  We examine the spectra of 23 fast radio bursts detected in a fly's-eye survey
with the Australian SKA Pathfinder, including those of three bursts not
previously reported. The mean spectral index of $\alpha = -1.6_{-0.2}^{+0.3}$
($F_\nu \propto \nu^\alpha$) is close to that of the Galactic pulsar
population. The sample is dominated by bursts exhibiting a large degree of
spectral modulation: 17 exhibit fine-scale spectral modulation with an rms
exceeding 50% of the mean, with decorrelation bandwidths (half-maximum) ranging
from $\approx$ to 49 MHz. Most decorrelation bandwidths are an order of
magnitude lower than the $\gtrsim 30\,$MHz expected of Galactic interstellar
scintillation at the Galactic latitude of the survey, $|b| = 50 \pm 5 \deg$. A
test of the amplitude distribution of the spectral fluctuations reveals only 12
bursts consistent at better than a 5% confidence level with the prediction of
100%-modulated diffractive scintillation. Moreover, five of six FRBs with a
signal-to-noise ratio exceeding 18 are consistent with this prediction at less
than 1% confidence. Nonetheless, there is weak evidence (88-95% confidence)
that the amplitude of the fine-scale spectral modulation is anti-correlated
with dispersion measure (DM) that would suggest it originates as a propagation
effect. This effect appears to be corroborated by the smoothness of the
higher-DM Parkes FRBs, and could arise due to quenching of diffractive
scintillation (e.g. in the interstellar medium of the host galaxy) by angular
broadening in the intergalactic medium.
