As an engineer, I can only regret I was born a bit too soon... how lucky of those who are learning thest things with amazing videos like this!

@luc7478

Жыл бұрын

I feel the same

@samurboi8007

Жыл бұрын

i feel like I was born too late, thats so much to learn even if i learn so much id still be behind 😭

@van4387

Жыл бұрын

I regret I started to appreciate maths too late

@mohdazminishak6387

11 ай бұрын

😂 even worse for that Fourier guy

@TheBigJohny

11 ай бұрын

bullshit. as an engineer you have had a lot of money to spare in order to buy cheap bitcoin. meanwhile those of those of us born later had shit and were not able to profit

This is the best discussion of wavelets I Have seen. Your graphics are in the best tradition of 3B1B. More please.

@Fred-mv8fx

Жыл бұрын

I agree. My masters-level classes covering Fourier and wavelet transforms were some of the only classes I ever really struggled with and resorted to rote in order to pass. I wish I had these videos to watch in concurrence with those classes. I remember almost nothing from them because I had no intuition about the subjects I was learning. This explanation is so simple and intuitive I actually want to revisit the subject and see what I missed by using a purely mathematical approach without a deeper understanding.

@user-xb7hk2yb8p

Жыл бұрын

@@Fred-mv8fx 2

@ChristianHohlfeld

Жыл бұрын

so true!

@moeal5110

Жыл бұрын

Now imagine him and 3b1b and vsauce work together on a topic

Man please don’t ever stop making these videos, they are extremely well done and edited and very entertaining while magnificently informative for such complex topics!!!

@romanscerbak5167

Жыл бұрын

god, someone watches videos from terror*ssians in late 2022 and likes it

@superlambmilkshake4904

Жыл бұрын

@@romanscerbak5167 what are you even trying to say?

@none5260

Жыл бұрын

@@romanscerbak5167 I don't see any terrorist here, only a scientist. Just go cry anywhere else.

This is like a third of a semester of intro to signals processing in computer science curriculum, packed into one half-hour video, and I actually understood more from it now than I did from lectures. Huge thanks for doing this! For those who wonder whether to watch: notable things include good mental models for complex numbers, Fourier transform, convolution and its relationship with vector dot product and functions as infinite-dimensional vectors, with an unexpected cameo from Heisenberg's uncertainty principle. This video is gold.

I can't imagine the amount of work that has gone into this masterpiece of a science yt video❤️🔥 Thank you very much, more content like this is needed😍!

@ArtemKirsanov

Жыл бұрын

Thank you! ❤️

@leif1075

Жыл бұрын

@@ArtemKirsanov Thanks for sharing Artem. I really hope you can respond to my other comment when you can. Thanks very much.

@leif1075

Жыл бұрын

@@ArtemKirsanov Hey Artem I hope you can respond when when question about the frequency values when you get a chance. I would appreciate it.. Thanks very much.

This video literally blown my mind about wavelets. There're been several weeks of works studying wavelets (in the discrete domain) for the work of my thesis. So far, more or less I have all the concepts explained in the video clear, but the amazing graphic representation of the signals and wavelets in the video, and also of the entire process of wavelet analysis almost filled all my remaining gaps! This video is incredible to understand wavelets!

@DannyOvox3

Жыл бұрын

What is your major?

@samuelequinzi3153

Жыл бұрын

@@DannyOvox3 I got master's degree in Computer Science at Roma Tre University; we're using wevelets to analyse BGP anomalous traffic

@DannyOvox3

Жыл бұрын

@@samuelequinzi3153 Oh wow, I am going for a CS degree. I know is a masters level where you are at but these topics seem alien to me, I thought this was related more to electrical engineering.

@Grateful.For.Everything

Жыл бұрын

@@DannyOvox3 this goes far deeper. As you drill down through the sciences in search of core truths, You will find that it all leads You to this, the Key to understanding this existence.

@THeMin1000

Жыл бұрын

@@DannyOvox3 You'll be surprised how much math is there in CS. CS is not the exact same as software engineering.

The subject is highly interesting. On top of that your video is amazing with all details. The music is very quiet but "opens" the space, the subtle effects on "static" graphs that make them dynamic, the not-so-subtle but entertaining and functional use of sound effects and the use of special effects in manim make this very nice to watch. I've played around with manim a bit and can only imagine how much work this must've been, holy heck.

