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 …

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

In the QM context, momentum and position are each other's Fourier duals, and as you just discovered, a Gaussian function that's well-localized in one space cannot be well-localized in the other.

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

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.

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 …

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 …

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

18 The Fourier Transform is a very useful and ingenious thing. But how was it initiated? How did Joseph Fourier composed the Fourier Transform formula and the idea of a transformation between periodic …