Time domain - tutorial 8: LTI systems, impulse response & convolution
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- čas přidán 21. 08. 2024
- In this video, the following materials are covered:
1) the beauty of linear & time invariant (LTI) systems
2) why the impulse response of an LTI system is so important
3) how to find an impulse response
4) how to connect all the dots (LTI and impulse response) and fully understand the convolution concept forever
Learn Signal Processing 101 in 31 lectures covering time, frequency and Laplace domain in about 8 hours all together:
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References:
[1] Alan V. Oppenheim, Alan S. Willsky, S. Hamid Nawab, Signal & Systems, 2nd Edition, Prentice-Hall, NJ, USA, 1996.
[2] Alan V. Oppenheim, Ronald W. Schafer, Discrete-Time Signal Processing, 3rd Edition, Prentice-Hall, 2009.
[3] Michael D. Adams, Continuous-Time Signals and Systems, University of Victoria, Canada, 2013. Free textbook and lectures (courtesy of Dr. Michael Adams):
Link to the Dr. Adams' textbook: bit.ly/37rkwDC
Link to the Dr. Adams' lecture slides: bit.ly/2WrwHKy
No way! How could you explain so well. My prof asked us to watch your video for revision but I he actually should play your video in the lesson.
Thanks for your kind words and good to know! Which university and who is the prof? Please thank him on my behalf.
You managed to do 1 hour of uni lecture into 13 informative useful minutes, big props.
Glad you enjoyed it!
This is ART. You are a gift to the collage students. You are so talented.
You are very kind Mohammad, thanks a bunch for the feedback ;)
You make everything very simple by providing real life examples. You are the best teacher for signal processing I had have. I request to make videos on communication systems as well.
Thank you very much for your kind words and the feedback. I will make more videos in the future but first I need to find a way to create content faster! That's why I am working on the Castofly project all day everyday for now :)
that WATERMELUN was great persian example! :))
thanks for all nice videos iman jan!
hahaaa, thanks a bunch Navid jan ;) cheers!
I spent all night trying to understand this concept and at 8 am I found this video and realized how easy it was. You are amazing!!
It is a great pleasure to help you understand the concept. cheers!
I can't believe you do these for free out of the kindness of your heart. I credit you for saving my grade in this course! Much love man. Keep up the great work.
Hahaa. Thanks a bunch Sam. Not sure about kindness of my heart but yes my vidoes are free. People can help by donation of course. Cheers!
The watermelon was a great example. Please keep going and provide us best tutorials. Appreciate your efforts!!!
Glad you liked it!
GENIUS! The watermelon example is so great!
Thank you very much!
Another really good explanation, especially showing that all frequencies are represented in impulse input! I am a mechanical engineer (retired) and learned Duhamels method (convolution for 1-dof vibrations), not knowing why it worked. Thank you. Watermelon example was Brilliant.
Thanks a lot for sharing! I am very happy that you enjoyed this lecture. The watermelon example is my favorite part :)
This is the best explanation to convolution I have ever seen! Thank you! Scientists may be in the making because of you!
Thanks for your kind words and pleasure to help!
I have only one word to say BRILLIANT!!!
cheers!
Get Brilliant for 30% off if you sign up now! 😂😂😂😂 jk I’m kidding
this channel deserves more views
Hopefully one day it gets more traction! Please recommend it to your friends!
Hi Iman,
Before watching your video, I understood how to determine the impulse response h(t), the system response y(t), and perform convolutions. However, I didn't know how they were all linked together. Your video series helped me bridge the gap between all three and really understand what was actually going on, as well as give me an appreciation of why LTI systems are so useful. Thank you so much for your time. You have really made this course a lot easier. You are an excellent teacher.
Thank you very much for your feedback. It is such a great pleasure to help you understand the course better. You are very kind. cheers!
one of the best I've seen, thanks for the brush up
Thank you!
U r a gem 💎💎 never commented on any of 1000 of lectures i have been through in youtube but bro u r gift 🎁🎁
Thank you very much for your kind words!
Iman, you have a true gift. Great videos. Congrats.
