I encourage anyone that watches this video to comment on it. If you have all the bases covered, this video does such a great job at explaining it. So please, do other learners a favor and put this high in the youtube algorithm
Steve, you have a fantastic content and a gift for conveying complex knowledge. I really appreciate them. If I may suggest one point though, would you be able to post a table of contents of your videos that subscribers can follow in a logical order? Unless this is already available, I think it'd be immensely helpful.
Which means you are computing a fixed bunch of dot products. The funny thing is only a very small sub-set of possible inputs will produce any noticeble spectral response. The rest will just produce Gaussian noise. It is an under-considered case that sometimes you might want to use a transform as a bunch of say orthogonal dot products without all the fancy spectral math. Then you often need only do something simple like apply a randomly chosen pattern of sign flip to the input of transform or a random permutation. Or you want some intermediate situation by using a sub-random pattern of sign flips.
What happens if I transform data that is longer than one period of a periodic dataset? I got very strange behavior trying this in matlab. It worked using the fft command, though.
Oh, sorry. This probably was because I had an indexing error (used signal that went from -N to N). It seems to make no difference. The coefficients should repeat, right? Then 1/N will even out the extra sum entries, right? The spectral coefficients look strange, though. They look like two transforms overlayed.
I guess if you had an image and a Hilbert curve. And as you followed the curve, sign flipped every second pixel and then did a fast transform that would result in an interesting sub-random semi-structured projection. Maybe🍸. When I get a raspberry pi 400 I'll check it out.
There is a fast method to generate the Hilbert curve in Matters Computational. Maybe you can do a video on the orthogonality aspects of the Fourier matrix. I don't quite have a grip on that.
@@Eigensteve haha of course, thanks for these videos. I feel like I'm not the only one who is learning Fourier analysis online. I think it is overlooked in more than half of the engineering disciplines.
I encourage anyone that watches this video to comment on it. If you have all the bases covered, this video does such a great job at explaining it. So please, do other learners a favor and put this high in the youtube algorithm
Do replies count?
can't wait to see more about FFT, thank you~
Thank you from the bottom of my heart!
Steve, you have a fantastic content and a gift for conveying complex knowledge. I really appreciate them. If I may suggest one point though, would you be able to post a table of contents of your videos that subscribers can follow in a logical order? Unless this is already available, I think it'd be immensely helpful.
Look under the playlists
this is brilliant material.. Thank you from the bottom of my heart! Also I love your "Thank you" at the end of every video :)
plz share the UI setup of MatLab as well, the black background is so cool
Those look like Moire patterns from the aliasing, pretty cool visualization
hi, professor, it's seem that there's a little error in video 15(the n-1 in the sum should be n)
if the data is at irregular intervals of time, is the DFT possible and if it is possible is the output really worth the effort?
awesome video! Thank you!
how do you do spectral derivative in DFT?
This video is coming up soon!
@@Eigensteve Can't wait!
Which means you are computing a fixed bunch of dot products. The funny thing is only a very small sub-set of possible inputs will produce any noticeble spectral response. The rest will just produce Gaussian noise. It is an under-considered case that sometimes you might want to use a transform as a bunch of say orthogonal dot products without all the fancy spectral math. Then you often need only do something simple like apply a randomly chosen pattern of sign flip to the input of transform or a random permutation. Or you want some intermediate situation by using a sub-random pattern of sign flips.
What happens if I transform data that is longer than one period of a periodic dataset? I got very strange behavior trying this in matlab. It worked using the fft command, though.
Oh, sorry. This probably was because I had an indexing error (used signal that went from -N to N). It seems to make no difference. The coefficients should repeat, right? Then 1/N will even out the extra sum entries, right? The spectral coefficients look strange, though. They look like two transforms overlayed.
super interesting
Thank you
You're welcome!
I guess if you had an image and a Hilbert curve. And as you followed the curve, sign flipped every second pixel and then did a fast transform that would result in an interesting sub-random semi-structured projection. Maybe🍸. When I get a raspberry pi 400 I'll check it out.
There is a fast method to generate the Hilbert curve in Matters Computational.
Maybe you can do a video on the orthogonality aspects of the Fourier matrix. I don't quite have a grip on that.
Long Story Short ❤️
nice
3:34 This is what humans would do.. This is what i did!
My wife read my human readable code and told me I needed to shape up with vectorized multiplication :)
@@Eigensteve haha of course, thanks for these videos. I feel like I'm not the only one who is learning Fourier analysis online. I think it is overlooked in more than half of the engineering disciplines.
@6:25 Python code
O lord why do I punish myself with MAE 384