@ArtemKirsanov

Жыл бұрын

Wow, thank you so much!! I really appreciate it

@laurenpinschannels

Жыл бұрын

I have to say, the subtle effects were a major negative for me - good video though!

@exoticcoder5365

6 ай бұрын

@@laurenpinschannels I definitely love those aesthetic subtle effects

Finally a video that uses manim without being a 3b1b clone. There's clearly a distinct personality here through the sound effects, fonts, and animations. Thinking about the "personality" of your math explainer is important, but unfortunately is neglected often.

Hands down the best video on Wavelets. This video packs so much information but in such a succinct & intuitive way, that makes watching it a delight.

everyone talks about how amazing are the animations, and forget how amazing is the explanation, Artem Kirsanov is truly a genius

Holy moly, with my startup, I am working on an image analysis project collaborating with hospitals in Spain and the next steps on the project are similar to what you just showed to us. You just gave me more ideas to test and your visualizations are the best! (it reminds me of 3b1b videos) I will send you some results as soon as we finish it :)

@ArtemKirsanov

Жыл бұрын

Wow, that's fascinating! Good luck ;)

This is absolutely mind blowing - especially when you bring in the complex wavelet. The gradual addition of concepts is extremely well done, and everything is well explained.

So many details touched upon, such clear imagination of the underlying geometric intuition. So many little programs written to produce those graphs, diagrams, and visualizations. So refreshing to not rely on the Haar wavelet for an introduction to the topic. This video is going to leave many lasting memories in many minds. I am in awe.

@brendawilliams8062

Жыл бұрын

Me too. Cookie cutters you can exit with a cube can leave many questions.

I can't tell you how much I learnt from this one video. Thanks a lot ! Please keep making these videos.

27' 33" is just gorgeous. It's wonderful to see visualisation tools that were undreamed of when I was studying Maths in the 1970s, and how expertly people like you can use them.

This is a MASTERPIECE, thanks for you for the huge effort to come up with such video.

The legend is back

You've done an amazing job. By far the best short exposition on wavelets on KZread. Please keep sharing your work with us!

Thank you so much Artem!

You are my favorite channel I’ve found all year. The production and information value of your videos is absolutely unheard of. Please keep doing this, it’s an incredible contribution to the informational commons!

It's out! I can't wait to finish it-- the first few minutes is already fantastic!

This is just amazing. The level of detail in this is just baffling. Keep it coming. Your videos are scintillating. I have read wavelet transforms back when i was in Undergrad but this level of detail, wish I had known these intuitive interpretations behind this. All the best to you. This made my day.

Your visualizations and presentation is truly inspiring. Thank you!

Thank you for this incredible video!

This video is an absolute masterpiece! Not only do you clearly have a gift when it comes to explaining things, but you clearly have an amazing work ethic as well. I can't even imagine how much effort must've gone into making all these gorgeous animations! Definitely gained a subscriber!

Excellent video! Explained in a really clear and logical way, with impeccable sound design and animations.

Beautiful - what a joy to watch 👏👏👏

Amazing explanation! Thank you.

This is incredible! Both, the wavelet transform itself and this amazing video explaining it! :D

Masterpiece, as usual. Спасибо!

Extraordinary work!

Great animations, clear explanations Artem for win!

You can tell how much thoughtfulness went into every visualization here. For example, during the dot product explanation the value of the dot product was mapped onto the distance of the angle marker from the origin, and scaled such that the right angle location made a perfect square. Little touches like that were abound in the video and really help drive home intuition. Every bit of information was there for a reason!

This is probably one of the best educational videos on youtube. Absolutely superb!

Awesome video! Every part of this was just perfectly explained and visualized

Thank you! Amazing work!

Masterfully done. Mindblowing animation, interesting and engaging topic, clear and well-structured script: you've got it all!

Просто блестящая работа! Спасибо!

What an amazing presentation!

What a beautiful material! Thks for sharing~

One of the best videos I have ever seen, and the best explanation of wavelet transform on the internet. I can't imagine how many hours of work you invested here , but it tells a lot about your passion on knowledge sharing. Kudos ! 👏

Excellent. You have an intuitive sense of pace and information that keeps the viewer fascinated and intrigued. This video alone should be mandatory viewing in any university's physics or electronics courses, and I hope you follow it up with others in the same vein.

Excellent presentation!!!

You're doing incredible work, thank you for the videos!

