  A one dimensional time domain analog signal s(t) can be visualized as a
trajectory of a moving particle in a force field with one degree of freedom.
Then the power of the particle at point t is P(s(t)) = s"(t)s'(t), which is the
rate at which kinetic energy is dissipated (assuming the mass of the particle
is unit) by the particle in order to create the trajectory or give shape to the
signal. Assuming meaning of the signal or the semantic information is in its
shape, we can say that P(s(t)) is the rate at which kinetic energy of the
particle is dissipated to encode semantic information in s(t) at t. After s(t)
is digitized (to make it s[n]) the discrete form P(s[n]) is valid. Considering
the sign changes of P(s[n]) it has been shown that in the smallest neighborhood
of n, in which n is the middle point, semantic information in s[n] can be
encoded in 13 distinct ways. This list is exhaustive. A deterministic finite
automaton (DFA) has been designed which can accept any finite length digital
signal and therefore collection of all finite length digital signals forms a
regular language. The DFA has been generalized to a weighted finite state
transducer (WFST), which has been used to identify action potentials in a spike
train and also to distinguish two speakers when uttering the same phoneme. It
has been shown that in any analog signal semantic information can be encoded at
a point in the form of the shape of its infinitesimal neighborhood in 17
distinct ways. The list is exhaustive. A new entropy measure called semantic
entropy has been introduced. It has been shown that a signal s(t) is traceable
on a piece of paper or in an oscilloscope, only if s"(t) exists on all but at
most a finite number of points within any finite interval. This is an essential
condition for a signal to be the trajectory of a moving particle.
