  We present a new method to estimate the average star formation rate per unit
stellar mass (SSFR) of a stacked population of galaxies. We combine the spectra
of 600-1000 galaxies with similar stellar masses and parameterise the star
formation history of this stacked population using a set of exponentially
declining functions. The strength of the Hydrogen Balmer absorption line series
in the rest-frame wavelength range 3750-4150\AA is used to constrain the SSFR
by comparing with a library of models generated using the BC03 stellar
population code. Our method, based on a principal component analysis (PCA), can
be applied in a consistent way to spectra drawn from local galaxy surveys and
from surveys at $z \sim 1$, and is only weakly influenced by attenuation due to
dust. We apply our method to galaxy samples drawn from SDSS and DEEP2 to study
mass-dependent growth of galaxies from $z \sim 1$ to $z \sim 0$. We find that,
(1) high mass galaxies have lower SSFRs than low mass galaxies; (2) the average
SSFR has decreased from $z=1$ to $z=0$ by a factor of $\sim 3-4$, independent
of galaxy mass. Additionally, at $z \sim 1$ our average SSFRs are a factor of
$2-2.5$ lower than those derived from multi-wavelength photometry using similar
datasets. We then compute the average time (in units of the Hubble time,
$t_{\rm H}(z)$) needed by galaxies of a given mass to form their stars at their
current rate. At both $z=0$ and at $z=1$, this timescale decreases strongly
with stellar mass from values close to unity for galaxies with masses $\sim
10^{10} M_{\odot}$, to more than ten for galaxies more massive than $ 10^{11}
M_{\odot}$. Our results are in good agreement with models in which AGN feedback
is more efficient at preventing gas from cooling and forming stars in high mass
galaxies.
