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...

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 transform of the …

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 …

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

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 $...

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.

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 transform in the first …

Dec 22, 2015 · Hence, the continuous fourier transform and the discrete fourier transform are related to each other by the trapezoidal rule of integration with the presence of a normalization constant in the …