Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral analysis, we propose a data-driven approach to time-frequency analysis that circumvents many of the shortcomings of classic approaches, including the extraction of nonstationary signals with discontinuities in their behavior. The method introduced is equivalent to a {\em nonstationary Fourier mode decomposition} (NFMD) for nonstationary and nonlinear temporal signals, allowing for the accurate identification of instantaneous frequencies and their amplitudes. The method is demonstrated on a diversity of time-series data, including on data from cantilever-based electrostatic force microscopy to quantify the time-dependent evolution of charging dynamics at the nanoscale.
翻译:时间序列分析对于科学和工程的多种应用至关重要。 通过利用现代梯度下沉算法、Fourier变换、多分辨率分析和Bayesian光谱分析的优势,我们提出了一个数据驱动的时间频率分析方法,以绕过经典方法的许多缺点,包括提取非静止信号及其行为不连续性。引入的方法相当于非静止和非静止的Fourier模式分解信号和非线性时间信号(NFMD ), 以便准确识别瞬时频率及其振幅。该方法通过时间序列数据的多样性,包括基于罐头的电动显微镜的数据,来量化纳米级充电动态的根据时间演变。