ABSTRACT
In this chapter, the authors aim to make explicit the connection between the v-factor mixed-radix fast Fourier transform (FFT) algorithms and the Kronecker product factorization of the discrete Fourier transform (DFT) matrix. This process results in a sparse matrix formulation of the mixed-radix FFT algorithm. Recall that a Kronecker product is de ned for matrices of arbitrary dimensions, but standard product is de ned only for conformable matrices. The list of Kronecker product properties is not exhaustive, and the selection is based on the authors needs to decompose the DFT matrix analytically. The extension from the two-factor case to the multi-factor case was made easy using the rules of matrix algebra for Kronecker products. The authors set out the corresponding Kronecker product factorization of the DFT matrix.
