Multilayer Hadamard Decomposition of Discrete Hartley Transforms

TL;DR

This paper introduces a multilayer Hadamard decomposition approach to develop fast algorithms for the discrete Hartley transform, achieving minimal multiplicative complexity for certain block lengths.

Contribution

It presents a novel multilayer Hadamard decomposition method to derive efficient fast algorithms for the DHT, meeting theoretical lower bounds.

Findings

Fast algorithms for N=4, 8, 12, 24 DHTs

Achieves lower bounds on multiplicative complexity

Decomposition into Walsh-Hadamard transform layers

Abstract

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.