A Vibration Energy Harvester (VEH) converts the kinetic energy of a moving source into electrical energy. Here we consider a one-dimensional electromagnetic vibration energy harvester (1D-EMVEH) which consists of three coaxial cylindrical permanent magnets enclosed in a tube, such that the middle magnet is levitating. The resulting movement of the middle magnet can then induce an electromotive force (emf) in one or more surrounding coils. Using an analytical model, we derive expressions for the 1D-EMVEHs characteristic frequency and output power by using Fourier space approach. First, the magnetostatic energy of the system as a function of the position of the levitating magnet is calculated. Its spatial gradient gives the force acting on a magnet, which drives its dynamics. Next, more accurate magnetic flux and emf expressions are obtained. The results are compared with experimental measurements, revealing an excellent agreement.