How to Understand Convolution ("This is an incredible explanation")

Explains signal Convolution using an example of a mountain bike riding over rocks.
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Full list of categorised videos and Summary Sheets: iaincollings.com
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[@undertaker7523]

This is an incredible explanation. I wish you the best professor!

[@iain_explains]

Glad it was helpful!

[@IDK_OR_DO_I]

Damn Zoro are you lost again?

[@user-vw4zx5dt4o]

Nothing happened!

[@hariharannair3281]

It's a joke that this kind of video has only 264 views it should be 2Million. God bless u sir

[@iain_explains]

Thanks for your endorsement. ... hopefully the word will spread, and more people will see it. Fingers crossed. This "shock absorber" explanation has been knocking around in my head for the past 20 years, since I first started teaching Signals and Systems. It was only when I saw the boardwalk, while also thinking about what my next video should be, that I put it all together. I wish my lecturer had explained convolution to me this way when I was a student. That's what I'm aiming for with each of my videos. I'm really glad you liked it.

[@larswassink2593]

Already passed my Signal Analysis course last year, but I never really understood the fundamental theory behind convolution. This explanation would have made my life significantly easier, since the way I have been tought convolution was, well, very convoluted... (it involved a lot of graphs that were very abstract...) Thanks Iain for making a fun video on a challenging concept on signals :D

[@iain_explains]

Thanks for your nice comment. I'm glad to hear that you like it, and that you think you would have benefited from it when you were studying it.

[@harshithramamurthy2820]

Teachers like you make world a better place for others..

[@iain_explains]

Thanks so much. I really appreciate your nice comment. I'm glad you like the videos.

[@VICTOR-cu2de]

Best channel of telecommunications by far. You are helping me to do my research for my degree final project. All the best for you from Spain

[@iain_explains]

I'm so glad the videos are helping. Good luck in your project. It's a few years since I last visited Spain. Thinking about it is giving me tapas and churros withdrawals. 😁

[@parthapratimboruah641]

How fascinating it is that we get to see people like you sharing knowledge in unique ways!!! You got the idea while riding a bike and there you are sharing that with us. Thanks

[@iain_explains]

Glad you enjoyed it! Indeed, it is fantastic to be able to use the KZbin platform to share education ideas.

[@mnada72]

That is a very intuitive explanation. Thank you

[@iain_explains]

Glad it was helpful!

[@ItsMeTheUser]

Really helped me to understand the concept! Thank you sir!

[@iain_explains]

Glad to hear that!

[@banaatti]

Amazing, watched just 3 of your videos about convolution and I feel like I learned more than any of my Uni materials and whatnot. Thanks!

[@iain_explains]

That's great to hear!

[@retiresoon2008]

Finally I got the idea of convolution! The sum of system responses to a series of impulse signals. Thank you so much for the excellent explanations!

[@iain_explains]

That's great to hear. I'm so glad the video was helpful.

[@creativemt4065]

This is one of the BEST examples ever! That is why I love MTB!!!! Thank you!

[@iain_explains]

I'm glad you liked it.

[@abcxyz-nd6xh]

Love your beautiful making use of the surrounding tools/materials to demonstrate the impulse responses!

[@iain_explains]

Thanks. I'm glad you liked it.

[@yourpersonaldatadealer2239]

Interesting analogy, reminds me of an audio compressor that’s saturated to the point of attack and delay being constant. I just found your channel and it covers everything I did at uni. Feel like a refresher now though so may work through your content.

[@iain_explains]

Thanks for your comment. It's great to hear that the content is helpful.

[@ivanchen3141]

This is amazing! I almost gave up on my course until I see your videos. The explanations are so good!

[@iain_explains]

I'm really glad I could help! It's great to hear that you haven't dropped the topic/course.

[@synapticmemoryseepage4447]

Excellent, thank you!

[@iain_explains]

I'm glad you liked it.

[@pratiraj1]

Great intuitive explanation prof. Ian collings. You are not only helping us understand different concepts effectively but also igniting a desire to observe things happening around us and apply our knowledge to understand them better 😊

[@iain_explains]

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

[@foxnevertelllies77]

Wonderful,Simple and Excellent explanation of convolution. Thank you Professor....

