What is Convolution? And Two Examples where it arises

Explains the concept of Convolution and explains how it arises is linear time invariant (LTI) systems and also in the probability of random variables.
Note that there is a minor "typo" at 8:14 min, where I wrote x(tau) when I should have written z(tau), inside the integral.
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[@yasameenmohammed4366]

You made hours of confusion disappear within just 4 mins! Thank you!

[@iain_explains]

I'm so glad to hear it. That's exactly what I am aiming to do with my videos.

[@bixstar1469]

I was struggling with this for 2 weeks, and my professor gave 2-4hr lectures on this. But you made me understand it in just 7 mins, excellent teaching. Thank you so much.

[@iain_explains]

I'm so glad to hear that my video has helped you so much. I had a similar experience when I was a student being taught the topic - which is one of the motivations for me to make these videos. Good luck with your studies, and don't forget my other videos on related topics: iaincollings.com

[@bixstar1469]

@@iain_explains I just had one q: if the delta functions have heights of 0.5 ( like 0.5δ(t)) when convoluted will the graph height at that point also be halved?

[@bixstar1469]

@@iain_explains glad to hear that

[@iain_explains]

Convolution is a linear operation, so if a function is convolved with a delta function that is multiplied by 0.5, then the entire result of the convolution will be scaled by 0.5. In other words, any multiplicative constant factors can be brought out the front of the integral in the convolution equation.

[@bixstar1469]

@@iain_explains thank you so much

[@naufaldybambang4231]

Very useful for whoever before getting your Signal & System course

[@bipinkoirala2962]

I am convinced that you need to have a gift for making students understand the concept.....not just degrees. Thank you for uploading

[@iain_explains]

Glad it was helpful!

[@lepthusmak9510]

Had been searching for a genuine video which could make me understand that formula of x(Tau).H(t-Tau). Since i am from pure mechanical background and was studying control system, this term came up and searched for 3-4 hours going through 5-7 videos. Thanks a lot for this beautiful and easy explanation of this concept.

[@iain_explains]

I'm glad you liked it. Perhaps you might also like this video that gives insight from a mechanical perspective: "How to Understand Convolution" kzbin.info/www/bejne/rmSplZdsi8R7pc0

[@kwanxhen3829]

Learning engineering is fun when it is taught like this! underappreciated content.

[@iain_explains]

Thanks for your nice comment. I'm glad you like the videos.

[@juliette3568]

this video is so clear - it has helped me understand the concept so much!

[@iain_explains]

That's great. I'm so glad it's helped.

[@sajjadrezaei91]

Thank you so much ... I've been struggling for years to understand this concept in an intuitive way ... really appreciate it

[@iain_explains]

Glad it was helpful! Have you also seen my other intuitive video on convolution? "How to Understand Convolution" kzbin.info/www/bejne/rmSplZdsi8R7pc0

[@inquisitiverakib5844]

it is the 1 & only lucid & concept clearing video on this topic i've got in youtube. thanks a lot for this.

[@iain_explains]

Glad it was helpful.

[@sophiaxie6933]

I am so excited to watch such a great lecture, all my confusions from my professor's class just went away completely.

[@iain_explains]

I'm so glad it was helpful!

[@sangkyunglee1343]

Perfect explanation! Convolution equation video was excellent as well!

[@iain_explains]

Glad they've helped!

[@mohaalk5635]

This channel is my no 1 reference when i want to really understand a concept. Thank you very much 😁

[@iain_explains]

That's great to hear. I'm glad you like the videos.

[@luandesouzasilva565]

That was the best explanation I've ever seen about Convolution. I've studied this over years and always felt like I was missing something. This video filled out my understanding about the fundamental of convolution.

[@iain_explains]

I'm so glad to hear that you found the video helpful.

[@Arif.mohmand]

You made it so easy and understandable, thank you very much.

[@iain_explains]

Glad it helped!

[@davidji149]

The video is so nice, it makes me so clear about origination of convolution. Thank you for such a nice explanation.

