The Discrete Fourier Transform

By R. Northrop. Essentials of Geophysical Data Processing, 2010

165 citations recorded by the source corpus.

These N numbers are called the Nth roots of unity. They can be viewed as the first N powers of e 2π N j , which is a rotation 1 N of the way around the complex Unit Circle. We will use the notation ωN e 2π N j ,1 so that the Nth roots of unity are ω0N , ω 1 N , . . . , ω N−1 N . 1Any power ωr N , where r is prime to N , will also generate all N roots of unity! This fact is amazing! Please ask me why in office hours!

View Paper: https://www.semanticscholar.org/paper/127add8b9d6def81c4c85e1ed2a78a91d277241d