[@iain_explains]

Glad you liked it!

[@adastra123]

You sir deserve a standing ovation. Brilliant. Thank you.

[@iain_explains]

Thanks so much. I'm glad you liked the video. If you haven't done it already, you might like to check out my webpage. It's got a categorised listing of all the videos on the channel, as well as summary sheets you can download. I've got lots more videos that I'm sure will help with understanding convolution, including some worked examples. iaincollings.com

[@adastra123]

@@iain_explains I did already. The radar one is brilliant 👏 too.

[@iain_explains]

Great.

[@closh1938]

i´m studying biomedical engineering in spain and your videos are helping me a lot, I hate just making the exercises your explication give me the intuition required for the subjects of signals and randomness to be fun, thank u very much, keep the work!!!

[@iain_explains]

That's great to hear. I'm glad the videos are helpful.

[@fifaham]

Very good analogy - thank you for your time and effort in creating those wonderful videos. I think 14K like in 1 year for this video is little, it should be 1 million. I took 5 courses on signals and systems back in late 80s and I got straight A, I do refresh and review to keep information fresh in my head. I love this subject a lot.

[@iain_explains]

Thanks so much for your nice comment. I'm glad you like the explanation in this video. I've been thinking about the best real-world explanation for the convolution equation for more than 20 years. Even though convolution occurs in every single linear time invariant system on the planet, none of the other real-world examples/analogies used to explain the equation "out there in other videos" are accurate - mostly they are not even convolution at all! I wish this video was being seen by 1 million people, like you say - I'm sure it would help them (I've been teaching this unit for over 20 years, and I know this topic is one that confuses a lot of people).

[@ashleyy.973]

The world ist so beautiful because of people like you. Your presentations many topics open another clearance and perspektive to learn and to undertand. Its far important and intersting to understand instead of just learning. Greeting from germany. Jing

[@iain_explains]

Thanks for your nice comment. And Hello from the other side of the world.

[@chengshen7833]

Really a brilliant and novel illustration about convolution! I'm from UNSW but really find the content of this channel much more helpful than EET's 2nd year course on signal and systems😅

[@iain_explains]

I'm really glad you're finding my channel helpful. It's great to hear.

[@ivanrodionov9724]

Wow! This is by far the best and most intuitive explanation of how convolution works with an LTI system! I knew the formulas for a descrete and the continuous case, but only now did it really click in my head how one comes from one formula to the next! I quite like the format of this video, showing how convolution can be tangibly grasped in the real world without resorting to excess formalism and keeping the video very much alive. Please keep up the amazing work sir and greetings from Germany!

[@iain_explains]

Thanks for your comment. I'm glad the video was helpful! I was in Germany at the start of 2020 just before Covid hit. I'm looking forward to the time when travel is freed up again. It would be great to visit again.

[@ivanrodionov9724]

@@iain_explains Ah yes the start of 2020 was quite the circus here in Germany. What part of Germany were you in if I may ask? If you are interrested, I would love to give you a tour of the TUM Campuses, labs and the Groundstation of the TUM sattelite fleet where I am working, if you happen to be going to Munich.

[@iain_explains]

Yes I was in Munich, as well as Berlin, Frankfurt, and around the tourist spots in the south. It was a great trip. Thanks for the offer to visit TUM. Not sure when I might be back in the region, but if I am, I'll get in touch.

[@user-ud6oh8ku7o]

wonderful explanation, love the nature background too. Thank you,

[@iain_explains]

I'm so glad to hear that the video helped.

[@larshoernle5400]

thanks the 3 videos in combination really give you an understanding of the topic

[@iain_explains]

Glad to hear that!

[@HarpreetSingh-ke2zk]

Salute to your dedication in putting a tough concept into practical terms. Unless the term "convolution" is used repeatedly without a nonmathematical explanation.

[@iain_explains]

Glad you like it.

[@MGTOW-nn9ls]

That was brilliant Sir. Thank you for sharing your knowledge

[@iain_explains]

I'm so glad you liked it.

[@ochimoto2151]

This helps a lot! Thank you so much!

[@iain_explains]

Glad it helped!

[@user-bx7xh3wy1b]

wonderful explanation! great, thanks Dr

[@iain_explains]

Glad it was helpful!

