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...

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 …

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

Jun 15, 2012 · I'm preparing for an exam in the signals and systems class I'm taking. One of the practice exams has a problem that requires you to take the Fourier transform of $\text {sinc} …

Aug 30, 2020 · This might be a good approach. However, the Fourier inversion theorem is valid only for a subset of functions, so it seems that more caution is required.

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 …

May 5, 2015 · Here is my biased and probably incomplete take on the advantages and limitations of both Fourier series and the Fourier transform, as a tool for math and signal processing.

Feb 28, 2020 · Edited to clarify question and give accepted answer in context. Looking at the table of Fourier Transforms on Wikibooks line 14 gives the Fourier transform of the triangle …

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, …

Let us consider the Fourier transform of 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 about …