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 …

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 the other.

Jan 15, 2015 · Fourier had to fight to get others to believe that he might be correct in his belief that such expansion could be general. Many still unfairly accuse Fourier of not having been precise at all. To …

Nov 24, 2013 · What are some real world applications of Fourier series? Particularly the complex Fourier integrals?

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

10 The Fourier transform is linear as a function whose domain consists of functions, that is, the sum of the Fourier transforms of two functions is the same as the Fourier transform of the sum. Same with …

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 …

11 Fourier Transform is a function. Fast Fourier Transform is an algorithm. It is similar to the relationship between division and long division. Division is a function, long division is a way to compute the function.

I am taking a fourier analysis course at the graduate level and I am unhappy with the textbook (Stein and Shakarchi). What I am looking for is a book that is less conversational and more to the po...