[@speedbird7587]

Hello professor, Actually you gave me a very good insight about convolution . The first term in the integral is the input impulse signal, and the second term involving t-T is the system which is going to do some change to the input signal X(t). And since the impulse is a continuous signal, the output is also continuous, and this implies the definition of the convolution integral! Just like a block diagram for PID controls! Thank you very much!

[@iain_explains]

I'm glad the video helped you to visualise the convolution operation.

[@rakeshpillai2919]

Thank you!

[@pritamroy3766]

Its what just I wanted so badly for so long... The best analogy, best mathematically enriched explaination, thatnk you Sir...

[@iain_explains]

I'm so glad you liked the video and found it helpful.

[@fotiskougionas3093]

Very Good explanation. I’m going through my signals and systems course for my electrical and electronic engineering degree and your videos have helped me a lot.

[@iain_explains]

Glad the videos have been helpful!

[@amazighkhermane-rz1mw]

Just perfect. THANK YOU

[@iain_explains]

I'm glad you liked it.

[@lounesbenali4889]

That was an awesome explanation, Thank you !

[@iain_explains]

Glad it was helpful!

[@cledieu]

The 2 pillars of pedagogy : repetition and reformulation ! Very helpful, Thank you Sir.

[@iain_explains]

Glad it was helpful! And I'm glad you like the approach and the examples.

[@user-bv1un9wk6n]

Amazing Explanation Sir.

[@iain_explains]

Thanks. I'm glad you liked it.

[@amirhoosinabbassi7533]

I have a signal and system exam tomorrow and I learned a lot through this video even though it was more helpful than my professor's explanation itself thanks

[@iain_explains]

Glad it helped!

[@indiaball5392]

Wow! I loved that explanation Brother!

[@iain_explains]

Glad you liked it!

[@tyroleanivan]

Just outstanding!

[@iain_explains]

Thanks. I'm glad you liked it.

[@DJ-yj1vg]

Pretty good analogy with the boards of width delta t. Good explanation.

[@iain_explains]

Glad it was helpful!

[@richardbrown2290]

great video. Thanks that helps explain convolution in a real world way. Thanks again.

[@iain_explains]

Glad it was helpful!

[@lawrencecohen1619]

This is the best explanation of convolution I have heard to date. As a life-long cyclist, I only wish I had heard the bicycle spoke analogy as a EE undergrad over 45 years ago.

[@iain_explains]

I'm so glad you like it. I've been using the shock absorber as an example for impulse responses in my teaching for about 20 years, but it was literally only as I was riding over the wooden board-way that I had the idea of linking it together with convolution. I've never been happy with anyone's so-called "intuitive" explanations of convolution before, but I'm proud to say I really feel I've cracked it with this one. I'm glad you agree.

[@Gate-zj4rx]

Best Imaginable way of understanding convolution in REAL LIFE. Thank you sir👍

[@iain_explains]

I'm so glad you found it helpful.

[@user-sv1ry7xi7t]

❤❤❤❤ Wow, lucky are those who have you as their teacher ❤ Much love and huge respect professor❤

[@iain_explains]

Thanks so much for your nice comment. I'm glad you liked the video.

[@wuzhai2009]

Good work, keep it up! I like this analogy. Analogies are like scaffolds that help students when they are building up their knowledge in a new area.

[@iain_explains]

I'm glad you liked it.

[@agustinlawtaro]

It's great ! A great explanation, thanks.

[@iain_explains]

I'm glad you liked it.

[@dees900]

lovely explanation. thank u very much

[@iain_explains]

Glad you liked it

[@melleniumster]

Thanks a lot Professor. Now I understood what the convolution actually is! Very intuitive explanation.

[@iain_explains]

Glad you liked it.

[@nanjiang4158]

This is brilliant!

[@iain_explains]

Thanks. I'm glad you liked it.

[@happyhayot]

Brilliant explanation

[@iain_explains]

Glad you liked it

[@gus_siles]

Many thanks.. very good example for teaching in class!!

[@iain_explains]

Glad you liked it

[@ritesha8050]

wow, great explanation, thanks a lot sir.

