© 2014, Gutiérrez et al.; licensee Springer. Multi-carrier (MC) signaling is currently in the forefront of a myriad of systems, either wired or wireless, due to its high spectral efficiency, simple equalization, and robustness in front of multipath and narrowband interference sources. Despite its widespread deployment, the design of efficient architectures for MC systems becomes a challenging task when adopting filter bank multi-carrier (FBMC) modulation due to the inclusion of band-limited shaping pulses into the signal model. The reason to employ these pulses is the numerous improvements they offer in terms of performance, such as providing higher spectral confinement and no frequency overlap between adjacent subcarriers. These attributes lead to a reduced out-of-band power emission and a higher effective throughput. The latter is indeed possible by removing the need of cyclic prefix, which is in charge of preserving orthogonality among subcarriers in conventional MC systems. Nevertheless, the potential benefits of FBMC modulations are often obscured when it comes to an implementation point of view. In order to circumvent this limitation, the present paper provides a unified framework to describe all FBMC signals in which both signal design and implementation criteria are explicitly combined. In addition to this, we introduce the concept of flexible FBMC signals that, unlike their traditional MC counterparts, do not impose restrictions on the signal parameters (i.e., symbol rate, carrier spacing, or sampling frequency). Moreover, our framework also proposes a methodology that overcomes the implementation issues that characterize FBMC systems and allows us to derive simple, efficient, and time-invariant transmitter and receiver architectures.