Thanks - I came to the comments to confirm this. If possible, can you please put an annotation in the video for this? (Even if it's just a text annotation.)
This makes more sense than those other proofs without including the condition, however there's sth that doesn't add up for me What makes this different from the usual FT condition of "f(t) must be absolutely integrable"? I mean we still dealt with that condition and got FT for stuff like constants, sin(t), u(t)
Really love this episode when you get derivatives involved. Most people have very vague idea about how useful Fourier is. Now, here as soon as you bring in the derivatives, everyone gets a light bulb moment when they realize that the derivative disappears with all their life time worries about calculus. It is quite a relief knowing that algebra is useful again.
Is it possible that I just watched 11 lectures without actually realizing it. Now I’m too old to cause any real damage with this knowledge but boy this is riveting!
Thanks for the lecture. Coded this up to get position, speed and accel out of a single measurement. Really interessting as you get smooth signals and low-pass filter by design. Might try integration as well.
Hello sir, your method of explaining any topic is so innovative and interesting that any difficult topic we can understand so easily. Can you please share some videos or any reference material for defining fourier transform on vector valued functions or particularly I want to define fourier transform on m×n matrix. Please suggest how to define?
There is one thing I am wondering and that is how The Fourier Transform is going to be visualized geometrically . The Fourier Series is easy to imagine when we have discrete Ck but that's not the case for Fourier Transform .
4:42 I'm not sure this is correct. The only requirement to write ℱ(f) is that f must be in L¹, which doesn't mean f(x) → 0 as x → +∞. As a counterexample, consider f to be a sum of triangle functions of width 1/2 and height 2n² each centered at integers n≥1. Its integral is π²/6 but it doesn't converges to 0 as x → +∞. Edit: I thought a little bit about it and this is definitely incorrect, even if f is C¹ (just replace triangles in my previous example with smooth bells). You need to assume that f is uniformly continuous for this argument to hold.
Having the same question, but finding that actually not all functions are able to do Fourier transformed. Thus in the case of constant, it's like F(c) = delta(w) (delta function) --> F'(c) = i*w*delta(w), and you can't find how to do inverse transformation. So intuitively, only the function f(x) → 0 can do derivative through Fourier Transform and inverse back.
It seems that taking the derivative of the 2nd Fourier equation also shows the transform of f'(x) is iw\hat{f}(w), is there any issue with that approach? or just an alternative?
It's called lightboard recording. But yes it's a camera infront of a big window on a black background. To get the text right you need to mirror the image.
Wow wow wow. Many physics professors don't understand where jw comes from and just say that imaginary j is just a "mathematical device", and you just have to be force fed with third words.
Correction at 8:30, right hand side of ODE should be -w^2 * c * uhat. I forgot the wavespeed "c".
Where did the Omega come from?
Thanks - I came to the comments to confirm this.
If possible, can you please put an annotation in the video for this?
(Even if it's just a text annotation.)
This makes more sense than those other proofs without including the condition, however there's sth that doesn't add up for me
What makes this different from the usual FT condition of "f(t) must be absolutely integrable"?
I mean we still dealt with that condition and got FT for stuff like constants, sin(t), u(t)
Not many people can deliver with such fluency in high speed, Thank You for taking time to make these videos. Really appreciate them
Really love this episode when you get derivatives involved. Most people have very vague idea about how useful Fourier is. Now, here as soon as you bring in the derivatives, everyone gets a light bulb moment when they realize that the derivative disappears with all their life time worries about calculus. It is quite a relief knowing that algebra is useful again.
Is it possible that I just watched 11 lectures without actually realizing it. Now I’m too old to cause any real damage with this knowledge but boy this is riveting!
you arent too old to do anything
@@yashsvnit7007 well... there are things... But not this.
3:54 To be more precise df/dx * dx == dv and -i*w*exp(-iwx)dx == du
A series on stochastic calculus would be appreciated with such smooth explanations :)
Thanks for the lecture. Coded this up to get position, speed and accel out of a single measurement. Really interessting as you get smooth signals and low-pass filter by design.
Might try integration as well.
Love your studio format sir .. itS amazing ..
i want to go to the UofW and take all my classes with this guy.
Hello sir, your method of explaining any topic is so innovative and interesting that any difficult topic we can understand so easily. Can you please share some videos or any reference material for defining fourier transform on vector valued functions or particularly I want to define fourier transform on m×n matrix. Please suggest how to define?
if it is possible to you make a course on legendre and bessel equations( in general orthagonal functions).thanks
There is one thing I am wondering and that is how The Fourier Transform is going to be visualized geometrically . The Fourier Series is easy to imagine when we have discrete Ck but that's not the case for Fourier Transform .
Is there a video on the properties of fourier transform.
how does this board work?
Try looking up 'Lightboard' by prof. Michael Peshkin from Northwestern
4:42 I'm not sure this is correct. The only requirement to write ℱ(f) is that f must be in L¹, which doesn't mean f(x) → 0 as x → +∞. As a counterexample, consider f to be a sum of triangle functions of width 1/2 and height 2n² each centered at integers n≥1. Its integral is π²/6 but it doesn't converges to 0 as x → +∞.
Edit: I thought a little bit about it and this is definitely incorrect, even if f is C¹ (just replace triangles in my previous example with smooth bells). You need to assume that f is uniformly continuous for this argument to hold.
So then how do we cancel out the uv term?
Having the same question, but finding that actually not all functions are able to do Fourier transformed. Thus in the case of constant, it's like F(c) = delta(w) (delta function) --> F'(c) = i*w*delta(w), and you can't find how to do inverse transformation. So intuitively, only the function f(x) → 0 can do derivative through Fourier Transform and inverse back.
Mind blown! Awesome lecture
great videos, big thanks from argentina
Doesn't Fourier transform come with some limitations?
Doesn't assuming we can move the partial operator also limit the answer?
Beautiful!! Thank you!
Excellent explanation
It seems that taking the derivative of the 2nd Fourier equation also shows the transform of f'(x) is iw\hat{f}(w), is there any issue with that approach? or just an alternative?
Does anyone know what video he starts working on the spectral derivative?
He looks like Harrison Wells, from The Flash show.
Why the signs of integral and transformer are oppisiote? I remember reading a book that says as I said!
what is dx
if f(x) = x^2 then df(x) is x and d2f(x) is 1
then why didn't d multiplied by x equal undefined?
what is df/dx
2:44 dv = dƒ / dx * dx, so that v = ƒ
Brilliant!
amazing！
Math is sometimes just beautiful
is he left handed writing on glass board filmed other side of the glass and the video is left right mirrored?
It's called lightboard recording. But yes it's a camera infront of a big window on a black background. To get the text right you need to mirror the image.
I found a goldmine.
Me too!!
Wow wow wow. Many physics professors don't understand where jw comes from and just say that imaginary j is just a "mathematical device", and you just have to be force fed with third words.
This is insane