中文摘要：

离散Hartley变换是一种有用的实值正交变换。文中对其快速算法进行研究，首先介绍利用算术傅里叶变换（AFT）计算离散傅里叶变换（DFT）可使其乘法计算量仅为O（N），然后文章根据这一特点，分析离散Hartley变换（DHT）的结构特征，通过DFT将AFT和DHT建立了直接联系，提出了一种新的快速DHT算法。算法的计算复杂度能够达到线性O（N），且算法结构简单，公式统一且易于实现，并与其他快速算法进行了比较，分析可知在数据长度不是2的幂次方时，文中提出的算法的计算时间明显比其他算法的计算时间要小。实验结果也验证了文中算法的有效性，从而为DHT的快速计算开辟了新的思路和途径。

英文摘要：

Discrete Hartley transform is a useful real-valued orthogonal transform. In this paper, the arithmetic Fourier transform （AFT） is used to compute discrete Fourier transform （DFT）. The multiplicity of the algorithm is only O（N）. Based on this feature,a fast algo- rithm for computing DHT is presented after analyzing the construction character of the DFr,and the multiplicity of the proposed algo-rithm is only O（N） ,the computation time of the proposed algorithm is significantly less than other algorithms while the data length is not a power of 2. The proposed algorithm is simple and its formula is unified and easy to implement,then,the proposed algorithm was com- pared with other fast algorithms and the results are also given. The results demonstrate the efficiency of the proposed algorithm and open up a new approach for the fast computation of DHT.