I appreciate that!
just randomly found this video .wish U best from iran :)
Thanks a lot Amir jan!
lol damn. spent the last two days doing all the convolution questions the prof assigned...after i mastered the process, i sat back and asked myself "what am i even doing? what does this mean?" I had the process mastered and memorized but I didn't even know what was happening. After this video I finally see! Thanks.
I love your comment! I am really happy to see amazing people like you who want to deeply learn the concept (not just memorizing equations) are interested in my videos. Cheers!
the convolution's explanation is one of the best on yt really helpful !
You are very welcome, my friend!
Dirac delta function is equal to infinity in continues time. In discrete time it's equal to 1.
Thank you very much!
Hey Alon, thanks for your comment. Technically impulse function is a rectangular function with the width of Delta and the amplitude of 1/Delta when Delta goes to zero. Thus the area under the curve is one. This definition is technically true but hard to digest. It is common to model this with the unit impulse function with the amplitude of 1 at the origin. Hope this clear things up.
Damn your sketches are on point and u made me understand so well dude !!
Thanks a lot Adhiraj ;)
Amazing video, everything is crystal clear now!
Glad you liked it!
This guy is awesome. Please keep doing the good work man. God bless you.
Thanks a bunch, Bulbul. Your comment made me really happy :)
Clear. Precise. Thanks.
Kind. Nice. Thanks a bunch ;)
Wow... thanks.. now I know the importance of impulse response... Great video... keep it coming!
Thanks a lot.
Why did i spend 4+ hours trying to grasp this by reading the course book when I could have watched this awesome video? THANKS!
Seriously why?? Your comment is amazing to be used as an ad for my channel ;) "Why do you wanna spend many hours to read boring books, watch sphacks videos to learn signal processing easy, fast, forever". Maybe this will help me get more subscribers :))) Thanks for your kindness. Best!
You are a gem bro.. Thanks from Bangladesh
You are most welcome
I finally feel I understand these concepts after this video
Thank you very much for your feedback!
Amazing lectures, great teacher, finally i got a feeling about the convelution, thanks a lot, Iman!!!
Thanks a lot, Fei. It is a great pleasure to help you understand convolution ;)
4:25 delta(t) is infinity at the origin, not 1.
Edit: Your motivation of the convolution theorem at the end was brilliantly done! Seeing how a system being LTI or not tells us whether we can use convolution theorem is very insightful! Thank you 😊
Thank you Ozzy!
Very clearly explained, thank you!
Glad it was helpful!
such a great explanation ! couldnt find an explanation like this anywhere else ! love it
Great to hear and thank you for your feedback!
one of the best videos on impulse and convolution
the example and the language and the way of explaining the concepts is so simple its impossible not to understand
HATS OFF YOU TO YOU
awesome teacher
Please Sir if possible can you make videos on FREQUENCY RESPONSE I.E H(z)
Thanks you very much for your feedback, Sanjeev. You are awesome. It is a great pleasure to help you understand signal processing. Best!
Great job Iman! Merci!
You are very welcome Nasim jan.
Thank you so much. I couldn't get its intuition anywhere else.
Pleasure to help, Sidharth!
May Allah be pleased with you, it is really a good explanation
Thank you very much Emre ;)
This is so helpful and cool!! Thank you so much for taking the time to communicate to all of us :)
You are so welcome!
Great video! thank you for helping people Iman
My pleasure and glad it was helpful!
Wow now I finished watching the convolution as well! I'm so excited, and think I'm about to lose my bladder control.
Lol, thanks a bunch for sharing your excitement with me my friend ;) You are awesome!
Amazing I never unserstood the derivation of convolution but this made it so so easy , amazingg
Glad my videos helped!
You are a talented teacher , awesomeee , keep posting these great videos.
Thanks a lot, Alaa! You are very nice ;)
This was crystal clear! Great explanations!
Glad it was helpful!
the best teacher ever!! thank you, man. I needed this
Thank you for contributing in me passing the signals course :D you make me engineer
Thanks for watching my videos and it is def a pleasure to help you learn the topic!