[@iain_explains]

Great to hear. Glad you liked it

[@ayberkm]

I've been searching the explanation of convolution all day and luckily ı seen your video.Thanks

[@iain_explains]

I'm glad it helped. You might like to check out the other videos on the channel that explain other aspects of convolution. See the full list at iaincollings.com

[@shahedahmed7267]

Excellent explanation. This is the beauty of a great teacher, who can think where the students might have questions and then give a clear and proper demonstration.

[@iain_explains]

Thanks for your nice comment. Glad the video was helpful!

[@jpenneymrcoin6851]

Feynman always said if you can't explain to a 5-year-old, you don't really understand it yourself. This guy understands it.

[@philparisi_]

You are the man Iain, thank you so much.

[@iain_explains]

Glad to help

[@lipshitdash4578]

I would say the best video on convolution intuition on KZbin ❤️

[@iain_explains]

Glad you think so!

[@aadharshram4975]

Damn, you finally made the concept click. Thank you for making the video!

[@iain_explains]

I'm so glad you found it helpful.

[@VanshJainBEC]

Thank You veeery much sir! I was having a lot of problem in understanding this concept but you explained it very excellently. Thank You once again.

[@iain_explains]

Glad you found it helpful. Perhaps this video might also add more intuition: "How to Understand Convolution" kzbin.info/www/bejne/rmSplZdsi8R7pc0

[@r.bhargavram3546]

Thank you 🙏

[@mohsinali-hw3mk]

thank you for this excellent explanation , i will do it to my students

[@iain_explains]

Great. I'm glad you liked it. Perhaps you might consider giving your students the link to my video, and to my channel more generally. All the videos are categorised at iaincollings.com

[@-PAUL-ub3bz]

good video sir...u explained how a student wants.. im amazed i saw many videos , but got clarity after watching your videos sir!

[@iain_explains]

Glad you like the video.

[@souravmzdr]

A very clear explanation. Thank you .

[@iain_explains]

Glad it was helpful!

[@andrewbetz535]

Awesome video man

[@iain_explains]

Glad you liked it

[@Cornerstone00]

lovely explanation

[@iain_explains]

Glad you liked it.

[@alialwanos9170]

Thank you Dr for this information

[@iain_explains]

My pleasure

[@zhoujeffery9863]

What an amazing video, it is very useful for a fresh acoustics student.

[@iain_explains]

Glad it was helpful!

[@zhoujeffery9863]

@@iain_explains Thank you for your video if it is ok to talk more about the Data Truncation?

[@omarjallow7102]

great explanation

[@iain_explains]

Glad you liked it

[@dirac9]

Thank you so much!

[@iain_explains]

My pleasure.

[@junbug3312]

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[@iain_explains]

Welcome aboard!

[@sksahil4374]

great video .

[@iain_explains]

Thanks. Glad you liked it.

[@dangakong6304]

Thank you very much. Its a very great video 📹

[@iain_explains]

I'm glad you liked it.

[@GrandNecro]

i love the way you exapln thing with examples. do you have a series on analog circuit analysis?

[@iain_explains]

Thanks for the suggestion. I don't have anything on that at the moment, but it's in the pipeline.

[@Nick_Dole]

Very good!

[@iain_explains]

Glad you think so!

[@moyeonkim]

Thank you oh so so much. Thank you so very much.

[@iain_explains]

You're welcome. I'm glad you found the video helpful.

[@edwinr4378]

Before completing the video, I give like to your video...bcoz I know it's amazing

[@iain_explains]

Thank you so much 😀

[@ahmetanadol5289]

Perfect explanation thanks sir

[@iain_explains]

Glad you liked it

[@bwlkwok]

Your voice is very attractive and can draw me into great attention .Otherwise I fell asleep . Great teacher

[@iain_explains]

Thanks. I'm glad you didn't get put to sleep. 😁

[@timliu1916]

Thank you!

[@iain_explains]

You're welcome!

[@user-vk6ed4vx3z]

Very very good. I comes from China，it really helps me！！！

[@iain_explains]

Glad to hear that!

