%0 Journal Article %A Singh, Pushpendra %A Joshi, Shiv Dutt %A Patney, Rakesh Kumar %A Saha, Kaushik %D 2017 %T Appendix A from The Fourier decomposition method for nonlinear and non-stationary time series analysis %U https://rs.figshare.com/articles/journal_contribution/Appendix_A_from_The_Fourier_decomposition_method_for_nonlinear_and_non-stationary_time_series_analysis/4750774 %R 10.6084/m9.figshare.4750774.v1 %2 https://rs.figshare.com/ndownloader/files/7790467 %K Fourier decomposition method %K Fourier intrinsic band functions %K analytic Fourier intrinsic band functions %K zero-phase filter bank-based multivariate Fourier decomposition method %K empirical mode decomposition %X 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. %I The Royal Society