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...

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 …

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

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.

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 …

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

Apr 24, 2012 · We know that the Fourier transform of the sinc function is the rectangular function (or top hat). However, I'm at a loss as to how to prove it. Most textbooks and online sources …

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, …

Apr 26, 2019 · So, yes, we expect a $\mathrm {e}^ {\mathrm {i}kx_0}$ factor to appear when finding the Fourier transform of a shifted input function. In your case, we expect the Fourier …

In our mathematics classes ,while teaching the Fourier series and transform topic,the professor says that when the signal is periodic ,we should use Fourier series and Fourier transform for …