  Discrete transforms such as the discrete Fourier transform (DFT) and the
discrete Hartley transform (DHT) are important tools in numerical analysis. The
successful application of transform techniques relies on the existence of
efficient fast transforms. In this paper some fast algorithms are derived. The
theoretical lower bound on the multiplicative complexity for the DFT/DHT are
achieved. The approach is based on the factorization of DHT matrices.
Algorithms for short blocklengths such as $N \in \{3, 5, 6, 12, 24 \}$ are
presented.