[@iain_explains]

You are most welcome

[@benimadimeva]

that was a perfect explanation thank you hocam

[@iain_explains]

Glad it was helpful!

[@fellag87]

Amazing explanation, thank you

[@iain_explains]

Glad you liked it

[@imlee67]

숲속 자전거 타기 그리고 convolution 당신의 열정에 👏 👏 👏 👏 보냅니다. 감사합니다

[@iain_explains]

Glad you liked the video.

[@BICIeCOMPUTERconGabriele]

Great bike!

[@sheshankjoshi]

Thank you so much for that.

[@iain_explains]

You're welcome. I'm glad you liked it.

[@serrafayaz]

This is the best explanation ❤❤❤ thanks

[@iain_explains]

Glad it was helpful!

[@irrationalpie3143]

Great video!

[@iain_explains]

Glad you enjoyed it

[@issacquantum]

THANK YOU!!

[@iain_explains]

You're welcome! I'm glad you liked it.

[@edmundkemper1625]

MY God!, an incredible , daresay revolutionary explanation of convolution , i will say !!! Kudos to you, Professor! Can you do a similar type of demonstration for Correlation as well and differentiate it practically with Convolution ? That would be so Good!

[@iain_explains]

Hopefully this video will answer your question: "How are Correlation and Convolution Related in Digital Communications?" kzbin.info/www/bejne/jZaYomh8f8iVmbc

[@sudiptamandal1518]

What an explanation 😍!!!!!!! Wish I could get you as my college prof. In India most of Electronics students find signals and system boring as we are not taught this way....

[@iain_explains]

Thanks, I'm glad you liked the video. I always think that examples are so important to help make maths accessible and interesting. Have you seen my other recent video discussing examples of the Fourier Transform? kzbin.info/www/bejne/jKXFg5iietOgqZo

[@quick_gaming250]

Best explanation ❤

[@iain_explains]

Glad you liked it

[@Megabyte403]

Thanks sir so much for clearing my doubt ❤❤

[@iain_explains]

I'm glad it helped.

[@edmondscott7444]

Like comparing power factor to horse towing a barge on a canal. I hope some people now understand convolution. If you do well done.

[@amanuelnigatu4621]

this is what i am looking for tnx sir!!!!!

[@iain_explains]

Glad I could help

[@artha3283]

Neither Google nor my college teachers could explain it in this intuitive way Up till now I was only memorising the formula and using it thinking of it as just the" Sum of products" operation but now i see the significance of it!!! Best explaination!!!! Thankyou so much Sir!!👍👍

[@iain_explains]

I'm so glad it helped. It's a topic that confuses a lot of people, and I'm glad this explanation seems to really help.

[@thaddeogarcia4608]

thanks a lot!!!!!!!!

[@iain_explains]

You're welcome!

[@monicabn3067]

It’s very inspiring ❤😊

[@iain_explains]

That's great to hear!

[@lebohangmonyai4341]

You are Gold my good sir

[@iain_explains]

Glad the video helped.

[@prasanth5264]

It was really amazing I wish professors like u to work India , but it selfishness professors like u should continue in digital media because many people will benefit from entire world , lots of love from India

[@iain_explains]

Thanks. I'm glad you like the videos.

[@HH-hk7nt]

This is beautiful

[@iain_explains]

Thanks. I'm glad you liked it.

[@mohchafik1752]

Brillant,intelegent smart man.

[@iain_explains]

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

[@hyggeligt007]

Just so that I understood the intuition with the example of cycling over the boardwalk with 'N' number of planks, the convolution is simply the sum of 'N' different delayed impulse responses. Here, the delay is related to the position of the plank and each impulse response is the behaviour/displacement of the shock absorber when cycling over any given plank. Is this correct? Really appreciate the effort and thought put into your channel. Tremendously helpful.

[@iain_explains]

Yes, you got it. And in the limit, when the "planks" are infinitely close together, then we move from a "discrete time" analogy to a "continuous time" analogy, and the "sum" becomes an "integral".

[@Gfdhj123-5df]

Thank you.

[@iain_explains]

You're welcome!

[@alpargur]

A very catchy and entertaining analogy. Once again a great example! Convolution concept is very clear to me but somehow i cannot build a strong connection of convolution and convolution neural networks (CNN). Could you give a brief explanation or make a video on that one too? Cheers

[@iain_explains]

Thanks for the suggestion. I'll add it to my "to do" list.

