Synthetic datasets are widely used in applications like missing data imputation, simulations, training data-driven models, and system robustness analysis. Typically based on historical data, these datasets need to represent specific system behaviors while being diverse enough to challenge the system with a broad range of inputs. This paper introduces a method using discrete Fourier transform to generate synthetic time series with similar statistical moments to any given signal. The method allows control over the similarity level between the original and synthetic signals. Analytical proof shows that this method preserves the first two statistical moments and the autocorrelation function of the input signal. It is compared to ARMA, GAN, and CoSMoS methods using various environmental datasets with different temporal resolutions and domains, demonstrating its generality and flexibility. A Python library implementing this method is available as open-source software.

中文翻译：

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具有相似性控制的合成随机环境时间序列生成，保留原始信号的统计特征


合成数据集广泛用于缺失数据插补、模拟、训练数据驱动模型和系统稳健性分析等应用。这些数据集通常基于历史数据，需要表示特定的系统行为，同时又足够多样化，以便通过广泛的输入来挑战系统。本文介绍了一种使用离散傅里叶变换生成与任何给定信号具有相似统计矩的合成时间序列的方法。该方法允许控制原始信号和合成信号之间的相似度级别。分析证明表明，该方法保留了输入信号的前两个统计矩和自相关函数。它使用具有不同时间分辨率和域的各种环境数据集将其与 ARMA、GAN 和 CoSMoS 方法进行了比较，展示了其通用性和灵活性。实现此方法的 Python 库作为开源软件提供。