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...

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 …

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 …

Jun 27, 2013 · 0 One could derive the formula via dual numbers and using the time shift and linearity property of the Fourier transform.

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 $...

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...

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 …

Nov 24, 2013 · What are some real world applications of Fourier series? Particularly the complex Fourier integrals?

May 12, 2020 · Explore related questions functional-analysis analysis fourier-analysis fourier-transform See similar questions with these tags.

Dec 15, 2012 · The Fourier transform projects functions onto the plane wave basis - basically a collection of sines and cosines. A Fourier series is also a projection, but it's not continuous - you sum …