Understand Fourier Transforms: A Comprehensive Guide

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Does anyone know a good site that covers the Fourier series/transform and its uses?
 
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its uses are too many to be covered by one site. the idea is to look at the duality between functions on a group such as R, and functions on the dual group, in this case the circle.

It has hugely many uses including generalizations to analysis of sheaves on abelian varieties and their dual varieties.why not just start searching and reading the sites you find? or go to the "library" (a building at your school where knowledge is stored in print in "books").
 
Good idea. I thought it was broad...just not THAT broad. Thanks alot. :smile:
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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