This video is so absolutely incredible, I'm in awe. Your script, your animations, your understanding and explanation of the mathematics... This is a masterclass in education videos.

I have been trying to get an intuitive understanding of wavelets for a lot time. This video explained it perfectly!

Wow, this video is fantastic. Beautiful colors, visualizations and sounds. Never stop making these videos 🙂

Great video at a perfect level of detail.

Great video, really appreciated the explanations and cool animations! I've been wanting to understand this topic for a while but couldn't quite get my hands on as I'd like, so this served as a great push. I'm getting close to using this technique in my work (not neuroscience though), so this was a nice way of getting a bit of contact with the topic before having to go deeper in the subject. It's funny that I found you a while ago by your videos about Obsidian and Zotero and didn't know you did videos like this one, now I'm definitely subscribed. Keep up the great videos!

This has to be the most well edited video I've ever seen. Can't imagine watching this all for free. Thank you so much for your contribution towards Science.

This is a masterpiece! Thank you!

Great video! Really well explained. Even the parts that is easy to miss or misunderstand is connected in a great way in this video.

You are unparalleled. I have never seen such a master piece on youtube. Please continue the noble efforts. Hope you will make more videos sooner than later . stay no blessed

This video is incredible! High production value and amazingly clear explanations! Not enjoying this kind of math is almost impossible after watching your beautiful video!

Excellent presentation, thank you lot

great video! very thorough and loaded with animations and color that convey meaning. love it

I literally just burst out with a loud "whoa" at 21:14, about the insight of similarity as captured by the inner-product interpretation of the integral. This video is too well done!!!!

You’ve truly done the World a great service by putting this together in such beautiful fashion.

Wonderful explanation and visualization!

Absolutely amazing and intuitive explanation! Many, many thanks!

Wow man what a video! Can't imagine how much work must have gone into producing such a great explanation of such an interesting and useful technique, really really good job. I'm currently doing a PhD in systems neuroscience and your videos like this really make me feel like I need to up my game when it comes to learning complex topics like this. Convinced I'll find the technique or insight that makes my work next level from this channel, I can't wait to go look into how this has been used. Is this all self researched or do you have a seriously top notch neuroscience professor somewhere?

@ArtemKirsanov

Жыл бұрын

Thank you! I really appreciate it! Well, I’m doing research in the Laboratory of Extrasynaptic signaling, led by Dr. Alexey Semyanov in Moscow, so I’d say I have really great supervisors ;) I’m using Wavelet transform in my work to write code for extraction and analysis of theta rhythms, recorded from hippocampus in freely moving mice. (We are currently preparing a publication on this topic, and I really hope it will be out in a few months) But surely writing a video script requires a lot of additional research. I feel like only after making the animations and going through the process myself, I can finally understand wavelet transform much better, even though I’ve been routinely using it for almost 2 years now 😅

@stafan102938

Жыл бұрын

@@ArtemKirsanov Best of luck to you, looking forward to seeing what comes next

@samuelequinzi3153

Жыл бұрын

@@ArtemKirsanov same for me in my thesis using wavelets. Your animations are amazing!

This video was amazing, thank you! The ideas seem very helpful in quantum mechanics as well

Amazed at how this came out!

I feel blessed to discover your channel, thankyou for your knowledge.

The bit at the end where you talk about the wavelet transform's adaptive uncertainty is neat, and explains something I was wondering about the entire time -- how is the wavelet transform different from a time-windowed Fourier transform? This seems to be the answer! Because the support of a wavelet varies over frequency, unlike the static window size of a windowed FFT, you can get more information where it matters.

