Computation of Discrete Fourier Transforms by Polynomial Transforms

As indicated in the previous chapter, polynomial transforms can be used to efficiently map multidimensional convolutions into one-dimensional convolutions and polynomial products. In this chapter, we shall see that polynomial transforms can also be used to map multidimensional DFTs into one-dimensional DFTs. This mapping is very efficient because it is accomplished using ordinary arithmetic without multiplications, and because it can be implemented by FFT-type algorithms when the dimensions are composite.