Stellar populations of galaxies in the ALHAMBRA survey up to $z \sim 1$.
  I. MUFFIT: A Multi-Filter Fitting code for stellar population diagnostics
  We present MUFFIT, a new generic code optimized to retrieve the main stellar
population parameters of galaxies in photometric multi-filter surveys, and we
check its reliability and feasibility with real galaxy data from the ALHAMBRA
survey. Making use of an error-weighted $\chi^2$-test, we compare the
multi-filter fluxes of galaxies with the synthetic photometry of mixtures of
two single stellar populations at different redshifts and extinctions, to
provide through a Monte Carlo method the most likely range of stellar
population parameters (mainly ages and metallicities), extinctions, redshifts,
and stellar masses. To improve the diagnostic reliability, MUFFIT identifies
and removes from the analysis those bands that are significantly affected by
emission lines. We highlight that the retrieved age-metallicity locus for a
sample of $z \le 0.22$ early-type galaxies in ALHAMBRA at different stellar
mass bins are in very good agreement with the ones from SDSS spectroscopic
diagnostics. Moreover, a one-to-one comparison between the redshifts, ages,
metallicities, and stellar masses derived spectroscopically for SDSS and by
MUFFIT for ALHAMBRA reveals good qualitative agreements in all the parameters.
In addition, and using as input the results from photometric-redshift codes,
MUFFIT improves the photometric-redshift accuracy by $\sim 10$-$20\%$, and it
also detects nebular emissions in galaxies, providing physical information
about their strengths. Our results show the potential of multi-filter galaxy
data to conduct reliable stellar population studies with the appropiate
analysis techniques, as MUFFIT.
