  We present a general framework for accurate spectral modeling of the low
multipoles of the cosmic microwave background (CMB) as observed in a boosted
frame. In particular, we demonstrate how spectral measurements of the low
multipoles can be used to separate the motion-induced dipole of the CMB from a
possible intrinsic dipole component. In a moving frame, the leakage of an
intrinsic dipole moment into the CMB monopole and quadrupole induces spectral
distortions with distinct frequency functions that respectively peak at 337 GHz
and 276 GHz. The leakage into the quadrupole moment also induces a geometrical
distortion to the spatial morphology of this mode. The combination of these
effects can be used to lift the degeneracy between the motion-induced dipole
and any intrinsic dipole that the CMB might possess. Assuming the current
peculiar velocity measurements, the leakage of an intrinsic dipole with an
amplitude of $\Delta T = 30\mu$K into the monopole and quadrupole moments will
be detectable by a PIXIE--like experiment at $\sim 40~$nK ($2.5\sigma$) and
$\sim 130~$nK ($11\sigma$) level at their respective peak frequencies.
