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 quite fit in Mathoverflow.

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, …

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.

Feb 13, 2019 · 0 Fourier Series of Triangular waveform this is the solution of Fourier series of a triangular waveform from the book Circuits and Networks: Analysis and Synthesis by …

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

Aug 11, 2018 · The full proof of the Fourier inversion theorem holds for absolutely integrable continuous functions, with absolutely integrable Fourier transforms.

I'm studying about Fourier series and transform and I get confused with the following Matlab example of Fourier transformation: Fs = 1000; % Sampling frequency T = 1/Fs; ...

May 6, 2017 · 1 I know that this has been answered, but it's worth noting that the confusion between factors of $2\pi$ and $\sqrt {2\pi}$ is likely to do with how you define the Fourier …

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 …