[@ahmedsherif843]

Thank you

[@iain_explains]

You're welcome

[@omarberraqui8193]

just wow thank u

[@iain_explains]

I'm glad you liked it.

[@FinalDestinationAllah]

Great❤

[@iain_explains]

Glad you liked it.

[@mehdiheidari9142]

wow very nice! one thing i still missing is how we describe our signal as series of impulses, imagine at a point signal value is 3, impulse value in every point is goes to infinite.

[@iain_explains]

To understand the answer, you might ask yourself what does it mean to say "a point signal value is 3"? More specifically, what is the value of a "point"? How narrow is the point? Is it infinitesimally narrow? And what are the units of the value "3" that you mention? In real life, nothing happens "instantly". Everything happens over a period of time (even if it is a very short period of time).

[@haritmohansaxena732]

Nailed it

[@iain_explains]

Glad you liked it.

[@kpk331]

Very good explanation. A word about energy storage and resulting lag and Lead would have been even more helpful... Impulse and trapped/stored energy (i.e, initial conditions) works in the same manner, is it not?

[@iain_explains]

Thanks for the suggestions. I'll add them to my "to do" list.

[@charlesgeorge85]

awsome

[@iain_explains]

Glad you liked it.

[@alfderbabybenz7092]

thats a really nice bike!

[@iain_explains]

Yes, it's perfect for the trails around where I live. kzbin.info/www/bejne/jKXFg5iietOgqZo

[@zhaobryan4441]

Hi Prof, could you please explain the impulse response at time T is h(t-T),shouldn't this be h(t+T)

[@iain_explains]

This video should help: "Shifting Functions" kzbin.info/www/bejne/o4HSZ3-hlq5-d7s

[@johnangelo2000]

Hi Ian, requesting again...Can you give intuitive explanation of DC NULL.....??

[@iain_explains]

According to DC Comics, Null is a meta-human enemy of Hawkman who can manipulate gravity, he is also one of Netherworld inhabitants. ... I guess that's not the DC Null you are talking about, though. I've got it on my "to do" list, but it's a long list sorry. Also, it's more of an "electronics" question, so I'm not totally familiar with it. Basically, my understanding is that it has to do with problems that come from DC power transfer in RF circuits causing inefficiencies and other undesirable phenomena, so there are advantages to making sure there is no DC component.

[@user-dp3xy3ki5u]

This is incredible, so engineer and so cyclist!!

[@iain_explains]

I'm so glad you like the video.

[@faridjafari1710]

[@iain_explains]

Glad you like it!

[@SchubertConsulting]

Very intuitive explanation. I doubt, however, whether the different pulses are really independent. In my view this point had to be discussed at least. Maybe you Implicity assume a linearity which is only a limiting case where you do not consider jumping etc.

[@iain_explains]

Sorry, but I'm not sure what you're trying to say here. In particular, what you mean by "really independent". The "pulses" are orthogonal to each other. They occur at different times, and do not overlap. The integral (over time) of delta(t-tau1) times delta(t-tau2) equals zero. Also, in terms of linearity, the convolution equation only applies to linear systems. I didn't make a big point of this in the video because the purpose of this video is to provide an intuitive understanding of convolution - not to provide a definition with full conditions/assumptions.

[@SchubertConsulting]

@@iain_explains Just for my background. I come from microwave sensorics and are well familiar with linearity in differential equations www.stereoscopicscanning.de/MIOP/MIOP95.pdf. First I watched kzbin.info/www/bejne/gaa7m6p4abGtiaM, in some sense, I could not follow, your video is much more intuitive. If the wheels are jumping then the system is no longer linear. If you have a big stone that makes the bike jump over the next rock, this second impulse is lost. I think the problem here is, when you have a spectator of the video who already well knows physics they will get distracted by these secondary effects. In a real-world situation, the wheels will jump from time to time and the tyre will get compressed completely occasionally, so the real-world situation is not linear. So, for understanding convolution, I must abstract from the real-world situation. Maybe the system can be considered linear for all sufficiently low speeds. If you add a phrase like: we will not consider situations where the wheels are jumping then also those already a little bit more familiar with the concept will not get lost. - Good continuation and thank you again for your excellent work.