Wonderfull example by you regarding watermelon
Lolll! Watermelon example is my favorite ;)
this is really awesome!! it saved my midterm :) thank u so much
胡安啦 pleasure to help ;)
The watermelon example was a good one :)
This is fucking better than Game of Thrones!
Lol, I am not sure about it but thank you Andrei ;)
You actually made me understand convolution!!! Thank you so much for that!
You are very welcome and thanks for the feedback ;)
Much better than my lecturer!
thanks :)
I have a great lecturer, but you are equally as helpful. I'm in luck!!
Lovely video! I want a 10-hour loop of you saying Watermeloan.
lolll, I will create a playlist on watermelon then ;)
Thank you so much Iman, you are the best
You are very kind, thank you!
Thanks Iman for the great content
Thanks a lot, Hossein.
Awesome!!! U are really a brilliant teacher!
Thanks!!! U are really a kind person ;)
Excellent video. I just subbed. Hopefully more Electrical engineering tutorials in the future
Thankyou so much, love your watermelon example :)
Thanks a bunch! Many folks loved the watermelon example :) I am gonna use more fruits in the upcoming tutorials!
Love you man, that one still helps me!
Love you too ;)
Great explanation. Many have knowledge but lack the ability to explain. You have both. Keep up the good work. Which is the tool you are using for recording the videos?
Thank you for your feedback. Castofly (my own software) which is available at www.castofly.com for Windows
Awesome, many thanks! It will be great if you add some resume docs!
Thanks for your kind words and feedback!
Your videos are very helpful. I shared your website with my class. My professor watched some of them and commented that they are awesome. Have you considered posting notes for each video?
Hey Jack. Sorry for my late reply, life has been hectic recently. Thank you very much for your feedback and sharing my work with your class & the prof. Regarding your question, I just wonder what kind of notes you are talking about. I haven't posted any notes for the videos but I guess it is a very good idea to post learning objectives for each lecture. By the way, which university are you at? If you have more ideas to help me expand my outreach, I would love to hear it. Please let me know. Cheers!
No problem regarding the delay. I understand hectic life. A full time career and working on a second bachelor degree in electrical engineering at the University of Michigan keeps me busy. Regarding the notes, I started to write out the material from your lectures but it is very time consuming. The Fourier Series lecture took me a couple hours to write and was five pages long. I thought you might have notes you used when you recorded each lecture. If not, please don't spend time on it. I would rather see you produce more lectures on Laplace and other topic related to signals and systems. The other idea I had was to take screen captures of each page in a lecture and then convert to a negative image to turn the background white. That way they could be printed on paper. Of course the colors you used for writing and drawing would all be negative too.
Awesome! Working full-time and studying elec eng must be damn difficult. Keep up the good work man. I didn't think about printing issues with black background!! Great feedback. I am thinking to publish the notes along with some assignments for each topic as a course book. I've made all the videos for this course ad-free to assure there is no distraction for students and I was hoping to get some support through donation to keep producing more lectures. Unfortunately, the donation was not very successful. I am planning to make the course book available with a very very small cost so that students can afford buying it. Honestly, I am not doing this for money, but I need to find a sustainable model to go beyond this course and produce many more videos. Producing these videos are very time-consuming.
Really incredible explication, thank you so much!
Thank you ;)
great explanation
Glad it was helpful!
great education
You are very welcome!
perfect ! Great video. Thank you
The watermelon example is pretty cool
Xiaotian Dai thank you Xiaotian ;)
Thank you! Great video! Great Watermelon!
Lolll, Great comment ;)
brilliant tutorial!!
Love your video. A question related to what you said about the “black box”, I still dont understand about this concept. If the system is LTI and we know about input and output, then why and what we need to know about that box? Mathmetically we can show if the system is LTI or not, but after we know it is LTI then what else we need to know about that system? Sorry if you understand my question or not. Thank you.
Knowing the system is LTI doesn't reveal any information about what the system does! If it is LTI, there is a scientific way to find out its behavior (using impulse response). Hope this helps!
crisp and clear.thank u . convolution should have been elaborated a little bit more,i think.
thanks a lot for your feedback. have you watched my tutorial on "convolution examples"? Hope that helps!
