21. Multilevel Hadamard Decomposition of Discrete Hartley Transforms

Discrete transforms such as the Discrete Fourier Transform or the Discrete Hartley Transform 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 a DFT/DHT. The approach is based on a decomposition of the
DHT into layers of Hadamard-Walsh transforms. In particular, schemes named Turbo Fourier Transforms for short block lengths such as
N=4, 8, 12 and 24 are presented.