By definition, a signal involves new information or an element of 'surprise' that cannot be predicted from the wave motion at an earlier time. One possible form for a signal (at the point of emission) is: f ( t ) = u ( t ) sin ⁡ ⁡ ω ω t , where u (t) is the Heaviside step function. Using such a form for a signal, it can be shown, subject to the (expected) condition that the refractive index of any medium tends to one as the frequency tends to infinity, that the wave discontinuity, called the front, propagates at a speed less than or equal to the speed of light c in any medium. In fact, the earliest appearance of the front of an electromagnetic disturbance (the precursor) travels at the front velocity, which is c, no matter what the medium. However, the process always starts from zero amplitude and builds up.