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...

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

Aug 19, 2012 · Fourier transform of even/odd function Ask Question Asked 13 years, 5 months ago Modified 2 years, 10 months ago

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 …

Apr 29, 2024 · I tried using the standard Fourier transform formula and then tried using the convolution theorem. I reached the correct answer by using the formula, but I seem to have the scaling factor …

Computing the Fourier coefficients and series for $\log (\sin (x))$ Ask Question Asked 11 years ago Modified 2 months ago

Jan 7, 2019 · I usually know that we use the continuous Fourier transform on non-periodic signals and Fourier series on periodic signals. However there're signals like cos cos, ei2πft e i 2 π f t and others …

Mar 10, 2025 · I have come across a $\\textbf{non-formal}$ proof of Fourier's Inversion theorem and I wanted to know if reversing the order of the proof one may still use it and gain formality. The proof is: …

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 …

The Fourier transforms in (1) and (2) above both assume the Fourier parameters $\ {0,\,-2\,\pi\}$. Question 1: What is the relationship between the Cosine terms in the distributional framework and …