye]

Very good video. The animations help decipher a challenging topic!

[@EugeneKhutoryansky]

Thanks!

[@stevehan7983]

At the time of 2:35. How can you represent an input signal with the sum of impulse signals? Impulse signal has infinite magnitude. How do you adjust the magnitude?

[@Mohammadoudat]

Gold, Thank you so much for making it easier to understand such concept. I have already send this to my students.

[@EugeneKhutoryansky]

Thanks. I hope your students like my video.

[@lybable]

I can't believe I missed this awesome video before!!!

[@ChurchOfThought]

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

[@MrDarkabdo]

these videos deserve all my semester money

[@EugeneKhutoryansky]

Thanks for the compliment.

[@LesleyLai]

The 3D visualization of the convolution is really cool! It is much more enlightening to me compared to the typical "flipping a function" 2D visualization of convolution

[@EugeneKhutoryansky]

I am glad you liked my visualization. Thanks.

[@AlexAlex-fo9gt]

Что можно сказать о единицах измерения для функции свёртки? Например, по формуле (7:15), если функция отклика (Unit Impulse Response) будет зависимостью напряжения от времени (Вольты), входное воздействие (Input Function) - тоже - напряжение от времени (Вольты), то размерность единицы измерения для свёртки получается Вольт x Вольт x Секунда. Судя по получившейся размерности это что-то типа функции энергии от времени?

[@shirinmadarshahian7117]

your explanation was like listening to a poem, thank you

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@opaaaaaaaaaaa]

How can you be beyond genius 👏👏👏👏 Thank you so much It was beautiful😢

[@EugeneKhutoryansky]

Thanks for the compliment. Glad you liked my video.

[@opaaaaaaaaaaa]

@@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!

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@opaaaaaaaaaaa]

@@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.

[@EugeneKhutoryansky]

Thanks.

[@chinthakaravinatha5230]

Thanks for the clever and crystal clear explanation! I was having difficulties to digest this concept.

[@EugeneKhutoryansky]

Thanks for the compliment. Glad my video was helpful.

[@rezwanzakaria1754]

Can anyone please tell me why the total output will be the sum of the red rectangles? Cant we just add the individual outputs to get the total output?

[@mnada72]

As usual, genius and again another black hole turned to be bright star 👏

[@EugeneKhutoryansky]

Thanks for the compliment.

[@jaikumar848]

I loved this video. ..great work

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you liked my video.

[@triggu6826]

literally i am searching every where to get this concept you killed it great work 💝 keep it up 1 like + 1 subscribe

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad to have you as a subscriber.

[@gktu.]

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.

[@EugeneKhutoryansky]

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.

[@hectorp5591]

Only someone who really masters the subject can explain it so well

[@EugeneKhutoryansky]

Thanks for the compliment.

[@orion33]

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.

[@EugeneKhutoryansky]

The Russian translation has now been updated as you suggested. Thanks.

[@japanlovescali]

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

[@ayushkumar1539]

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

[@sheo5212]

In the last part tau is along the beach of red rectangles but substitutes the height in the formula. Why?

[@vladislavkrastev1746]

I've said it before, I'm saying it again - the best sh*t on KZbin is on this channel. Period. Still no idea how people in the past studied without the access to things like that......

[@EugeneKhutoryansky]

Thanks for the compliment.

[@usmanzafar4751]

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.

[@noimnotyourex]

this is fantastic. Amusing. Amazing. I'm at a loss for words.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video that much.

[@strutter789]

4:18 got me hype as hell, lets GOO

[@meenakshi_here]

Very nicely explained. Found it at the right time. Thanks

[@EugeneKhutoryansky]

Thanks.

[@drj9403]

I didnt get one point, to get height of red rectangle why is impulse response function(tau) and Input Function(t-tau) multiplied?

[@jing-chingchen2333]

Questions why the height is unit impulse response(Tau) x input function( time - Tau) ???

[@jarkre]

Hands down the best convolution tutorial I have seen. After watching this you feel like Keanu Reeves in Matrix saying "I know kung fu".

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@virgenalosveinte5915]

Absolutely crazy, beautiful, amazing video. Thank you very much!

[@EugeneKhutoryansky]

Thanks for the compliment about my video. I am glad you liked it.

[@suhailkumar792]

Always waiting for ur video is like waiting for new moon.......love ur work😊

[@fosheimdet]

I don't get how the any input signal can be thought of as a sum of unit impulses. Isn't a unit impulse infinite in height? Wouldn't any sum of unit impulse functions be infinite in value at each point?

[@EugeneKhutoryansky]

These input pulses are not true unit impulse functions because their height is not infinite. You can think of a pulse with a height of 1 as a unit impulse function multiplied by "d tau", where "d tau" approaches zero. Hence, its response would them be the unit impulse response multiplied by "d tau." And this is precisely what happens in total output, since the contribution of each individual output function is multiplied by "d tau."

[@Gamma3]

This is one of the better things in internet

[@b_40_princekumargupta51]

Another Master piece 😍😍😍

[@EugeneKhutoryansky]

Thanks !

[@seandafny]

I needed this about 2 years ago Eugene -_- u always do this

[@seandafny]

Still rock wit u heavy tho. No love lost.

