  Methods are developed for constructing spectral representations of cold
(barotropic) neutron-star equations of state. These representations are
faithful in the sense that every physical equation of state has a
representation of this type, and conversely every such representation satisfies
the minimal thermodynamic stability criteria required of any physical equation
of state. These spectral representations are also efficient, in the sense that
only a few spectral coefficients are generally required to represent
neutron-star equations of state quiet accurately. This accuracy and efficiency
is illustrated by constructing spectral fits to a large collection of
"realistic" neutron-star equations of state.
