Nov 24, 2025 · What is the Fourier transform? What does it do? Why is it useful (in math, in engineering, physics, etc)? This question is based on Kevin Lin's question, which didn't quite fit in MathOverflow. …

Then the proof proceeds by taking the Fourier transform on this "collapsed" line. Now, due to the linearity of the Fourier transform, it feels like there should be another way: instead of summing up the …

Aug 11, 2018 · The full proof of the Fourier inversion theorem holds for absolutely integrable continuous functions, with absolutely integrable Fourier transforms.

May 16, 2025 · sequences-and-series fourier-analysis fourier-series uniform-convergence See similar questions with these tags.

Apr 9, 2020 · 7 Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its …

Jun 27, 2013 · Fourier transform commutes with linear operators. Derivation is a linear operator. Game over.

Feb 9, 2026 · Explore related questions limits fourier-series See similar questions with these tags.

Let us consider the Fourier transform of $\\mathrm{sinc}$ function. As I know it is equal to a rectangular function in frequency domain and I want to get it myself, I know there is a lot of material...

Jan 15, 2015 · Fourier had to fight to get others to believe that he might be correct in his belief that such expansion could be general. Many still unfairly accuse Fourier of not having been precise at all. To …

While saz has already answered the question, I just wanted to add that this can be seen as one of the simplest examples of the Uncertainty Principle found in quantum mechanics, and generalizes to …