  Two major features of the prestellar CMF are: 1) a broad peak below 1 Msun,
presumably corresponding to a mean gravitational fragmentation scale, and 2) a
characteristic power-law slope, very similar to the Salpeter slope of the
stellar initial mass function (IMF) at the high-mass end. While recent Herschel
observations have shown that the peak of the prestellar CMF is close to the
thermal Jeans mass in marginally supercritical filaments, the origin of the
power-law tail of the CMF/IMF at the high-mass end is less clear. Inutsuka
(2001) proposed a theoretical scenario in which the origin of the power-law
tail can be understood as resulting from the growth of an initial spectrum of
density perturbations seeded along the long axis of filaments by interstellar
turbulence. Here, we report the statistical properties of the line-mass
fluctuations of filaments in nearby molecular clouds observed with Herschel
using a 1-D power spectrum analysis. The observed filament power spectra were
fitted by a power-law function $(P_{true}(s) \propto s^{\alpha})$ after
removing the effect of beam convolution at small scales. A Gaussian-like
distribution of power-spectrum slopes was found centered at -1.6, close to that
of the one-dimensional velocity power spectrum generated by subsonic
Kolomogorov turbulence (-1.67). An empirical correlation, $P^{0.5}(s_0) \propto
<N_{\rm H_2}>^{1.4 \pm 0.1} $, was also found between the amplitude of each
filament power spectrum $P(s_0)$ and the mean column density along the filament
$<N_{\rm H_2}>$. Finally, the dispersion of line-mass fluctuations along each
filament $\sigma_{\rm M_{line}}$ was found to scale with the physical length
$L$ of the filament, roughly as $\sigma_{M_{line}} \propto L^{0.7}$. Overall,
our results are consistent with the suggestion that the bulk of the CMF/IMF
results from the gravitational fragmentation of filaments.