@markmcla

Жыл бұрын

I was wondering the same thing 🙂

@MrSonny6155

8 ай бұрын

There's two major differences between wavelet transforms (WT) and windowed FTs (say STFT/DFT) that I would highlight, along with their practical implications. 1) First is the multiresolution, stemming from the non-static frequency-time windows (as you've mentioned). Of course, the obvious benefit is that we can collect more time information at frequencies too high to care about discerning accurately instead of simply dropping all that info, which is great for something like any audio processing with a human auditory factor in it, or anything produced by an animal. But the biggest application is that do all sorts of multiresolution analysis like analysing rapidly changing frequencies without having to run FFT several times per frequency or narrowing your frequency as to lose time information. As it turns out, there's a huge amount of nonstationary signals out there in the real world that this perfectly solves. For example, you need to detect gravitational wave which produce a characteristic chirp. Windowed FTs really struggle with these since the output spectrogram ranges from "some ringing artefacting" to "it's literally smaller than my window size". Maybe it shows up somewhat alright, but you may lose some complex features along the way. But if you look at your WT's scalogram, you get a really nice curve, a distinct and empirically detectable feature. This actually works really well for all sorts of transients like discontinuities which may go undetected with windowed FTs. This is great for fault detectors. And detecting and characterising heart irregularities or complex brain wave features. (Technically, there are multiresolution windowed FTs. One of these was a STFT variant called the Constrant-Q transform, developed before wavelet transforms kicked off in full power around the 2000s. In actuality, this is really close to a modern WT, but had certain downsides that come with a less developed understanding of wavelets, like the difficulty in inverting your signal back and some of the jankery that comes with STFTs.) 2) The second is the ability to use different wavelets. This is a much more powerful tool than you would expect. Certain mother wavelets are well suited for certain applications, such as Ricker wavelets for superior seismic processing, or Daubechies for closely spaced features and DWT. A lot of work has been done here, so you have a pretty big toolbox for hotswapping wavelets for your needs. The coolest thing is that you can design your own wavelet tailored for pattern matching your known signal or picking out the set of features you want. Side note (DWT): It's worth noting that there are currently two major categories of WTs, being continuous wavelet transforms (CWT) and discrete wavelet transforms (DWT). Most discussions are implied to be around CWT, since it simply works for both continuous and discrete signals, but DWT offers a whole set of other applications. As you can guess, convolution can be an expensive operation. You are comparing every point of some decently long wavelet to an equal number of points, which is done across every point of the input signal. Sure, you can do some optimisations using FFT itself or adjust your wavelet parameters, but CWT is still generally slow enough that you just can't do certain things with it. Not to mention that its extra redundancy (which windowed FTs also have to some extent) leaves some to be desired for speed and memory performance. The DWT family of algorithms uses a different approach from raw convolution, instead using a fixed set of child wavelets like a filterbank. It loses its redundancy, limits it to certain mother wavelets, and locks it to frequency-time windows to powers of 2. In exchange, it gains better speed and memory performance in a purely discrete environment, allowing it reach its full practical potential. It turns out that this is often enough (or even ideal) for many digital computing applications. The perfect reconstruction with no redundant information makes it an excellent choice for audio/image compression or performant denoising of images. You'll also find it used in real-time applications where CWT just isn't built for, but require multiresolution that FFT can't provide. Damn, that was a long comment.

@a52productions

8 ай бұрын

@@MrSonny6155 This was very informative, thank you!

Outstanding explanation ever!!!! I have never come across something this clear. Please don't ever stop making such videos please you are helping mankind to grow at multiple dimensions. I support your work from my heart. ❤❤

Endlessly fascinating

Can't be explained better! WOW for the explanation and the great animations!

As someone with a background in signal processing: amazing video, explanation wise as well as animations. I wish that would have been the introduction at university. beautiful work!

Thanks for nice content dude.I would like to know how to learn this complex topics in neuroscience, math, programming and have one of the best video compositions (about the visual effects and aesthetics as whole)I ever seen on youtube

Absolutely amazing video

This is an incredible mathematical explanation I've ever seen. Thank you!

This is indescribably well explained, I can't thank you enough for this feat! I have been looking into this subject for some time every once in a while, but could never accomplish something that could be honestly called a grasp on this matter. My work is related to non-destructive testing and the analysis of acquired signals, so, Wavelet Transform can obviously very much enhance the way in which we handle the signals, store them and derive useful information from them. I know that medical ultrasonics is relying heavily on such signal processing, like IQ-demodulation for the sake of Doppler-measurements of blood stream velocity differences. Applied to non-biological targets, we are dealing with different challenges, but Wavelet Transform is bound to improve the way we handle ultrasonic echoes, once we get to harness initial successes on this path.

Amazing video! Just a remark about 5:25 : it's not that we lose sense of time, rather that the decomposition gives us pure sine waves, meaning they stretch from -inf to inf.

@RealNovgorod

Жыл бұрын

The relative timing of the different sine waves is represented in the phase of the Fourier transform.

This is the best summary and visualization of WT I have ever seen. Thumbs up!

Absolutely breathtaking. Thank you for this.

Oh nice topic!

@thankyou3634

Жыл бұрын

Oh, best topic!

