Notes on the FFT

K. Levasseur - Discrete Structures II

Objective

Given a list of N values from a field F,  [Graphics:Images/FFT_gr_1.gif], the discrete Fourier Transform of [Graphics:Images/FFT_gr_2.gif] with respect to [Graphics:Images/FFT_gr_3.gif] is

    [Graphics:Images/FFT_gr_4.gif]
    
If you evaluate each of these sums separately, you need [Graphics:Images/FFT_gr_5.gif] multiplications.

Primitive Roots of Unity

Binary Splitting

The FFT - multiple binary splitting

The Inverse DFT

Complex Primitive Roots of Unity

Links

An example of the FFT in industry:
http://www.edtn.com/scribe/reference/appnotes/md000503.htm

Information about Alexandre Théophile Vandermonde

Converted by Mathematica      May 10, 2000