An introduction to the wavelet transform (and how to draw with them!)

Рет қаралды 32,726

Күн бұрын

The wavelet transform allows to change our point of view on a signal. The important information is condensed in a smaller space, allowing to easily compress or filter the signal.
A lot of approximations are made in this video, like a lot of missing √2 factors. This choice was made to keep things as simple as possible.
You may also notice some oral mistakes, like saying transformation instead transform for example. And sorry for the English pronunciation, it's not my native language! ;)
The drawings presented at the end of the video were realized in the context of a scholar project (INSA Toulouse/ENSEEIHT). Participants of the project were Ayoub Alkarim, Benjamin Drai, Sebastian Legrand and myself, under the supervision of Charles Dossal.
Link to the 3b1b video presented in the introduction about drawing with the Fourier transform: • But what is a Fourier ...
The complex wavelet coefficients are extracted from the paper "Complex Daubechies Wavelets" available at www.sciencedirect.com/science...
All animations have been realized using the python library ManimCE, a community-maintained fork of the Manim library developed by 3b1b.
docs.manim.community/en/stabl...
github.com/ManimCommunity/manim
This was my first video using Manim, any feedback would be appreciated!
All the code is available on GitHub: github.com/leleogere/manim-pr...
I composed the music specifically for this video.
This video is my entry to the 3b1b's SoME1 competition.

Пікірлер: 119

@abhishekmajumdar6523 2 жыл бұрын

This is the simplest yet detailed explanation of the wavelet transform that I've ever seen.

@leleogere 2 жыл бұрын

Thanks you very much!!

@marine_technology 17 күн бұрын

Both the wavelet transform and your introduction are elegant. Thanks for your introduction!

@supersnowva6717 Жыл бұрын

This is the best explanation on wavelet transform I could find on KZfaq, this is exactly what I needed, can't thank you enough for making this! Saved my day!

@duke0200 2 жыл бұрын

This was incredibly helpful for me to understanding wavelet functions when I couldn't understand them in my Master's class. Thank you so much!

@vohiepthanh9692 10 ай бұрын

You are a genius, thank you so much !!!

@aaryannakhat1842 2 жыл бұрын

You're an absolute legend! Top-quality visualization of a hard-to-grasp topic! Cheers mate.

@leleogere 2 жыл бұрын

Thanks a lot! 😁

@ALEX-zx6hz Жыл бұрын

This video helps me understand the DWT a lot. You're such a genious.

@db5511 2 жыл бұрын

Wow! Fantastic video! I was having a very difficult time understanding wavelet functions but the animations and the construction from average really helped me understand. Thanks!

@leleogere 2 жыл бұрын

Thanks for your comment!

@sergniko 2 жыл бұрын

Thank you! You did a great job. Very interesting and very clear presentation. Not touching much detailes - but really provides ground for understanding!

@Number_Cruncher 2 жыл бұрын

I like it as it is. Although I don't know anything about wavelets, but I could follow your analogy to the Fourier transform and the mean value transformation. Thanks a lot.

@leleogere 2 жыл бұрын

Thank you very much! 😁

@ps9195 23 күн бұрын

Concept is explained so clearly! Thank you

@valentinakaramazova1007 9 ай бұрын

I loved the math, the French accent, and the music! :D great video!

@agale652 Жыл бұрын

What an amazing demonstration! .. bravo🎉

@mrmastaofdesasta6994 2 жыл бұрын

That was actually very comprehensible, thank you! I would have loved to see more about more complex wavelets, if not a full explanation, at least a demonstration. I kind of missed an explanation how the wavelet function relates to the decomposition.

@meetuptoyosu4945 2 жыл бұрын

You are a hero. I was searching for this!!

@GauravDevdikar-if2xn Жыл бұрын

Absolutely amazing. Loved it.

@mayankthakur2158 Жыл бұрын

that video was insanely good!!! thank you. when you made the image at the end it blew my mind lol

@cakcinar 2 жыл бұрын

Hi Léo, thank you for voluntarily conveying the essence of your insight, it's invaluable. I'm sure it took a lot of time to prepare such an informative presentation. I look forward to seeing similar videos on your channel.

@brixomatic Жыл бұрын

This was a very cool and easy to understand explanation for the Haar Wavelet. Unfortunately I don't really get the jump to the Daubechies Wavelet. The scaling function and the wavelet functions are different, so far so good, and how they're added to get back the original signal seems trivial, but what was trivial in the haar-case, i.e. taking the mean and the diff and putting it to the scaling and wavelet space, completely escapes me for the Daubechies wavelet case. Also I would have loved to be walked through the complex plane, as you did walk us through the 1d case. I'm currently trying to bridge exactly this gap and did not fund a good tutorial yet. Anyway, thank you for this great explanation.

