Dear Steve, Your lectures give very clear and good visual realization of the contents. Thank you very much. it is the best video in this context I have experienced. (y)
OMG, feeling excited!!!!! yesterday I tried a time-frequency analysis based on a complex mother wavelet. I appreciate the time and effort for these great lectures! :)
Really good overview. I recommend Ingrid's 10 Wavelets and Stephane's book A Wavelet Tour of Signal Processing. Ron Coifman and Yves Meyer have made massive contributions as well. Someone who has studied Fourier theory and functional analysis will appreciate the technical details of wavelet theory which impacts a lot of techolofy behind the scenes.
I guess there is a small error in 6:33. Bigger "a" will actually make psi function wider and smaller in amplitude. The analogy with Gaussian function would be its standard deviation, which is placed in the denominator of negative exponent. Great lectures otherwise. Thanks for your work!
Thank you! I`ve been reading scientific papers on the application of the Wavelet Transform for neural spike sorting, and this video made It all come together.
Super high quality educational content in all of your videos (from your playlist), with the right balance of math and intuition to learn every topic. Highly recommended. Great exposition that keeps you engaged and good progression of topics using nice short videos.
Love your lectures. Thank you. Just wanted to point out that JPEG used DCT, but close enough in this situation I suppose. Glad they went to wavelet. It almost seems like magic to me. That and error diffusion.
nice orderly lecture with minimal hysteria and stammering and with good english diction.....i'm not math inclined so its interesting to see people who are fluent in math and who give the impression that math has flow and continuity and some kind of mental image structure......we as a culture are mostly not math oriented and most people find higher math to be quite foreign............i wish as a 6 or 8 year old in grade school we had immediately commenced with calculus math and began each day with doing an integral followed by 2 derivatives and then fleshing out the algebra and geo-trig around the nucleus of calculus.......i wish entire mornings were devoted to cutting up curves into miniscule paper rectangles and adding them up to find the area we always leave the hardest subjects to the very last.....we should start with the hardest subjects first at age 6 when the brain is most plastic and elastic and absorbing every new idea like a sponge.........then many people would be more mathy.
very very new to all this wavelet stuff, but I could get a very good basic idea of it. plus your English was very clear and easy to understand for me, a non-English speaking
At 8:35 when you say the signal goes from +1 to -1 only in the left half can you please explain? It looks like you are squeezing the signal from +1 to 0
8:43 why is it psi(a=1/2, b=0), not b=-1/2? This is maybe an error. Also in the second function the shift is b=+1/2. you put a lot of effort into you video. Of couse it can happen that one or another error occurs. Your videos are great and help a lot of people.
A very nice explanation. I am following most of your videos and have learnt from these. However at 6.39, as scale (a) increases, fequency decreases, so should not as a increases, it should be directed downwards to lower frequencies ? Please excuse me if I have missed something.
Thanks Steve for excellent video,Quick question, is the DWT and its inverse a unique mapping? I mean is there an absolute one-to-one correspondence between the signal and its transform? Thanks
The intermediate calculations of the Hadamard transform are very wavelet like. You can pick the one with highest magnitude, remove it, and make consistent all the calculations. And repeat. In such a way you can make quite a good compression algorithm. The FFT can be your friend that way too I suppose.
Hi, I'm just a curious student, lately have been studiying Deep learning, and i'm asking myself if there are some wavelet transform that could preserve the main information of image (compressed) of different sizes and then use a fixed size on different basis to feed a neural network. I tried it with FFT2 and it appear that keep the main information in the corners. maybe there are some wavelets that keep it in the center. Just curiosity.
Awesome video, very informative. I am learning about this subject at the moment. It was very confusing for me to make a destiction between the "actual" wavelet transform, the continous WT, the discrete one and then the decomposition. Would have appreciated this video even more if you mentioned this aswell. This is just me, i got so overwhelmed when looking into wavelets for the very first time. Otherwise, spot on!
