The discrete double Fourier transform (DDFT) was developed to search for large-scale multi-periodic patterns in the presence of noise and is based on detection of the equidistant series of harmonics generated by the periodic patterns in the discrete Fourier transform (DFT) spectra. As DDFT retains all generic features of the Fourier transform, the corresponding pattern correlation function (PCF) related to DDFT can be introduced similarly to the data correlation function (DCF) related to DFT on the basis of the Wiener–Khinchin relationship. Peaks in PCF indicate the number of periodic patterns in a dataset under analysis and have direct correspondence with the counterpart peaks in the DFT spectrum. The close correspondence between positions of the peaks in the PCF and DFT spectra strongly enhances statistical significance of detected periodicities. Similar PCFs can also be defined for the cepstrum transform. The combined DFT–DCF and DDFT–PCF technique was applied to the detection of cycles in geomagnetic activity using disturbance storm-time (Dst) index. In addition to the known 27-day, semiannual and 11-year cycles of geomagnetic activity, we have also found the annual cycle of activity. The results were compared with those obtained by the cepstrum transform. A multiple cross-check makes the combined technique much more efficient and robust in comparison with the detection based on a unique particular method.

中文翻译：

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用离散双傅里叶变换检测大规模噪声多周期模式。二、模式间相关性研究

离散双傅里叶变换 (DDFT) 是为了在存在噪声的情况下搜索大规模多周期模式而开发的，它基于对离散傅里叶变换 (DFT) 光谱中周期模式产生的等距谐波系列的检测. 由于 DDFT 保留了傅里叶变换的所有通用特征，因此可以在 Wiener-Khinchin 关系的基础上引入与 DFT 相关的数据相关函数（DCF）类似的与 DDFT 相关的模式相关函数（PCF）。PCF 中的峰值表示正在分析的数据集中周期性模式的数量，并且与 DFT 频谱中的对应峰值直接对应。PCF 和 DFT 光谱中峰位置之间的密切对应强烈地增强了检测到的周期性的统计显着性。也可以为倒谱变换定义类似的 PCF。将 DFT-DCF 和 DDFT-PCF 组合技术应用于使用扰动风暴时间 (Dst) 指数检测地磁活动的周期。除了已知的 27 天、半年和 11 年的地磁活动周期外，我们还发现了年活动周期。将结果与倒谱变换得到的结果进行比较。与基于独特的特定方法的检测相比，多重交叉检查使组合技术更加有效和稳健。半年和 11 年的地磁活动周期，我们也发现了年活动周期。将结果与倒谱变换得到的结果进行比较。与基于独特的特定方法的检测相比，多重交叉检查使组合技术更加有效和稳健。半年和 11 年的地磁活动周期，我们也发现了年活动周期。将结果与倒谱变换得到的结果进行比较。与基于独特的特定方法的检测相比，多重交叉检查使组合技术更加有效和稳健。