Optimal Signal Reconstruction Based on the Fourier Decomposition Method

The Fourier decomposition method (FDM) is the newest time-frequency-energy analysis tool for signals. Using the FDM, any signal can be represented by the sum of a small number of band-limited orthogonal functions termed Fourier intrinsic band functions (FIBFs). In its present form, however, the FDM is not based on an optimality criterion. The lack of optimality limits the signal recovery capability of the FDM in the presence of disturbances. To find a solution to this limitation and therefore to enhance the capability of the FDM, this paper proposes to adapt two thoughts that are previously applied for the empirical mode decomposition to the FDM. The other contribution of this paper is that we propose faster procedures than the conventional FDM in finding the FIBFs of a given signal. Simulations show that the proposed approaches result in satisfactory performance in reconstructing the original signal under undesired disturbances.