Convolution and Unit Impulse Response 

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

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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.

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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.

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

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

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.

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.

I am soo sooo happy that u starts uploading videos 🙏

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

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

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

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.

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

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

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.

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!

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

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

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

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

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.

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

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 ❤️

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

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

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..

This is one of my favorite videos of all time.

Finally! A video on convolution that I understand.

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

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

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.

Absolutely the best video on convolutions on the internet

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

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

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

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

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!

Simply awesome as always

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

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

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

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.

Another Master piece 😍😍😍

one of the best vid of convolution explanation !!

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

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

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

I love your videos! You are the best. THANK YOU!

Needed this one.. Convolution.. Thanks!

Wonderful! Thank you Eugene!

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

Awesome art!! Keep on doing these videos!!

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

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

This is one of the better things in internet

Simply amazing.Thank you

Best video I’ve seen on the topic

Excellent explanation. Thank you so much.

Awesome Explanation! Splendid. Love from India.

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

Very good, basic concept behind DSP

Thanks for making this..so much help

Thank you for this explanation, it was great !

this is the best video i have ever seen

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!

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

thank you for your hard work!

Incredibly well animated Visualization

Amazing! What a great explanation. Love it.

Thanks for excellent explanation

This was absolutely fantastic! Thank you very much for this amazing explanation! I have subscribed to your channel now :) Keep up the good work!

Really helped be understand convolution, thank you!

Thank you so much , Sir !

Unbelievable, somebody would do this. Amazing explanation! More videos for controls please.

Amazing! Thank you!!!

Wow, I sure wish I had this video when way back in the day I was learning this in school!

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)

excellent job! Thanks!

many thanks

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

the best of its kind 💓

thanks for making this video

your explanation was like listening to a poem, thank you

This is really amazing!!!!!!

great explanation !!!

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.

Amazing animation

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

Great video.

I loved this video. ..great work

Thank you, this is great

You enlightened me!

Fucking beautiful. Thank you so much. I may actually pass my first signals and systems exam thanks to this video.

Thanks for this!

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?

these videos deserve all my semester money

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.