Thank you for your lecture Finally wavelets, is there any way to relate wavelet coefficients to energy in terms of dB, like can we do some sort of relationship between fft and wavelets to get the corresponding energy in terms of dB for wavelet coefficients.
Thanks for your efforts! Can you also make a lecture about the use of wavelets in pdes? I think they are really interesting due to their (sometimes) N-scaling behaviour and variable choice of boundary conditions.
Thank you very much for your informative and inspiring videos. You presentation style is great too. Can you please do a video about how to do an interactive presentation mixing slide show and real time talking.
Completely unrelated to subject matter! Could you explain ring? I always thought righthand wedding ring was a Germanic/Russian European thing, whereas Anglos & italians wear rings on their left hand. Unless this is a signet ring of the intelligentsia.
@@Eigensteve I would love to see this as well. I come across an article explaining that the SVD of a Hankel matrix has direct interpretable physical meanings related to space-time POD, but I find the jargons too difficult for someone who have no exposure to fluid dynamics to understand.
The Haar mother wavelet (mathworld.wolfram.com/HaarFunction.html) starts from 0 and returns to 0 like every every other mother wavelet. Nevertheless, the explanations hold. Great video!
Your explanation of what the Haar wavelet is was misleading. Its support is [0,1] and the transition from 1 to -1 happens at 1/2. This is very different that what you described
I understand this, and I can follow quite well (I think); I suppose it is not that difficult? But then all the weird characters, names (psy, wtf?) and I suppose mathamethical notation is added and it becomes difficult beyond my wildest dreams. When I close my eyes and listen I 100% understand, but then I look at what he writes down and I am so, so lost. The pictures make sense, but the text and equations might as well be in Chinese. To clarify: my mental concept of what he just explained is in no way, shape or form reconcilable with what he's written on the board. Am I stupid? I don't understand not understanding 🤯
Dr Brunton's hair parts right in real life (the Clark Kent look). But in these videos, his hair parts left (like Superman). Does this answer the question?
I read an article from University of Washington that Steve Brunton was left-handed. In the video, it appears as though he's writing with his right hand. He could have trained himself to write in reverse with his right hand but I think it's also possible for the video to be digitally altered (mirrored) after recording. Imagine you were standing behind him as he drew a straight line from left to right (i.e., the normal direction English is written in) onto a transparent (glass) surface. You'd observe that the line was drawn left to right. Now if you were to stand behind the glass surface, you'd observe the line drawn right to left. Imagine you magically turned into a camera and recorded what you saw behind the glass surface. With the video recorded, you're then able to 'mirror' every frame and end up with this recording. Steve would still be writing comfortably with his left hand. You can verify this with an experiment. Use a transparent plastic container, sharpie, and a smartphone (with a front-facing camera). Place the camera inside the plastic container and have it record video (as you would if you were taking a video selfie). Write normally on the outside wall of container that's being recorded. If you look at the video, you'd see that the "world" looks normal but the text you wrote looks reversed. Now, the i-phone allows you to play back your video with each frame flipped across a vertical. If you do that, the *text* appears normal but the "world" looks reversed (which is fine -- we don't care that Steve is left handed!).
It's incredible that you could understand these concepts without formal education, you are privileged. Definitely you should consider going to college, you would find mentorship, and you would be exposed to a great amount of ideas. With those tools, you could make a great contribution, for sure.
I think this is a complicated question. It's probably similar to why it's good to find a basis where the basis vectors are orthogonal to one another in linear algebra. A non-orthogonal set can still span the space, but there are advantages in being able to interpret the coordinates if they are independent of one of another. In spectral techniques this may lead to functions that express independent information about the frequency content of whatever data you're looking at. For the fourier transform the cosines and sines at a specific frequency are orthogonal to those at another frequency and that means the information about the frequency content at each frequency is independent of the frequency content at any other frequency. I don't know if that's a great answer, but that's my understanding of it.
