fourier

Beautiful explanation of the Quantum Fourier Transform and some practical aspects of quantum computing without any domain-specific math.

The FFT is one cycle of a Discrete Fourier Transform, and since this data is both discrete and in regular intervals, it should behave identical to just sampling an audio signal.

Loved this the last(?) time a discussion on Fourier visualizations was on the front page.

As a bonus, you can directly derive the formula from the description, and things like Fourier series are a logical extension.

One of my favorite questions to Math Candidates, that are potential employees: In Fourier transform, what is being transformed to what?

Neil Young does not understand mathematics based on the Fourier Transform, especially sampling theory.

Wonder what happens if you use a regularization constraints in fourier space, optimizing the 2DFT of the image, with restraint increasing with frequency...

Similarly, it's considered basic undergrad work to understand Fourier decomposition; but the notations and clarity we get the insight from is the result of two centuries from the 1807 paper by Fourier.

As such it is transmitting a fourier transform of the signal it is transmitting between the cells (but with different basis functions, not cosines).

My favorite way to understand fourier transforms is the linear algebra approach.

I'm surprised nobody has yet linked to the video of Fourier series for drawing Homer Simpson.

When Fourier Analysis became a thing 300 years later, it was shown that indeed any periodic function can be modeled with epicycles of certain radii.

Note that this is extremely similar to the various kinds of data weighting "windows" (Hamming etc.) that are necessarily used with the Fast Fourier Transform.

One method that's been used to attack the Goldbach conjecture is the "Hardy-Littlewood circle method", which is useful for a whole lot of other kinda-similar problems in number theory; it's kinda-sorta an application of Fourier transforms to number theory.

Maybe using Fourier/wavelet/whatsoever transform would be the way to go, just like in digital watermarking techniques.