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...

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, …

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 · Fourier transform commutes with linear operators. Derivation is a linear operator. Game over.

Oct 27, 2019 · What are some real world applications of Fourier series? Particularly the complex Fourier integrals?

You seem to be assuming that it is an either/or situation. It isn't. A wave can be all three: odd (OR even), have half wave symmetry, and also have quarter wave symmetry. All your examples …

Jun 15, 2012 · I'm preparing for an exam in the signals and systems class I'm taking. One of the practice exams has a problem that requires you to take the Fourier transform of $\text {sinc} …

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 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 …

May 6, 2017 · Does that mean that the function is valued 2π−−√ 2 π at all points in the frequency domain? I think this is reasonable because such function i.e. f(t) = 1 f (t) = 1 in the time domain …