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. …

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...

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 …

Fourier transform commutes with linear operators. Derivation is a linear operator. Game over.

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 …

Nov 24, 2013 · What are some real world applications of Fourier series? Particularly the complex Fourier integrals?

May 12, 2020 · Explore related questions functional-analysis analysis fourier-analysis fourier-transform See similar questions with these tags.

Oct 26, 2012 · The Fourier series is used to represent a periodic function by a discrete sum of complex exponentials, while the Fourier transform is then used to represent a general, nonperiodic function by …

Dec 15, 2012 · The Fourier transform projects functions onto the plane wave basis - basically a collection of sines and cosines. A Fourier series is also a projection, but it's not continuous - you sum …

Aug 4, 2022 · Is $ [0,1/2]$ the a fundamental domain of the Fourier series? Or do you envision a larger period, for instance $2\pi$ with domain $ [-\pi,\pi]$, and want to control the convergence on the …