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, …

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

11 Fourier Transform is a function. Fast Fourier Transform is an algorithm. It is similar to the relationship between division and long division. Division is a function, long division is a way to …

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 …

May 6, 2017 · Does that mean that the function is valued 2π−−√ 2 π at all points in the frequency domain? I think this is reasonable because such function i.e. f(t) = 1 f (t) = 1 in the time domain …

I've been practicing some Fourier transform questions and stumbled on the following one. To start off, I defined the Fourier transform for this function by taking integral from $-\\tau$ to $0$ and $...

9 A trigonometric polynomial is equal to its own fourier expansion. So f (x)=sin (x) has a fourier expansion of sin (x) only (from [− π, π] I mean). The series is finite just like how the taylor …

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.