  Broad-band measurements of flux for galaxies at different redshifts measure
different regions of the rest-frame galaxy spectrum. Certain astronomical
questions, such as the evolution of the luminosity function of galaxies,
require transforming these magnitudes into redshift-independent quantities. To
prepare to address these astronomical questions, investigated in detail in
subsequent papers, we fit spectral energy distributions (SEDs) to broad band
photometric observations, in the context of the optical observations of the
Sloan Digital Sky Survey (SDSS). Linear combinations of four spectral templates
can reproduce the five SDSS magnitudes of all galaxies to the precision of the
photometry. Expressed in the appropriate coordinate system, the locus of the
coefficients multiplying the templates is planar, and in fact nearly linear.
The resulting reconstructed SEDs can be used to recover fixed frame magnitudes
over a range of redshifts. This process yields consistent results, in the sense
that within each sample the intrinsic colors of similar type galaxies are
nearly constant with redshift. We compare our results to simpler interpolation
methods and galaxy spectrophotometry from the SDSS. The software that generates
these results is publicly available and easily adapted to handle a wide range
of galaxy observations.
