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. An...

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...

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 …

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 …

Jun 27, 2013 · 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 …

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 …

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

Jul 20, 2025 · The notion that the Fourier transform is the limit of the Fourier series as the period P → ∞ P → ∞ seems to have led to a bit of confusion as there are several related questions on Math …

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