0 One could derive the formula via dual numbers and using the time shift and linearity property of the Fourier transform.

Dec 29, 2019 · What is the Fourier transform? What does it do? Why is it useful (in math, in engineering, physics, etc)? This question is based on the question of Kevin Lin, which didn't …

The theory of Fourier transforms has gotten around this in some way that means that integral using normal definitions of integrals must not be the true definition of a Fourier transform.

In the QM context, momentum and position are each other's Fourier duals, and as you just discovered, a Gaussian function that's well-localized in one space cannot be well-localized in …

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, …

Jan 23, 2015 · The periodic functions can be represented by a Fourier series. If you add up the Fourier series, you get a series that represents their sum. But their sum is not periodic, yet you …

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 …

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.

May 9, 2017 · That's a case when the "sufficient" and "necessary" properties of statements come into play. Although the square wave function really doesn't satisfies the Dirichlet conditions …

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 $...