This paper provides an introduction to an intriguing geometric phenomenon that can occur when considering narrowband bivariate signals. This so-called geometric phase may appear when the signal normalized second order instantaneous moment follows a smooth curve in the curved projective space. The resulting geometric phase is independent of the signal frequency and magnitude. Well known in quantum mechanics, optics or non-holonomic dynamical systems, the geometric phase can be computed using the concept of Bargmann invariant. It is associated to the time evolution of polarization parameters for bivariate signals. Numerical simulations on signal processing examples illustrate the pecular phenomenon of geometric phase.