Computing the DFT Matrix

[@picumtg5631]

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

[@shdyo]

Do replies count?

[@leixu7116]

can't wait to see more about FFT, thank you~

[@priyamourya6452]

this is brilliant material.. Thank you from the bottom of my heart! Also I love your "Thank you" at the end of every video :)

[@JIANCHUANYANG]

Thank you from the bottom of my heart!

[@s25412]

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.

[@sambroderick5156]

Look under the playlists

[@vandaliztik9266]

plz share the UI setup of MatLab as well, the black background is so cool

[@JulioDiaz614]

Those look like Moire patterns from the aliasing, pretty cool visualization

[@SajjadKhan-cn6mv]

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?

[@xhstom3887]

hi, professor, it's seem that there's a little error in video 15(the n-1 in the sum should be n)

[@oldcowbb]

how do you do spectral derivative in DFT?

[@Eigensteve]

This video is coming up soon!

[@oldcowbb]

@@Eigensteve Can't wait!

[@nami1540]

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.

[@nami1540]

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.

[@AJ-et3vf]

awesome video! Thank you!

[@somethingnew7538]

Long Story Short ❤️

[@hoaxuan7074]

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.

[@NickFilipovic]

3:34 This is what humans would do.. This is what i did!

[@Eigensteve]

My wife read my human readable code and told me I needed to shape up with vectorized multiplication :)

[@NickFilipovic]

@@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.

[@yt-1161]

@6:25 Python code

[@ohm1914]

super interesting

[@hoaxuan7074]

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.

[@hoaxuan7074]

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.

[@dylanmagleby4330]

Thank you

[@Eigensteve]

You're welcome!

[@damiangames1204]

nice

[@p4rkoursnip3r47]

O lord why do I punish myself with MAE 384