  It is shown that differential Doppler shift of different patches of the
blastwave front in the fireball model at varying angles to the line of sight
could provide an intrinsic smoothing mechanism for the spectra of gamma-ray
bursts (GRBs) and the associated afterglows at lower energy bands. For the
model parameters of interest, it is illustrated that a monochromatic spectrum
at $\nu$ in blastwave comoving frame is smoothed and observed to have a
half-width-half-maximum (HWHM) of $\sim (0.6-2.0)\nu$. Some other implications
of this smoothing process are discussed. In particular, if the circumburster
medium is uniform and electron and magnetic energies are fixed fractions of the
total post-shock energy with time, the observed GRB or afterglow spectra cannot
be steeper than $\nu^{-\alpha}$ with $\alpha=0.75-1.25$, regardless of the
intrinsic spectra in the comoving shock frame; i.e., a very steep electron
distribution function (with $p>3$) could produced an observed spectrum with
$\alpha\sim 1$. In addition, a generic fast-rise-slow-decay type of GRB
temporal profile is expected.