[@adonis7419]

Great video

[@rohanajageer4856]

Excellent work sir I was hoping if you could make a video on solving convolution using analytical method

[@iain_explains]

I'm not sure what you mean exactly. Have you seen my other videos on iaincollings.com ? For example, "Convolution of two Exponentials" kzbin.info/www/bejne/apCvc2asiayLd9U and "Convolution Square with Exponential" kzbin.info/www/bejne/oqSrnIp8d9JmqdE

[@sarathjeeva28]

Good video bro..., Keep doing it👍 And also put a separate video on What is Correlation & Autocorrelation?..... I'm waiting

[@BruceWayne-dh5hy]

Ayya.. Professor akkum. Ungalk eppadi avargale bro kupida mudiyum??

[@iain_explains]

I know you've seen the new video already, but for others who might be reading this comment, check out the new video on Autocorrelation and Power Spectral Density at kzbin.info/www/bejne/jojcpYaCj7-DZ6M

[@michaelgad4187]

Wonderful explanation my friend! Life cannot be easier :D

[@iain_explains]

Glad you think so!

[@madhusudhan5856]

Good stuff. Can you make your voice much clearer, finally conceptual explanation is super.

[@iain_explains]

Thanks. I'm looking into getting a better microphone. Hopefully it will make things clearer.

[@zuzukouzina-original]

You reminded why I studied electronics 25 years ago. You also showed my we had some terrible teachers 🤦🏻‍♂️

[@iain_explains]

I'm glad you found the video interesting - even after so long since needing to do exams!

[@nanjiang4158]

h(t)->h(t-\tau) has a flip on x axis, it would be helpful if you can point out that, otherwise, people may get confusion how h(t-\tau) sliding on the x axis.

[@iain_explains]

Well, I prefer not to think in terms of "flipping" and "sliding". I find that only confuses people. I prefer my method of thinking about convolution, described in this video: "Convolution Square with Exponential" kzbin.info/www/bejne/oqSrnIp8d9JmqdE

[@kashifkhan5565]

I wish my teacher had the same skill set of explaining things, rather than dumping.

[@iain_explains]

I'm glad you found the video helpful. Let me know if there are other topics you'd like to hear about (that aren't already on the channel).

[@dimified]

Noice!

[@Matchat11]

waw

[@godfreypigott]

What exactly do you mean by the first function being time invariant? h(t) is not a constant, so it literally varies with time.

[@iain_explains]

Hopefully this video helps: "What is a Linear Time Invariant (LTI) System?" kzbin.info/www/bejne/a3umpqSiet2HrNE

[@jihadal-najjar8517]

at moment 09:10 why we supposed that the output signal would be like that ?! I think it's gonna be a straight line lying on the t-axis why my idea is wrong as the Z(t) is an infinite number of delta functions?

[@iain_explains]

Sorry, I don't understand what you're saying. I'm not drawing time domain waveforms here. I'm drawing the probability density function. In binary digital communications there are only two possible values that the data can take (at any given time), and there is 0 probability of having any other values. That's why the data's pdf has two delta functions. Perhaps you might find this video helpful: "What is a Probability Density Function (pdf)?" kzbin.info/www/bejne/oIapk4xrqpJ3g9U

[@ShahadetHosenPolash]

why we need to flip the tau in definition? what will happen if we dont flip? what is the intuition behind this?

[@iain_explains]

We don't "need to flip". We're not choosing to do it. Convolution is what happens in linear filters. We don't get a choice in the formula. Perhaps this video will help: "How to Understand Convolution" kzbin.info/www/bejne/rmSplZdsi8R7pc0

[@ranam]