@leleogere Жыл бұрын

Thank you for your comment! Unfortunately, I haven't manipulated wavelets in a while so everything is not that clear in my mind! 😅 Basically, wavelets are represented by a certain set of coefficients, and mathematically speaking, using another wavelet is only using another set of coefficients. The coefficients of the Haar wavelet have a very nice geometrical interpretation which is storing the mean and the diff. However, other wavelets are less friendly, and visually animating the way they work is quite challenging. While I do think it is possible, I don't know any video that would get into visual constructions. I did not have the time to get into details about the Daubechies wavelet as animating only the Haar wavelet was already a quite long process as I'm not really familiar with animation! If by chance you come across such a video in the future, don't hesitate to post it here, I would be very interested in their approach to explain this topic!

@pradiptahafid 2 жыл бұрын

Monsieur, thank you very much for the video. I have spent weeks to understand about wavelet transformation but with this visualization, i can get the clear picture on the relationship between the number and the graph.

@vinaykumartheyoutuber5386 Жыл бұрын

kzfaq.info/sun/PLOUHOQsIOpRF43dwJzVEeoFdEOlf7-fWW

@heyasmusic7553 Жыл бұрын

I Love this video. This is by far the best explanation about wavelets I've seen. I hope to see more videos from you in the future.

@leleogere Жыл бұрын

Unfortunately, I do not have the time to make more videos... This one took already took me way too much time 😅

@jeunjetta Жыл бұрын

Nice work! Really. Good practical way of explaining. Thanks for sharing your code. ..It might help me to get started with manim as well. Cool that you composed your own music 😛

@7898xd 2 жыл бұрын

Wow that's an extremely good first try at doing a math video!

@zbqmaktmxj 2 жыл бұрын

Thank you for making such a great lecture!!

@ekm507 2 жыл бұрын

Great video Thanks. I learnt a lot

@mikaelairene4427 2 жыл бұрын

An excellent explanation of the discrete wavelet transform. I wish the music weren't as distracting, but it wasn't that bad.

@mariannatsapali 4 ай бұрын

The best difficult math concept video I've ever seen!

@HermanWillems 2 ай бұрын

Hope you do more of these video's they are amazing. :)

@mauriciovinco6143 2 жыл бұрын

Wow, that was very helpful. Before I never quite understood why wavelets the way they are, the construction from average was quite illuminating. Seeing how wavelet compression would have distorted the picture of sigma vs how Fourier did it would have been superb!

@leleogere 2 жыл бұрын

Thank you for your comment it means a lot! The simplest compression you can imagine is to simply cut off details spaces and set the value of all coefficients to zero. You are only left with the biggest approximation space : kzfaq.info/get/bejne/pph3qdehmbDTeWQ.html If you keep this approximation space, but you also keep the first detail space, you get this : kzfaq.info/get/bejne/nZqjl9V-tKmYiH0.html With two detail spaces you get this : kzfaq.info/get/bejne/id1oa5CjtZfVdYk.html And so on. Each additionnal detail space will add details to the reconstitution. However, the "partial" reconstitutions are a bit less satisfying to watch than the Fourier ones, as the basis functions are way less regular than the circles we can observe in the Fourier Transform. So the traced path is kind of chaotic

@xiaomingyuan9636 Жыл бұрын

This video help me have a better understanding for wavelet, thank you.

@ardavalilable 2 жыл бұрын

You're awesome, thank you for this beautiful and very informative video!

@user-id5fg1oc8o 2 жыл бұрын

Unbelievable video. You saved me.

@23lkjdfjsdlfj Жыл бұрын

Fantastic! Thank you for making this video.

@AttiDavidson 2 жыл бұрын

Thank you very much! Super nice video!

@yk-il6dn 7 ай бұрын

Great video! Was lost in the sea of equations until I stumbled upon this video

@guohaozz4715 2 жыл бұрын

A really good introduction. It really brought me new views about mathematics. Thanks a lot

@leleogere 2 жыл бұрын

Thank you!

@JorgeDiaz-ej3bn 2 жыл бұрын

loved this video, thank you!

@guitarraenllamas 2 жыл бұрын

This is great, thank you!

@saeedmirzaee8315 2 жыл бұрын

Thank you sir,keep going powerfully

@leleogere 2 жыл бұрын

Thanks!

@lcfrod 3 ай бұрын

Fantastic!!. Thanks much for sharing.

@momoi5512 8 ай бұрын

Awesome video! Thank you a lot!

