The paper analyzes the feasibility of cost-effective fiber sensors for the measurement of small vibrations, from low to medium-high frequencies, in which the complexity of the measurement is moved from expensive optics to cheap electronics without losing too much performance thanks to signal processing algorithms. Two optical approaches are considered: Bragg gratings in standard telecom fibers, which represent the most common type of commercial fiber sensors, and specifically developed sensors made with plastic optical fibers. In both cases, to keep the overall cost low, vibrations are converted into variations of the light intensity, although this makes the received signal more sensitive to noise. Then, adaptive filters and advanced spectral estimation techniques are used to mitigate noise and improve the sensitivity. Preliminary results have demonstrated that the combined effect of these techniques can yield to a signal-to-noise improvement of about 30 dB, bringing the proposed approaches to the level of the most performing sensors for the measurement of vibrations.