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 1 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 .