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...

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 …

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

Oct 27, 2019 · What are some real world applications of Fourier series? Particularly the complex Fourier integrals?

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 …

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 …

Aug 19, 2012 · Fourier transform of even/odd function Ask Question Asked 13 years, 4 months ago Modified 2 years, 10 months ago

The theory of Fourier transforms has gotten around this in some way that means that integral using normal definitions of integrals must not be the true definition of a Fourier transform.

Oct 30, 2021 · One can consider 2D Fourier transform as a sequence of two 1-dimensional discrete Fourier transforms: applied to the first variable and then to the second. The properties follow …

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...