Abstract: To reduce the high complexity of the window computation using the biorthogonal relationship between the analysis window and the synthesis window in the Real-valued Discrete Gabor Transform（RDGT） for infinite or long sequences, this paper presents a fast algorithm based on the Discrete Hartley Transform（DHT）. By transforming the equation set of the biorthogonal relationship into the form of DHT, the equation set can be separated into several independent sub-equation sets so that the computational complexity can be reduced. The experimental results also indicate that the proposed fast algorithm is correct and effective.

Key words: long sequences, Real-valued Discrete Gabor Transform（RDGT）, fast algorithm

摘要： 为了降低在无限（长）序列实值离散Gabor变换（RDGT）中利用分析窗与综合窗之间的双正交关系计算窗函数的复杂度，提出了一种基于离散Hartley变换（DHT）的快速求解算法。通过将双正交关系式写成离散Hartley变换的形式，原方程组可被分解成若干个独立的子方程组以降低计算的复杂度。实验结果也验证了提出的快速算法的正确性和有效性。

关键词: 长序列, 实值离散Gabor变换, 快速求解算法