  In this work we have proposed a rigorous mathematical definition for the one
dimensional time domain electrophysiological signals and established its
relationship with two of the three Dirichlet's conditions. We have argues that
any such signal can be represented as the trajectory of a particle moving in a
force field with one degree of freedom. At point on the trajectory, that is, on
the signal, the kinetic energy dissipated by the particle embeds semantic
information into the trajectory or the signal in terms of giving its shape. We
have shown that the rate of kinetic energy dissipation operator or the power
operator P is of importance in shape analysis of the signal by considering its
sign changes. Operating the P-operator on digital signals we have
mathematically proved that its sign change can induce 13 different shapes to a
three successive point configuration. In other words, semantic information at
each point in a digital signal can be embedded by a syllable of 13 different
letters. We have shown some preliminary applications.