The sines and cosines are an orthogonal basis under an inner product defined by integrals. This is great because it allows us to use Graham Schmidt to find the coefficients of basis vectors! If they weren’t orthogonal, we wouldn’t be able to do this
Dear Steve, Your lectures give very clear and good visual realization of the contents. Thank you very much. it is the best video in this context I have experienced. (y)
Many thanks!
This is possibly the best educational series on any topic I have ever encountered. I just got your book, and I trust it'll be amazing too.
Thank you!
Finally wavelets🔥
Your videos saved my internship, thank you
Biologist here, I needed to understand image processing, your videos are very clear, thank you.
OMG, feeling excited!!!!! yesterday I tried a time-frequency analysis based on a complex mother wavelet. I appreciate the time and effort for these great lectures! :)
Wonderful!
Really good overview. I recommend Ingrid's 10 Wavelets and Stephane's book A Wavelet Tour of Signal Processing. Ron Coifman and Yves Meyer have made massive contributions as well. Someone who has studied Fourier theory and functional analysis will appreciate the technical details of wavelet theory which impacts a lot of techolofy behind the scenes.
I guess there is a small error in 6:33. Bigger "a" will actually make psi function wider and smaller in amplitude. The analogy with Gaussian function would be its standard deviation, which is placed in the denominator of negative exponent. Great lectures otherwise. Thanks for your work!
Yes, corrected @8:50
Thank you!
I`ve been reading scientific papers on the application of the Wavelet Transform for neural spike sorting, and this video made It all come together.
That sounds like very cool research!
Super high quality educational content in all of your videos (from your playlist), with the right balance of math and intuition to learn every topic. Highly recommended. Great exposition that keeps you engaged and good progression of topics using nice short videos.
Thank you for this, always wanted to know more about wavelets!
Glad it was helpful!
A clear and direct approach to make sense of the idea. Thankyou
this is a fantasitic lecture. you vividly clearify what is wavelet from perspectives both of math and human sense
Love your lectures. Thank you. Just wanted to point out that JPEG used DCT, but close enough in this situation I suppose. Glad they went to wavelet. It almost seems like magic to me. That and error diffusion.
nice orderly lecture with minimal hysteria and stammering and with good english diction.....i'm not math inclined so its interesting to see people who are fluent in math and who give the impression that math has flow and continuity and some kind of mental image structure......we as a culture are mostly not math oriented and most people find higher math to be quite foreign............i wish as a 6 or 8 year old in grade school we had immediately commenced with calculus math and began each day with doing an integral followed by 2 derivatives and then fleshing out the algebra and geo-trig around the nucleus of calculus.......i wish entire mornings were devoted to cutting up curves into miniscule paper rectangles and adding them up to find the area
we always leave the hardest subjects to the very last.....we should start with the hardest subjects first at age 6 when the brain is most plastic and elastic and absorbing every new idea like a sponge.........then many people would be more mathy.
THE best basic lecture on the subject, Thx !
very very new to all this wavelet stuff, but I could get a very good basic idea of it. plus your English was very clear and easy to understand for me, a non-English speaking
Great lecture series. Love the presentation style.
You have the gift to teach complicated stuff effectively!
Question:
Do you have a good source for the inverse wavelet transformation?
Steve .You are a legend teacher. ı havent seen before as you.Thank you very very much this expilaniton
At 8:35 when you say the signal goes from +1 to -1 only in the left half can you please explain? It looks like you are squeezing the signal from +1 to 0
8:43 why is it psi(a=1/2, b=0), not b=-1/2? This is maybe an error. Also in the second function the shift is b=+1/2.
you put a lot of effort into you video. Of couse it can happen that one or another error occurs. Your videos are great and help a lot of people.
well, I though it should be a=2, and b=1 :D
thank you sooooo much. I was so confused about this theory. After your Video I can finally understand well. Thank you
Nicely presented. Really beautiful! Thanks!
The explanation was complete. so much dear Steve
Great Videos Love It. Awesome. Is there any Daubechies Wavelet videos from you? Or any video lectures you can please share it
A very nice explanation. I am following most of your videos and have learnt from these. However at 6.39, as scale (a) increases, fequency decreases, so should not as a increases, it should be directed downwards to lower frequencies ? Please excuse me if I have missed something.