Oh. My. God. If this video doesn't win SoME2, I'll lose my mind. What did you use to make the video?

@ArtemKirsanov

Жыл бұрын

Thank you!! The basis for animations was done in manim and matplotlib python libraries and Blender for 3D surfaces. Then everything was synced and composed in Adobe After Effects

This is the best explanation I have seen. Thank you!

Great explanation, and a beautiful visualization

Отличная работа! Все понятно и довольно просто, как для введения в вейвлеты. Спасибо за работу!

Good introduction to wavelets! But you give the Fourier transform too little credit :).. It DOES contain information about the time sequence/"order" of the frequency components, after all it's a "dual" representation of the time-domain signal, right? That temporal order is contained in the spectral phase - and that's what most people miss about the Fourier transform, since they only plot the magnitude (or power) spectrum but forget about the phase and lose half of the contained information (which happens to be about the timing order).

This video is excellent, showing many concepts in functional analysis in a very simple and clear way with great visualizations. Please add more!

Awesome content and animation! First time I've ever felt motivated to donate. Way more bang for your buck than my vibes classes were

8:00 I don't think that uncertainty in the time domain would mean that you're not sure what a value is at a given moment. Rather I see it as when you take a fourier transform of a signal that is defined over a long period of time, it will have a more specific fourier transform. Think of a cosine in the time domain which translates to a delta function in the frequency domain. This function is defined at exactly one value for the frequency. Therefore we observe that the longer and less determined a signal is in the time domain (cosine's domain extends from minus infinity to infinity) , the more determined it gets in the frequency domain and visa versa. The problem therefore is that when you take a fourier transform of a too short signal, that the frequent domain will start to show less specifically which frequencies are contained. That's the trade off you need to make.

@THeMin1000

Жыл бұрын

@pyropulse It have to do with uncertainty if we are taking about uncertainty as given in Information theory tho. Its not exactly the same thing as we consider uncertainty in real life, but what it really says is about information entropy.

@RealNovgorod

Жыл бұрын

It's very similar to the waterfall spectrograms in audio software (spectrum analyzers). It just shows you the Fourier transform of the X recent milliseconds of the audio signal, so the frequency definition of a pure sine wave will be limited to the inverse of the chunk length in time. Wavelet transform does basically the same in a mathematically smarter way (convolution instead of Fourier transform, though they are very related) using the optimum window shape, which allows for the "dynamic" trade-off between time and frequency resolution. In a simple waterfall-plot spectrum analyzer this trade-off is fixed and defined by the chunk length.

No phase in frequency space?!

@ArtemKirsanov

Жыл бұрын

You're absolutely right - there is definitely a very important notion of phase both in the case Fourier transform and Wavelet transform (computed as the angle of the resultant complex number). I didn't really have the time to mention this in the video, not to make it too overwhelming. But the Morlet wavelet, being a complex function, has amazing capabilities of dealing with phase of the oscillations. One example of such is the Cross Wavelet Analysis, which allows us to compare two signals and study the relative phase shifts. Thank you for pointing this out!

This is absolute class, thank you so much for the work you put into this. Every part of it was totally clear.

This is a beautiful summary

How about wavelet isit orthogonal matric, like DCT

@ArtemKirsanov

Жыл бұрын

If you are using discrete wavelet transform (DWT), then the wavelets of different scales indeed form an orthogonal basis. The key difference of DWT, compared to the continuous wavelet transform (which I showed in the video), is that the scale parameter (a) can be varied only discretely, to make sure that wavelets of different scales are orthogonal. It depends on the particular application and what type of wavelet you are using. For example, the Morlet is a continuous one, while many other wavelets (such as Haar, Daubechies) are used only in the discrete case

Thank you for making such a great video. Amazing!

Nice work ... great video. I look forward to seeing others on your channel. Cheers

This is incredibly well made, thank you so much.

amazingly easy to follow explanation and insights

This is the best video to explain wavelets. Thanks!

Such a great explanation, god bless !!

I’m blown away by how clear and informative this video was. Nicely done - it’s an inspiration to communicate this clearly.

Great overview of wavelets, really helpful!

Wow. This is a full lecture with a very effective set of graphics. Well done! I think I understood most of it and was never bored or overwhelmed.

Amazing animations! They really help make wavelet transform intuitive to understand

This is my favorite video on wavelets! 😊Thank you for making such great content and for the KZread algorithm for recommending it.