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, nonperiodic function by …

Apr 9, 2020 · 7 Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its …

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

Jun 12, 2020 · Fourier Transform for triangular wave Ask Question Asked 11 years, 10 months ago Modified 6 years, 9 months ago

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 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 8, 2026 · Inverse Fourier transform for the square root of the Ohmic bath spectral function fourier-transform Nov 26, 2025 at 13:59

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 …

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 …