But what is the Fourier Transform? A visual introduction.

This is an explanation (from the amazing three blue one brown) of the DFT not the DCT, but this was the first thing that ever really made sense to me. It is explained by someone who really knows math incredibly well and is an amazing teacher, with amazing visuals: [VIDEO]

Dude really needs to subscribe to 3Blue1Brown: [VIDEO] (but anyone interested in stuff like this should be. I guess I'm surprised to see someone like this writing a blog post who isn't regularly checking out that channel)

I never understood how multiple electrical frequencies can be in a copper cable. I always thought they must merge and therefore it must be impossible to find the right set of original frequencies and their strength. Then I learned about the Fourier transform in this beautiful video: [VIDEO]

I can also highly recommend 3Blue1Brown's treatment of the topic: [VIDEO] (...which I see now is cited in the video that you link to!)

This is what made it click for me, can recommend it: 3Blue1Brown -- But what is the Fourier Transform? A visual introduction. [VIDEO]

Grant makes some amazing content. His visualization of the Fourier Transform[1] actually enabled me to understand the how it was happening behind the what was happening with one of the most used algorithms in computing. [1] [VIDEO]

It's an absolutely brilliant bit of maths that breaks a complex waveform into the individual components. Kind of like taking an orchestral song and then working out each individual instrument's contribution. Learning about this left me honestly aghast and in shock that it's not only possible but that someone (Joseph Fourier) figured it out and then shared it with the world. This video does a great job explaining what it is and how it works to the layman. 3blue1brown - [VIDEO]

3Blue1Brown has an extremely good explanation[1] of the intrinsic uncertainty, and why it's separate from measurement uncertainty. (the previous episode[2] is a recommended prerequisite for background on how the Fourier Transform works) > emerges through a different, as yet unknown, mechanism. In 3Blue1Bron's explanation[1], he shows how the intrinsic uncertainty is an inherent trade-off of trying to measure both position and frequency. A short wave packet only a few wavelengths long correlates with a narrow (precise) range of positions, but also correlates well with a very wide range of frequencies due. A Heisenberg-like uncertainty exists any time you are working with weave packets with length near the wavelength. 3Blue1Brown gives a very good example using Doppler radar. [1] [LINK] [2] [VIDEO]