In this problem you will use the fast fourier transform on

\displaystyle {\ }\quad
\vec{\mathbf{f}} = \bigl( -2, 1, -2, 2, 3, -2, 2, -1 \bigr)

**(A)**
Split

**(B)**
Compute the Fourier transforms of the even and odd components:

**(C)**
Combine the Fourier transforms of the even and odd components to get the transform of

You can earn partial credit on this problem.