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 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 …

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 …

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.

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.

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 …

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

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 …