  Discrete transforms such as the discrete Fourier transform (DFT) or the
discrete Hartley transform (DHT) furnish an indispensable tool in signal
processing. The successful application of transform techniques relies on the
existence of the so-called fast transforms. In this paper some fast algorithms
are derived which meet the lower bound on the multiplicative complexity of the
DFT/DHT. The approach is based on a decomposition of the DHT into layers of
Walsh-Hadamard transforms. In particular, fast algorithms for short block
lengths such as $N \in \{4, 8, 12, 24\}$ are presented.
