# Fourier Transform Question

1. Feb 24, 2007

### bodensee9

1. The problem statement, all variables and given/known data

Hi, Can someone explain the following?

This is in the book but I wasn't clear. So, I am given the following formulas for constructing the "y" vector from the equation Fc= y, and since I'm doing a fast fourier transform, I am supposed to construct the "y" from these "half-y's". The formula is

So I am supposed to split the "c" into even and odd components. And then apparently, the jth component of y, yj = y(even)j + w^j*y(odd)j, for j = 0 .... m - 1
and the j+m component of y, y(j+m) = y (even)j - w^jy(odd)j. for j = 0 .... m - 1.
w should be the root to the jth power from the equation w^n = 1.

Can someone explain what that means or how I would go about constructing such a vecto? There are no examples in the book. So, suppose that I rearrange and multiply by a fourier matrix F and I get half vectors [40000000] (vertical vector), how would I go about finding vector y?

Thanks.