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This paper presents a unified framework for the formulation of synchronization algorithms dealing with the general class of Filter-Bank Multi-Carrier (FBMC) communication signals. This is a wide family of signaling formats that includes Orthogonal Frequency Division Multiplexing (OFDM), for instance, as just one of many particular cases. One of the main contributions of this work is the proposal of a novel matrix signal model for so-called flexible FBMC signals, in which no restrictions are imposed on the signal design parameters (i.e., pulse shaping, symbol rate, carrier spacing, sampling frequency, etc.), unlike the type of multicarrier signals currently deployed. As an example of application of the proposed matrix signal model, blind joint time-delay and frequency estimators will be derived under both the Conditional Maximum Likelihood (CML) and the low-SNR Unconditional Maximum Likelihood (UML) principles, for any FBMC signal propagating through an arbitrary multipath channel. These estimators will be specialized first for the case of critically sampled cyclic-prefix OFDM (CP-OFDM) signals in frequency flat fading, leading to simple architectures amenable to a hardware implementation. Later on, and for the low-SNR UML principle, the special case of critically sampled CP-OFDM in multipath channels will be addressed, where a novel synchronizer will be proposed.