一些离散Hartley变换矩阵的因子化方案
A Factorization Scheme for Some Discrete Hartley Transform Matrices
AI总结：
本文提出了一种高效算法，通过Hartley变换矩阵的因子化方法，达到了DFT/DHT的理论下界乘法复杂度，并给出了短块长的算法。
摘要：
离散变换如离散傅里叶变换（DFT）和离散Hartley变换（DHT）是数值分析中的重要工具。变换技术的成功应用依赖于存在高效的快速变换。本文推导了一些快速算法。DFT/DHT的乘法复杂度理论下界得以实现。该方法基于DHT矩阵的因子化。对于短块长如$N \in \{3, 5, 6, 12, 24 \}$的算法被提出。
英文摘要：
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.
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