[@yuvrajsiyagg]

we arrive at a conclusion that height of each red rectangle depends on both the input function and response function but after that how is the height a multiplication of these two, it can be anything like product of one and square of another ???

[@keepitsimple7720]

Simply awesome as always

[@EugeneKhutoryansky]

Thanks for the compliment.

[@industrialdonut7681]

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!

[@EugeneKhutoryansky]

I am glad my video was helpful. Thanks.

[@ErgoCogita]

Conceptually, wouldn't each output function in the series past T @3:00 also change (increase) as you change (increase) the input function at that point in time? In the beginning of the video the models show definite acceleration and deceleration curves in the graph which surely overlap across T. Depending on where a specific impulse was terminated, the next impulse would pick up the work before much deceleration occured which would allow for a peak in acceleration to occur sooner. Or is my question beyond the scope of what this demonstration was meant to convey?

[@EugeneKhutoryansky]

No, the other output individual functions which started in the past would not change, but they would still contribute to the total output function.

[@ErgoCogita]

@@EugeneKhutoryansky Thanks for the answer but I was referring to the output functions after (past as in beyond, not past as in the past) the point in time at which you increase the output function as demonstrated @3:00. I expected to see the rest of the future series increase a bit as well. It seems as though you are confirming that the total output function *would* change if we were to change that individual function so conceptually it seems like the rest of the future series should have increased a bit in the demonstration. It was late when I watched the vid and I might have missed something important so forgive me if my question was answered in the vid.

[@DELee-qo6kv]

Incredibly well animated Visualization

[@EugeneKhutoryansky]

Thanks for the compliment.

[@trungdau2109]

one of the best vid of convolution explanation !!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@masonmault979]

this is the best video i have ever seen

[@EugeneKhutoryansky]

I am glad you liked my video. Thanks for the compliment.

[@ambientsoda106]

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...

[@EugeneKhutoryansky]

Thanks for the compliment. Yes, I make all the animations for my videos myself. Thanks.

[@usmanzafar4751]

Also if unit impulse has infinite height. Then how can a function with finite height can be composed of impulses.

[@Summer_Xia]

It's a huge loss to have found these videos so late

[@Nudnik1]

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.

[@chiahungmou8010]

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.

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@ravindrasahu8243]

Awesome Explanation! Splendid. Love from India.

[@EugeneKhutoryansky]

Thanks.

[@vahidy2002]

What a coincidence I am studying total response of impulse function right now and I got this video 😮😮😮

[@xmanxmansyr3147]

it's inevitable.

[@AlexAlex-fo9gt]

7:00 Очень не хватает картинки получившейся свертки. Вроде бы подробно разбирается пример, наглядно выводится и объясняется как возникает формула для получения функции свертки. Расписывается как свертка получится сложениями площадей фигур. Но почему бы тогда в конце этот объяснения не показать графическое изображение получившейся свертки? Вполне можно было бы разместить ее на картинке в правой части.

[@engiboye9893]

Does anyone understand why the sum of the red rectangles is the total output of the function? (at 3:28 ) In my understanding the output of the function should be the sum of the heights of the rectangles not the area. Or is the width of the rectangles equal to one? I would appreciate it if someone could clarify that. Thank you in advance.

[@EugeneKhutoryansky]

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.

[@engiboye9893]

@@EugeneKhutoryansky Thank you for your answer however I am still confused. I find the three dimensional modelling of the problem confusing. For example why does the unit impulse at 1:40 have width perpendicular to the time axis? Does that width (not the height) perpendicular to the time axis have a physical meaning? I understand that this area somehow relates to the width of the red rectangles at 3:30. I am sorry for the late follow up but other exams came in the way. Thank you very much for making these videos and thank you in advance for your answer. edit: I think I understand it now, I think the width of the red rectangles is in someway how in many unit impulses we separate the original input function.

[@usmanzafar4751]

I couldn't understand why you go perpendicular to time axis. Why at time t-tau output is tau? I am more confused now.

[@altuber99_athlete]

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.)

[@qleonardolp]

Indeed my friend... kzbin.info/www/bejne/aZandYd8mLh2lbs

[@thedorantor]

@3:00 isn't the height of the impulse pulse always infinite because the area must be 1 and the width approaches zero?

[@altuber99_athlete]

In calculus not all things make intuitive sense. The integral itself doesn't make sense: you're multiplying by _dt_ (or _dx_ or whatever) at the end, but we know _dt_ approches zero, so shouldn't the whole integral approch/be zero? It looks like it should, but it doesn't.

[@EugeneKhutoryansky]

Yes. These input pulses are not true unit impulse functions because their height is not infinite. You can think of a pulse with a height of 1 as a unit impulse function multiplied by "d tau", where "d tau" approaches zero. Hence, its response would them be the unit impulse response multiplied by "d tau." And this is precisely what happens in total output, since the contribution of each individual output function is multiplied by "d tau."

[@thedorantor]

@@EugeneKhutoryansky Oooh, I think i understand it now! Thank you so much for all these wonderful video's, especially the video about the Laplace transform. It was a real eye-opener for me.

[@EugeneKhutoryansky]

Thanks.

[@ChurchOfThought]

Dirac delta function, which isn't a real function. Just a probability distro which can be used in indeterminate forms in integrals n whatnot to solve problems