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...

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

Aug 19, 2012 · Fourier transform of even/odd function Ask Question Asked 13 years, 5 months ago Modified 2 years, 10 months ago

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 …

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 …

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 …

Apr 29, 2024 · I tried using the standard Fourier transform formula and then tried using the convolution theorem. I reached the correct answer by using the formula, but I seem to have the scaling factor …

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...

Aug 5, 2018 · 21 The reason for this question is to make a list of the known proofs (or proof ideas) of Fourier inversion formula for functions f ∈ L1(R) (obviously adding appropriate hypothesis to get a …

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 …