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Fourier Transforms

The basic equation for the fourier transform.

F(k) = \int f(x) e^{(-2 \pi k x)} dx

Here we want to solve

f(x) = sgn(x)

begin{align*} f(x) \\ & = -1 if x >0\\ & = 1 if x < 0\\ \end{align*}

(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}

Description of Problem

Results

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Results

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