2019年12月29日 · What is the Fourier transform? What does it do? Why is it useful (in math, in engineering, physics, etc)? This question is based on the question of Kevin Lin, which didn't …

2017年5月9日 · That's a case when the "sufficient" and "necessary" properties of statements come into play. Although the square wave function really doesn't satisfies the Dirichlet …

2012年12月15日 · The Fourier transform projects functions onto the plane wave basis - basically a collection of sines and cosines. A Fourier series is also a projection, but it's not continuous - …

2015年12月22日 · 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 …

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 …

0 One could derive the formula via dual numbers and using the time shift and linearity property of the Fourier transform.

2012年4月24日 · We know that the Fourier transform of the sinc function is the rectangular function (or top hat). However, I'm at a loss as to how to prove it. Most textbooks and online …

2012年10月26日 · 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, …

2020年8月30日 · This might be a good approach. However, the Fourier inversion theorem is valid only for a subset of functions, so it seems that more caution is required.

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 …