Amazing explanation.
I just have one doubt that why the impulse response is defined only for LTI systems.
It will be a great help if you reply to this.
The impulse response can be defined for any system but if it is LTI the response is a full representation of the system. Hope this helps!
@@imanmoaz Thanks for the reply.
Can you please elaborate that how we can characterise the LTI systems fully by impulse response.
Of course your example with watermelon was amazing. But I still had some confusion regarding this.
@@piyushsoni4100 please explain it to me If you got the answer.
@@vintibhatia5365 I got this.
But it is a bit conceptual to explain with a reply.
great explaining, easy, simple
thanks man
thank you ;)
hey iman !
you are awesome man !
I am sure you will be a great teacher !
your explanation is perfect !
keep it up brother !
srinivasa krishna thank you very much!
you're a genius
you're kind :)
Hi Iman, thanks for this great tutorial!
I only have one question. @11:29 shouldn't the result of the sifting property x(tao) instead of x(t)?
I mean, we said tao is the time shift, so the sigma signal is only defined at this point -> tao but instead you said -> t ..
Also, is there a significance in using tao in both signal in: x(tao) sigma(t-tao)?
Hi Mohamed, thanks a lot for the feedback. Regarding your question, it must be x(t) not x(tao). Please note the the integral variable is tao ... inside the integral you can see t as some sort of constant. When tao is changing from minus infinity to plus infinity, x(t) is one value (i.e. the value of x at time t) and independent of tao. When tao is equal to t, the impulse function becomes one and you can apply sifting property. Hope this helps.
@@imanmoaz Thanks for your reply!
I am still not getting how we are mixing between t and tao in both (integral variable, time shift) but I might be getting the whole picture in a way or another.
1) In step 3: The system is linear and we multiply input by an arbitrary value x(tao) .. x(tao) here *is a single value NOT a function*, right?
2) In overall: We are constructing the function/graph x(t) by adding multiple x(tao)s where tao is changing from -infinity to infinity using the equivalence property of the sigma signal?
Am I correct with this approach?
Hey. I am sorry if the approach is confusing. The variable inside the integral (tao) is the thing that is changing from -infinity to +infinity. Inside the integral you can see t as a constant. Regarding your first point, yes at that step you can see x(tao) as a single value . Regarding the second point, yes we add integral and then use sifting property to replace the integral on the left by x(t). Hope this helps.
You are great man !
Thanks a bunch, u 2 ;)
Thanks for being a G ma dude
what is G ma? Grandma? :)
very good one!
nice video, helps me a lot ;)
Glad I could help!
4:30: I think an impulse should be written as: delta(t) = infinity, at t = 0 and 0, elsewhere. This is called Dirac Delta. An impulse of magnitude 'a' at t = 0 can be written as a*delta(t).
Hello. Very nice series. I have a question: At example with y(t) = integral from t-2 to t of impulse(tau)dtau :D when we find h(t) why do we assume the function impulse(tau) is 1 at origin and 0 everywhere else?
Thank you very much. That is the definition of impulse function, please watch my tutorial on the elementary signals.
3 LTI systems connected in series with shock responses are given
ℎ1(𝑛) = 2𝛿(𝑛) + 3𝛿(𝑛 − 1)
ℎ2(𝑛) = 4𝛿(𝑛) + 5𝛿(𝑛 − 1)
ℎ3(𝑛) = 6𝛿(𝑛) + 7𝛿(𝑛 − 2)
how to Calculate the total impact response??
Hi Iman,
Very great video! Thank you for saved my exam and my life, even I'm still doing your series. ;)
One question: Are the final blackboards downloadable or is there any chance to make them downloadable as a pic (or pdf or something)? Your explanations are very great and useful, but once I've got that, it would great that I would be able to just check something quickly as a reminder.
Hey Daniel. Thank you very much for your feedback. I will make the lectures' notes available as a PDF in the future.
great , cleared my all doubt
pleasure to help my friend ;)
Great video! I definitely was not expecting such a handsome man to pop up on screen slapping a watermelon to explain signal processing, but was pleasantly surprised haha.