Thanks Steve for excellent video,Quick question,
is the DWT and its inverse a unique mapping? I mean is there an absolute one-to-one correspondence between the signal and its transform?
Thanks
Thanks! Yes, this is a unique and invertible mapping.
The intermediate calculations of the Hadamard transform are very wavelet like. You can pick the one with highest magnitude, remove it, and make consistent all the calculations. And repeat. In such a way you can make quite a good compression algorithm. The FFT can be your friend that way too I suppose.
Hi, I'm just a curious student, lately have been studiying Deep learning, and i'm asking myself if there are some wavelet transform that could preserve the main information of image (compressed) of different sizes and then use a fixed size on different basis to feed a neural network.
I tried it with FFT2 and it appear that keep the main information in the corners. maybe there are some wavelets that keep it in the center.
Just curiosity.
Awesome video, very informative. I am learning about this subject at the moment. It was very confusing for me to make a destiction between the "actual" wavelet transform, the continous WT, the discrete one and then the decomposition. Would have appreciated this video even more if you mentioned this aswell.
This is just me, i got so overwhelmed when looking into wavelets for the very first time. Otherwise, spot on!
Thank you for your lecture Finally wavelets, is there any way to relate wavelet coefficients to energy in terms of dB, like can we do some sort of relationship between fft and wavelets to get the corresponding energy in terms of dB for wavelet coefficients.
are there upper bounds on the highest frequency of wavelet? what are the highest a's and b's?
What an amazing explanation. Great job, and thanks!
Great presentations... What tool are you using for creating the videos?
are there constraints on what kind of waves can be used as mother wavelet?
what are the a's and b's that we can use in the wavelet?
Keep doing this stuff, you're good at it! Helped a bunch, thanks.
Thanks for your efforts! Can you also make a lecture about the use of wavelets in pdes? I think they are really interesting due to their (sometimes) N-scaling behaviour and variable choice of boundary conditions.
Thanks for this nice introduction.
I came here for a lucid explanation of wavelets, but wow! Do you actually write backwards?
really good explanation big thanx😃
Thank you very much for your informative and inspiring videos. You presentation style is great too. Can you please do a video about how to do an interactive presentation mixing slide show and real time talking.
Beautiful explanation !!
Absolutely awesome. Thank you so much for your content!
Hi Steve, The Haar wavelet transform of order n can transform data of length 2^n . How can we apply a Haar wavelet transform on data of length 12?
Obrigada por esse video! Estava precisando!
Hello! are you familiar with Jonathan Regele's work (From U of Iowa? I believe) in wavelet driven CFD meshes?
Can you make one video on TQWT ?
Very informative, thank you
Sir please send your wavelet transform playlist link
How does the camera perspective work?!
Sir can you help how to solve pdes using wavelet transform method..
is it correct to say that wavelets are used for nonstationary/highlynonstationary signals?
Thank you very much, this was very clear !
This was very helpful.
Hello sir, how to thresholding wavelet coefficients by higher order statistics (skewness, kurtosis)
Nice!Well explained!
Is there any code for this? Please send the link if anyone knows
Can we also use wavelet transforms to solve PDEs?
thanks for such explanation
Completely unrelated to subject matter!
Could you explain ring? I always thought righthand wedding ring was a Germanic/Russian European thing, whereas Anglos & italians wear rings on their left hand.
Unless this is a signet ring of the intelligentsia.
Thanks!
Lecture on SPOD would be nice, I don't find any information on them in your books 🤓
I would love to cover this, because then I would have a good reason to learn it better. On the list.
@@Eigensteve I would love to see this as well. I come across an article explaining that the SVD of a Hankel matrix has direct interpretable physical meanings related to space-time POD, but I find the jargons too difficult for someone who have no exposure to fluid dynamics to understand.
I'm gonna call it "The sombrero" from now on.
