TY - DATA T1 - Appendix A from The Fourier decomposition method for nonlinear and non-stationary time series analysis PY - 2017/03/14 AU - Pushpendra Singh AU - Shiv Dutt Joshi AU - Rakesh Kumar Patney AU - Kaushik Saha UR - https://rs.figshare.com/articles/journal_contribution/Appendix_A_from_The_Fourier_decomposition_method_for_nonlinear_and_non-stationary_time_series_analysis/4750774 DO - 10.6084/m9.figshare.4750774.v1 L4 - https://ndownloader.figshare.com/files/7790467 KW - Fourier decomposition method KW - Fourier intrinsic band functions KW - analytic Fourier intrinsic band functions KW - zero-phase filter bank-based multivariate Fourier decomposition method KW - empirical mode decomposition N2 - For many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of bandlimited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms. ER -