Thanks Nigel, I am not sure about the handsome thing but pretty happy about your comment ;) Cheers!
good explanation
Since for transfer function of LTI system, we apply input signal in frequency domain(from the definition, Laplace transform of output to that of input). So, where does the time domain used in context of transfer function? We need transfer function for every model right?
Shouldn't the dirac delta function be Infinity (not 1) at zero and 0 everywhere else? Those integrals would evaluate to zero if the delta function is finite at the origin. Is there something I am missing?
Convolution - the simple way we can use all of those AI hardware TOPS to bring value to us :)
That's a good point
Truly Awesome !!! i have one question :P ... why is an impulse function considered an unstable ? although it gives a finite response 0 for infinity as input
Thank you for your feedback. Can you elaborate your question more? which impulse response are you talking about?
incredible video, thank you so much :)
Thank you very much Hank!
Thank you!!! So much!!
Cheers!
Thanks a lot 🤗
Thank you for watching ;)
Excellent Explanation! O_O
Cheers!
I understand convolution even though it's supposed to be harder. But no matter what I can't understand or accept impulse response. I don't get it! How can you put a function into a system? Is the blackbox the input function? Are you applying the input function into the black box? Then what is the blackbox? Another function? Why would you apply a function into anther function in this case? What is the purpose? So so confused.
I am really sorry that my explanation didn't help you grasp the concept. Convolution is a bit complicated concept and I feel you. Please pinpoint which part you don't get. I will try to explain it better.
@@imanmoaz When I think LTI system I think a process (like a programming loop) that performs a linear sequence of operations? Is that a correct assumption?
Secondly, if it's a linear sequence of operations on an input sequence(impulse unit in this case), then shouldn't it's output sequence be equal in length to is input(impulse)? Ex. I input [0,0,0,1,0,0] 6 length input sequence. Shouldn't I get back an out of 6 length also? I'm assuming the system takes each element in the input sequence, operates on it and produces an element for it's output sequence (output here being the impulse response)? I've seen LTI system examples where the impulse response length does not match the input length, information is being lost or added.
Finally, why bother with an impulse response? The system works. Why not just take your input, pass it into the system get your output.. why get an impulse response and convolute it with the input? Seems roundabout.
I understand convolution btw. From mathematics. Just don't get the point of an impulse response when you have the system and the input and you could just give it the input and forget the impulse response.
Hey again, regarding the first question, LTI means linear and time invariant! Linear stuff is happening in the system but it is not exactly a for loop. Please watch my lecture on system properties to learn what linear and time invariant mean.
second question: what you said is true for a memoryless system, the output at any time only depends on the input at that time. If the system has memory the length is different. Again, watch my lecture on system properties.
last question, I am not sure what you meant. The main goal is to identify/understand the system! Please clarify your question.
@@imanmoaz Yes I know the properties of a linear time invariant system. f(x + y) = f(x) + f(y) etc. Can you please give me some real examples of an LTI system? Abstract is great and all, but I need to know what a tangible LTI system looks like.
Understanding a system via it's impulse response is great. I support the goal 100%. Obviously though you and I know that using the system is the real goal. That's why it's impulse response is used in a convolution with an input. Now why doesn't that feller just input his input into the system. Why does he need to obtain a response then use convolution?
doesn't the delta function have a height of infinity and not 1?
Yeah, that's correct but the integral/energy under the curve is one. It's just easier to assume the amp is one at zero (but technically this is not def correct).
thankx dude!!
thank you thank you thaaaank youuuu
you are very welcome my friend :)
Sir can you give some real life examples for time invariance and LTI systems like impulse response as you shown with watermelon??
Plz
Thank u
Hi Haseem. Here is a quick example:
www.quora.com/What-are-some-real-life-examples-that-helps-to-understand-the-LTI-Linearly-Time-Invariant-system
Hope this helps!
Why is the variable t often used as a limit of integration when dtau is used in the integrand. Nobody has been able to clearly explain this to me.