Abstract
Fourier decomposition method (FDM) is an adaptive data-driven time-frequency analysis tool developed recently for nonlinear and non-stationary time series. This method intrinsically decomposes any signal into a small number of band-limited zero-mean orthogonal functions called as Fourier intrinsic band functions (FIBFs) via zero-phase ideal band-pass filters, and can represent the signal by these functions completely. As a result of using ideal band-pass filters, however, the FDM is not appropriate for analyzing multicomponent signals with intersecting instantaneous frequencies. It results in dispersed time-frequency representation (TFR) of such signals. To offer a solution to this inadequacy of the FDM, a generalized version of the FDM, termed interwoven FDM (IWFDM), is proposed in this paper. Unlike FDM, the IWFDM decomposes signal into analytical FIBFs through the zero-phase non-rectangular band-pass filters. The characteristics of these filters are determined such that the sum of all FIBFs guarantees the full reconstruction of signal. Similar to FDM, the IWFDM is an adaptive data-driven method. Through the IWFDM, clear TFRs of the multicomponent signals are provided. Comparisons made with the FDM and the empirical mode decomposition method on several multicomponent signals confirm the success of the IWFDM.
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