Algebraic Derivation of General Radix Cooley-Tukey Algorithms for the Real Discrete Fourier Transform

We first show that the real version of the discrete Fourier transform (called RDFT) can be characterized in the framework of polynomial algebras just as the DFT and the discrete cosine and sine transforms. Then, we use this connection to algebraically derive a general radix Cooley-Tukey type algorithm for the RDFT The algorithm has a similar structure as its complex counterpart, but there are also important differences, which are exhibited by our Kronecker product style presentation. In particular, the RDFT is decomposed into smaller RDFTs but also other auxiliary transforms, which we then decompose by their own Cooley-Tukey type algorithms to obtain a full recursive algorithm for the RDFT