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ColdFusion85

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**[SOLVED] Trouble Understanding the Fourier Integral**

I am having a bit of trouble understanding how to use the Fourier Integral Formula.

The integral is [tex]\int_{0}^{\infty} [A_{\omega}cos(\omega x) + B_{\omega}sin(\omega x)]d\omega[/tex]

Where,

[tex]A_{\omega} = \frac{1}{\pi}\int_{-\infty}^{\infty} f(\xi)cos(\omega\xi)d\xi[/tex]

and

[tex]B_{\omega} = \frac{1}{\pi}\int_{-\infty}^{\infty} f(\xi)sin(\omega\xi)d\xi[/tex]

The example in the book doesn't help because f(x) is 1 for -1<=x<=1, and 0 for |x|>1. This doesn't clear up my confusion as to what the integral is supposed to look like with [tex]f(\xi)[/tex] inserted. What is [tex]f(\xi)[/tex]? Is it the function given, f(x)? Like if I had f(x) = sin(x) on [-2, 2], would A_w look like:

[tex]A_{\omega} = \frac{1}{\pi}\int_{-2}^{2} sin(x)cos(\omega\xi)d\xi[/tex],

with sin(x) being treated as a constant that can be brought outside the integral, or am I supposed to make A_w be

[tex]A_{\omega} = \frac{1}{\pi}\int_{-2}^{2} sin(x)cos(\omega x)dx[/tex]?

This is where I am confused.