[@iain_explains]

OK sure. But I've been thinking about "real world" examples that demonstrate convolution, for more than 20 years, and this is the best one I've come up with. All other "examples" I've ever seen/heard are _way_ off being linear, or even being "convolution" (apart from the noise a machine gun makes - but I'd prefer to avoid using weapons in my videos). If you can suggest a better real world example, which illustrates the "impulse response", then I''m keen to hear about it. The main problem is that "impulses" and "impulse responses" are not real - they are simply a mathematical tool to model what's really going on.

[@iain_explains]

Anyway, at 0:22 I say "we're going to think about the suspension fork of my bike as being the system". In other words, the frame of the bike is explicitly _not_ part of the system, and is implicitly assumed to remain in a constant state (ie. the frame of the bike does not go up and down - only the forks compress). So I was ruling out jumping in the air. Also at 0:59 I explicitly said "and if the suspension forks are a linear system ...", so again, I think I did set out all the assumptions. .... Anyway, thanks for your comment. I'm glad you found the example interesting.

[@JazzInATinCan]

This made so much sense when you were not brought up in a mathematical environment.

[@iain_explains]

I'm glad it helped.

[@the_hasnat]

"Was out on my bike ride this morning, and I was thinking about convolution"

[@iain_explains]

... doesn't everyone? 🤣

[@zyctc000]

This is brilliant! Another analogy: I have a linear pain response when slapped, which is H. My father always slap me when I fail in math exams which is the input X. One time I messed up so bad that my dad decided to slap me continuously all day. So my pain level at any given moment t during that day is the convolution of (X*H )(t) !😂

[@edmundkemper1625]

Kindly correct me if iam wrong Professor. So convolution is an entirely different way of representing input-output relationship. Like every input function in the world, just differently affects the magnitude of impulse response and gives rise to tadaa😂 the output of a system . Am i Right?

[@iain_explains]

I'm not sure I understand what you mean when you say "an entirely different way". Convolution is _the_ way of representing the output signal in terms of the input signal for linear time invariant (LTI) systems.

[@edmundkemper1625]

​@@iain_explains I meant it in a more abstract mathematical way Professor. Let me try to elucidate what i mean , generally when we try to represent the relation between 2 things, there are so many ways, some of them being functional representation, set to set mapping, system/operator representation etc and convolution was one of those different ways of expressing relationship between two quantities( in this case the input and output function) . This is how i comprehended convolution to be .

[@iain_explains]

Sure. But it's not just about input and output relationships. Convolution also arises in other contexts, for example when adding two random variables, the resulting random variable has a probability density function that is the convolution of the two individual pdf's of the random variables being added. See this video which explains this more: "What is Convolution? And Two Examples where it arises" kzbin.info/www/bejne/jmPGe2usdshjg7c

[@edmundkemper1625]

@@iain_explains will check it out . Thanks !

[@adeddy8138]

Ohh shit I found this channel so late if i saw these videos a year earlier I would have got interest in my second year (ETC)and got 10 cgpa instead of 8 .

[@iain_explains]

Oh well, I'm glad you've found the channel now, and that you think the videos are interesting.

[@emanueleziglioli499]

I've heard there's a periodicity of cicada seasons, some years they don't come out

[@iain_explains]

I'm not sure about that - maybe. They seem to be a constant part of summer in Sydney.

[@suvetar]

Thank you Iain!! Where were you when I was studying!! 😀I do believe Einstein really hit the nail on the head; If you can't explain it simply, you don't understand it ... Well, I don't truly believe it applies in *every* case, but 99% of the time! If it's not a truism, it should be ... Thanks again!

[@iain_explains]

Yes, I fully agree! I'm glad you like the video.

[@ankurakansh]

explained like god

[@ankurakansh]

love u

[@iain_explains]

I'm so glad you found the explanation helpful.

[@ankurakansh]

grateful sir you made me realize what is impulse atleast watching again to get the full juice @@iain_explains

[@pavansharmajanapati9687]

👌❤❤

[@johndunn5272]

This is the theory side of EEVblog