Telling the application of convolution in terms of signal processing may help a part of people in the telecommunication and eee engineers but when convolution meets signal processing it also is used as a filter but my question is I have read convolution even it's useful for mechanical engineers such that in resonance when a failure occurs not due to massive force hitting an object results in large deformation could cause failure or an large impulsive force acting on it for a duration of time could cause failure but there is an another phenomenon where the natural frequency of any object is reached the energy builds in it very high and could cause a failure in this manner a small disturbance which accumulates over a time and causes a high energy to build in the system due to energy very high it causes stress and the system collapses this is highly different from stability perspective of control system being not stable does not mean it's accumulating energy inside it but in case of amplifier there is an capacitor or inductance device which causes the attenuation in the electrical signal and filters some frequencies but in other perspective amplifier amplifies the signal such that it stack ques and scales the signal but I don't know this is done by capacitor or am inductor but convolution is useful to both mechanical civil eee ece and every applied scientist and engineers hence it's used as a filter in an circuit or used to amplify but even transistor amplifies the signal without an capacitor or an inductor I guess also mechanical engineers can use it to model resonance hence the energy inside the system build high by periodic accumulation of the system reaching its natural frequency which leads to failure and I can also tell you that when amplifier filter or amplifies the signal it used convolution hence it's useful to every applied scientist and engineers but not to mention the pure Mathematicians use it of convolution of kernels thankyou guys some of my inference could be wrong if somebody or the author of the video is familiar with it please correct the above and educate me thank you for the wonderful video sir

[@iain_explains]

Yes indeed. Convolution happens whenever an input is applied to a linear system ... _any_ linear system. It can be an electrical circuit, a mechanical device, a civil structure, a wireless communication channel, - anything that is linear. Here's another video on my channel where I use a mechanical shock absorber as the example: "How to Understand Convolution" kzbin.info/www/bejne/rmSplZdsi8R7pc0

[@ranam]

@@iain_explains thank you for the reply sir i watched it and it was great thank you for educating me

[@ranam]

@@iain_explains but what about damper which in the bikes shock absorber absorbs but in resonance accumulates the energy for destruction

[@iain_explains]

Many/most systems in the real world are non-linear (although we often like to make approximations and model them as linear).

[@ranam]

@@iain_explains yes sir but how a system which scales and amplifies the input impulse signal in resonance or bump can also be used as a filter convolution is used both in modeling resonance and also attenuation of signals as a filter but the same time I am asking in amplifier the signal is amplified due to the internal component capacitor or inductor hence it stacks ques and scales the signal

[@rishabhsrivastava7494]

Can the convolution of two non-zero signals be a zero??

[@iain_explains]

Sorry, I don't know what you mean by "be a zero". I guess you mean that the resulting signal = 0 (ie. for all time - assuming they are time domain signals we're talking about.) It might help if you think in the frequency domain. Convolution in the time domain, is the same as multiplication in the frequency domain. So if a function equals 0 at a particular frequency (in the frequency domain), then if you convolve it (in the time domain) with a sinusoidal signal at that frequency, then the resultant signal would be 0 for all time.

[@adityasingamsetti1316]

Sir I'm struggling with one doubt here that if we approximate our x(t) as the sum of impulses which are very close to each other. Suppose before approximating x(t) as impulses at particular time say t=1 it will have some finite value. If we approximate it as impulse then at same time t=1 we get infinite value because amplitude of impulse is infinity. Kindly please solve my doubt

[@iain_explains]

Yes, it can seem odd, but don't forget the width of the impulses is infinitely narrow. It's the area that is important when you're "putting them together" to make a real signal. This video might help: "How to Understand the Delta Impulse Function" kzbin.info/www/bejne/rqmqlHxvjLuiebs

[@leolau6378]

You can imagine x(t)*d\tau to be the area in the integration. That would make sense.

[@prasanthr3875]

Supeeeerrrrrr

[@DARPANGUPTA-gn9ld]

How can we write x(0)h (t) +x(1)h(t-1)+x(2)h(t-2) as we know x(0)=infinite as it is height of impulse?

[@iain_explains]

Yes, technically you're correct. Technically, I should have written "the area of the delta function that is centred on t=0" and "the area of the delta function that is centred on t=1", etc. But I didn't have room on the page to write all that, so I just used x(0), x(1), etc as a sort of "short hand".

[@DARPANGUPTA-gn9ld]

@@iain_explains thankyou for your response

[@taichenglee6240]

at 8:14, x(t) or z(t)?

[@iain_explains]

Yes, sorry, that's a "typo".