@user-wp7et8wt6u 2 жыл бұрын

amazing video, thanks！！！

@leleogere 2 жыл бұрын

Thank you!

@teeg-wendezougmore6663 2 жыл бұрын

great video!

@leleogere 2 жыл бұрын

Thanks!

@carlosayam 2 жыл бұрын

Great video. Note that the approximation to the drawing is _much_ better with wavelets than with circles (harmonics). This is also an interesting property of wavelets 👍

@leleogere 2 жыл бұрын

Thank you very much! Actually it will depend on how you sample points along the shape, and on how many coefficients you use to draw it. If you use as many coefficients as the number of points, then both methods would result in the points being exactly drawn (so same precision). If you use less coefficients than the number of points, then depending on which coefficients you decide to thrown away, you will get differents approximations for the two methods. If the last animation was that precise, it was because I used a lot of coefficients (maybe even all of them, I can't remember), and I probably used less of them on the harmonic representation. The idea of the video was more about presenting another approach for drawing shapes in a similar way as the harmonic method, but I did not really compared them in terms of approximation quality.

@carlosayam 2 жыл бұрын

@@leleogere , I see. The theory says that for the same amount of points and in certain function spaces [like the shape you draw], wavelets have better approximation properties. Anyway, the first time I've seen someone drawing one of these shapes using wavelets instead of harmonics - super cool!

@leleogere 2 жыл бұрын

@@carlosayam Yeah you're right, while the Fourier transform is well suited for regular and smooth shapes, the wavelet transform will perform better with less regular shapes, and even discontinuous signals. And about the drawings I have never seen them elsewhere neither. They were realised on the context of a school project, even our professor wasn't sure if we would be able to get something in the end

@vinsternadeen9461 Жыл бұрын

Really good one. Thank you so much.

@mariapaulamartinezhuertas3107 Жыл бұрын

Maravilloso video. Muchas gracias, saludos desde Colombia.

@CppExpedition Жыл бұрын

WOWWOOWOWOWW 🤯🤯🤯🤯🤯🤯🤯🤯 Love your explanation!

@mirabirhossain1842 Жыл бұрын

Thank you very much. It may sound really pathetic, but I was trying to know what is wavelet transform since December 2021. I am not good at studying from complicated resources. So I couldn't understand most of the things that I read in books, lecture notes and other resources. It is February 2023 and I finally got what wavelet transform is doing basically. I have wasted more than 1 year. I wish I watched this earlier. Thank you.

@impossiblemission4ce Жыл бұрын

Amazingly helpful.

@utkarshgupta6134 Ай бұрын

incredible video ! mind blown!

@tanvir_ahmed 2 жыл бұрын

Amazing video!

@SEOTADEO 2 жыл бұрын

Thanks! That helped me a lot!

@ArifHussain-fs5jz 2 жыл бұрын

just amazing

@chriskiwi9833 Жыл бұрын

Excellent!

@aman.chandra 2 жыл бұрын

great video, thank you!

@vinaykumartheyoutuber5386 Жыл бұрын

kzfaq.info/sun/PLOUHOQsIOpRF43dwJzVEeoFdEOlf7-fWW Subscribe for full series on wavelet transform

@nipunvashistha6352 2 жыл бұрын

Thank you very much!

@olivercort9189 5 ай бұрын

Great explanation!

@rifdahrofifahz3877 Жыл бұрын

good explanation. could u help me to find out the manual calulation of Daubechies 6 scle 2 ?

@DiamondSane Жыл бұрын

Thanks man. An interesting report

@vinaykumartheyoutuber5386 Жыл бұрын

kzfaq.info/sun/PLOUHOQsIOpRF43dwJzVEeoFdEOlf7-fWW SUBSCRIBE THIS CHANNEL FOR WAVELET TRANSFORM FULL SERIES

@Malvici. 2 жыл бұрын

Thank You!

@AZ-hj8ym Жыл бұрын

great video！

@INNoMATHsforyou Жыл бұрын

why so less subs? you are so intelligent.

@leleogere Жыл бұрын

Probably because I haven't posted a single video ever since 😂

@INNoMATHsforyou Жыл бұрын

@@leleogere You should upload more. It helps people like me. Thank you for the efforts you are making.

@leleogere Жыл бұрын

@@INNoMATHsforyou maybe one day, but probably not soon. I spent uncountable hours on this video, and do not have any time to prepare another video for now unfortunately...

@jpopelish 7 ай бұрын

I look forward to your tutorial on choosing the best wavelet basis function for a given task, if that makes sense. I am not too clear on the terminology.

