离散Hartley变换的多层Hadamard分解
Multilayer Hadamard Decomposition of Discrete Hartley Transforms
摘要：
离散傅立叶变换（DFT）或离散哈特莱变换（DHT）等离散变换是信号处理中不可缺少的工具。变换技术的成功应用依赖于所谓快速变换的存在。本文给出了满足DFT/DHT乘法复杂度下界的快速算法。该方法是基于分解成层的沃尔什-哈达玛变换的DHT。特别是，快速算法短块长度，如$N \in \{4, 8, 12, 24\}$。
英文摘要：
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.
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