A review of the discrete Fourier transform. 1. Manipulating the powers of two

Since fast algorithms for the discrete Fourier transform (DFT) were first introduced, they have had a major impact on signal processing and are now a basic part of every electrical engineer´s education. However, some of the options and advances are not as widely known as they deserve. Over two papers. The fast algorithms for the DFT are reviewed. The first paper considers why the DFT works and looks at the various fast algorithms for transforms whose orders are a power of two