Discrete Fourier Transform (DFT): The most important math tool ever

[@gustinian]

Excellent stuff. Every video helps to build better understanding of arguably the most useful discovery in science and mathematics. Thank you again for your amazingly clear graphical illustrations of this slippery concept. Looking forward to your FFT animations.

[@wangkuanlee3548]

the mathematical expression of signal analysis, corresponds to various physical phenomena are explained very clearly. very impressive. Thank you so much !

[@MKDSLeone]

Looking forward to seeing your treatment when it renders the higher-quality versions c:

[@joy2000cyber]

I didn’t understand my undergraduate text book on DFT because it cannot display 3D animation. Love your work ❤

[@adirem1983]

Thank's a lot! Your video is a masterpeace of teaching high graduate math and communication engineering in an advanced range. You have found the right way to explain some complex system-theory in an easy breathtaking scenery of 4th dimensions! Shannon would have a lot of respectation on your works indeed! Parfait!

[@MR-fs2pc]

This is amazing, thank you for making such a complex subject so clear.

[@avinasha237]

at 3:12 n=1 k=1 ; sin(pi/4) =cos (pi/4) = 1/sqrt(2). Its written as 1.

[@nemoyaori4579]

High quality video! Thank you so much❤.

[@pontusvangen702]

Amazing video

[@carlosperez847]

Hi Mr Silicon Guy. Very good videos May i ask you which tool you use for the animations ?

[@TheSiGuyEN]

Manim is community-maintained Python library originally created by grant sanderson (3blue1brown) for creating mathematical animations.

[@iwbnwif]

Please can you explain how you are adding the two signals (e.g. at 8:50). Clearly, for a given discrete value of k, it isn't as simple as adding the real and imaginary components of the two signals at that interval. Thank you for an excellent video.

[@TheSiGuyEN]

it is just a simple addition of the real and imaginary parts of the two signals. Do you have a question about that?

[@iwbnwif]

@@TheSiGuyEN thank you for answering. I tried to create signals with angular frequency 1, 2, .. ,8 in Python. But if I sum the real and imaginary parts at each discrete interval, then the radius is large near the 'ends' and small in the middle. By ends I mean 0 and 2.Pi of the wave with an angular frequency of 1. I must be doing something wrong! Will try again and put the code here.

[@iwbnwif]

I have asked a question on Math Stack Exchange about this. It seems KZbin doesn't like me to link to it, but searching 'summing complex exponentials to understand the Discrete Fourier Transform' should work

[@iwbnwif]

​@@TheSiGuyEN oh I see it now! k is -ve to +ve in the second set of examples starting around 8:31. Thanks again for these videos they're amazing 😊