@user-kz9gm2kb9k Жыл бұрын

This is brilliant

@Raf4le Жыл бұрын

excellent video

@andytroo Жыл бұрын

whats the differences between the two different plots - would be great ot see the E from the two different transforms.

@swartzsteinswartzstein8809 2 жыл бұрын

@Léo Géré Wow! The music you composed for this video is really nice! I came to learn about Wavelets and I had to pause to video to ask you: Can you upload a music only version of this music you wrote? Or can you let me have a link to the file of the song? It's really nice I like it alot. Please upload please upload

@leleogere 2 жыл бұрын

Thank you very much it means a lot! 🤗 You can find a similar version here: kzfaq.info/get/bejne/qNuYldCWnuDTknk.html (it is way shorter and a bit different, but it is the same chords progression and the same style). If you prefer the long version in this video, let me know and I'll post it! You can also find a lot of short pieces here if you like that one: instagram.com/le_opiano

@swartzsteinswartzstein8809 2 жыл бұрын

@@leleogere Can you upload the long version? Thanks!

@romajimamulo 2 жыл бұрын

Am judging, would have loved if you started by what is a wavelet first, and focused on producing any wave instead of any drawing because it starts off really clunky

@leleogere 2 жыл бұрын

Yeah I realized that when the editing was finished, but it was too late to record and animate a new intro... Thanks for the feedback!

@periklisdrakousis6537 2 жыл бұрын

Wonderful video. I have a question although. What will I do if my starting points are 6 and not 8

@leleogere 2 жыл бұрын

First option is to compute a less deep transform. Second option is to "complete" your signal to obtain a length of a power of 2. You can do so by completing by periodicity if your signal is periodic, or by mirroring the end of the signal, or by padding with zeros or with the last value of the signal

@vikassingh5628 6 ай бұрын

awesome

@julius4858 2 жыл бұрын

Thanks for this video. Way too little views for the effort you put in. Well done!

@vinaykumartheyoutuber5386 Жыл бұрын

kzfaq.info/sun/PLOUHOQsIOpRF43dwJzVEeoFdEOlf7-fWW Subscribe for wavelet transform

@jasonbourne8628 3 ай бұрын

well made

@neggaznabil7570 9 ай бұрын

Good explanation. There is the possibility to share the PowerPoint presentation

@leleogere 9 ай бұрын

Thank you! The different parts of the video are generated using the python library Manim (code in description), and then assembled in a classic video editor, so no PowerPoint presentation sorry!

@sikriatno361 Жыл бұрын

Hi, thanks for the great explanation. But I want to ask, in the Haar Transformation is it divided by 2 or √2 ? Some references say it is divided by √2

@leleogere Жыл бұрын

Thank you! What are you talking about that is divised by 2?

@craighalpin1917 Жыл бұрын

So how are you able to go from the simple form (where your average space is one) to the more complex space (where your wave is complex) Do you just use integration to find the average?

@leleogere Жыл бұрын

I'm not sure to really understand what you mean 😅

@craighalpin1917 Жыл бұрын

@@leleogereI guess in simple terms I understand the first part where the approximation space is one and you scale it accordingly but when you go from simple functions to the more complex functions is where it becomes a bit confusing. Maybe it has to do with the question to where and how those complex functions come from. I can see how you take the average and difference in the first part and it gives you an appointment space but on the second part you have this appointment space which seems as if it has nothing to do with your original points. I'll watch it a few more times to see if I can put it together.🤔

@leleogere Жыл бұрын

@@craighalpin1917 when you talk about compex functions, you mean functions with values in the complex plane (imaginary numbers, like 3+2i), or juste more "complicated"/less simple functions?

@matthewpublikum3114 Жыл бұрын

There might be more to say, but how it is said is important too

@hemantsharma2751 2 жыл бұрын

how to find decomposition with a filter ??

@vinaykumartheyoutuber5386 Жыл бұрын

kzfaq.info/sun/PLOUHOQsIOpRF43dwJzVEeoFdEOlf7-fWW SUBSCRIBE THIS CHANNEL FOR FULL WAVELET SERIEA

@tobiasjennerjahn8659 Жыл бұрын

Hi, I see that you've removed the github repository for the animation code. Would you be willing to make it public again? I'd love to take a look at it.

@leleogere Жыл бұрын

Woops my bad! Completely forgotten to mark it back as public. It should be fixed now!

@tobiasjennerjahn8659 Жыл бұрын

@@leleogere Awesome, thank you!

@ruthhuijgens 2 ай бұрын

nice video, cute accent :) I think it would be better though if you could lower the volume of the background music compared to the volume of your voice, because I find it hard to hear what you are saying at times.