Are you writing backwards SIr ?
You are my Hero
بسیار عالی و زیبا ممنون
I'm sorry, the video is amazing, but are you writing in mirror image? I mean what... how...?
The Haar mother wavelet (mathworld.wolfram.com/HaarFunction.html) starts from 0 and returns to 0 like every every other mother wavelet. Nevertheless, the explanations hold. Great video!
Please, can I know which kind of software do you use for creating your video
for the interactive visuel contents
Your explanation of what the Haar wavelet is was misleading. Its support is [0,1] and the transition from 1 to -1 happens at 1/2. This is very different that what you described
I understand this, and I can follow quite well (I think); I suppose it is not that difficult? But then all the weird characters, names (psy, wtf?) and I suppose mathamethical notation is added and it becomes difficult beyond my wildest dreams. When I close my eyes and listen I 100% understand, but then I look at what he writes down and I am so, so lost. The pictures make sense, but the text and equations might as well be in Chinese. To clarify: my mental concept of what he just explained is in no way, shape or form reconcilable with what he's written on the board. Am I stupid? I don't understand not understanding 🤯
wait...does he write backwards?
Dr Brunton's hair parts right in real life (the Clark Kent look). But in these videos, his hair parts left (like Superman). Does this answer the question?
How did he record this video?? Anybody knows? It's like a mirror or something like that, isnt it?
I read an article from University of Washington that Steve Brunton was left-handed. In the video, it appears as though he's writing with his right hand. He could have trained himself to write in reverse with his right hand but I think it's also possible for the video to be digitally altered (mirrored) after recording.
Imagine you were standing behind him as he drew a straight line from left to right (i.e., the normal direction English is written in) onto a transparent (glass) surface. You'd observe that the line was drawn left to right. Now if you were to stand behind the glass surface, you'd observe the line drawn right to left. Imagine you magically turned into a camera and recorded what you saw behind the glass surface. With the video recorded, you're then able to 'mirror' every frame and end up with this recording. Steve would still be writing comfortably with his left hand.
You can verify this with an experiment. Use a transparent plastic container, sharpie, and a smartphone (with a front-facing camera). Place the camera inside the plastic container and have it record video (as you would if you were taking a video selfie). Write normally on the outside wall of container that's being recorded. If you look at the video, you'd see that the "world" looks normal but the text you wrote looks reversed. Now, the i-phone allows you to play back your video with each frame flipped across a vertical. If you do that, the *text* appears normal but the "world" looks reversed (which is fine -- we don't care that Steve is left handed!).
@@MinhTran-wn1ri you are totally right
Sehr gut
this is awesome, thank you!
I never whent to college but can allways understand stuff like this ... I wonder if I should go tho 🤔
It's incredible that you could understand these concepts without formal education, you are privileged. Definitely you should consider going to college, you would find mentorship, and you would be exposed to a great amount of ideas. With those tools, you could make a great contribution, for sure.
So cool
Is he writing a mirrored version for himself, so we can see it normal? :)
I'm wondering, if he really writes mirrored, or just mirrored the Video
if it was mirrored you would see him writing from left to right, so I think he actually writes backwards, which is crazy *o*
Can someone explain me why it is so important, that the basis-functions are orthogonal?
I think this is a complicated question. It's probably similar to why it's good to find a basis where the basis vectors are orthogonal to one another in linear algebra. A non-orthogonal set can still span the space, but there are advantages in being able to interpret the coordinates if they are independent of one of another. In spectral techniques this may lead to functions that express independent information about the frequency content of whatever data you're looking at. For the fourier transform the cosines and sines at a specific frequency are orthogonal to those at another frequency and that means the information about the frequency content at each frequency is independent of the frequency content at any other frequency. I don't know if that's a great answer, but that's my understanding of it.
The sines and cosines are an orthogonal basis under an inner product defined by integrals. This is great because it allows us to use Graham Schmidt to find the coefficients of basis vectors! If they weren’t orthogonal, we wouldn’t be able to do this
just perfekt