This is the best explanation on wavelet transform I could find on RU-vid, this is exactly what I needed, can't thank you enough for making this! Saved my day!
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!
Thank you! You did a great job. Very interesting and very clear presentation. Not touching much detailes - but really provides ground for understanding!
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.
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.
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.
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
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.
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!
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.
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!
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 : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-p2Gvtp4JoI0.html If you keep this approximation space, but you also keep the first detail space, you get this : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-g4sdrMOC4XI.html With two detail spaces you get this : ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Sw88-rP1qEU.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
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.
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 👍
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.
@@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!
@@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
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 😛
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.
@@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...
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!
@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
Thank you very much it means a lot! 🤗 You can find a similar version here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ruhbme9zobE.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
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
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?
@@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.🤔
@@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?
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.
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.
