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 …

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 …

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 …

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 $...

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

Sep 29, 2014 · Remember that you're not computing coefficients for two different functions - you're computing the coefficients of one function, except you will have two integrals when computing the …

Aug 15, 2016 · What is meant with 'Fourier mode'? Ask Question Asked 9 years, 3 months ago Modified 8 years, 4 months ago

Dec 1, 2024 · In Stein and Shakarchi's Fourier Analysis, they often invoke the fact that differentiation with respect to time commutes with the Fourier transform with respect to space variables. For …

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