Extraction of Instantaneous Frequencies and Amplitudes in Nonstationary Time-Series Data

Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths modern gradient descent algorithms, Fourier transform, multi-resolution analysis, Bayesian spectral we propose data-driven approach to time-frequency that circumvents many shortcomings classic approaches, including extraction nonstationary signals with discontinuities their behavior. The method introduced equivalent {\em mode decomposition} (NFMD) nonlinear temporal signals, allowing accurate identification instantaneous frequencies amplitudes. demonstrated on time-series data, data from cantilever-based electrostatic force microscopy quantify time-dependent evolution charging dynamics at nanoscale.