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Fast radio bursts (FRBs) can present a variety of polarization properties and some of them are characterized by narrow spectra. In this work, we study spectral properties from the perspective of intrinsic radiation mechanisms and absorption through the waves propagating in the magnetosphere. The intrinsic radiation mechanisms are considered by invoking quasi-periodic bunch distribution and perturbations on charged bunches moving on curved trajectories. The narrowband emission is likely to reflect some quasi-periodic structure on the bulk of bunches, which may be due to quasi-periodically sparking in a "gap" or quasi-monochromatic Langmuir waves. A sharp spike would appear in the spectrum if the perturbations were to induce a monochromatic oscillation of bunches; however, it is difficult to create a narrow spectrum because the Lorentz factor has large fluctuations, so the spike disappears. Both the bunching mechanism and perturbations scenarios share the same polarization properties, with a uniformly distributed bulk of bunches. We investigated the absorption effects, including Landau damping and curvature self-absorption in the magnetosphere, which are significant at low frequencies. Subluminous O-mode photons cannot escape from the magnetosphere due to the Landau damping, leading to a height-dependent lower frequency cut-off. The spectra can be narrow when the frequency cut-off is close to the characteristic frequency of curvature radiation, however, such conditions cannot always be met. The spectral index is 5/3 at low-frequency bands due to the curvature self-absorption is not as steep as what is seen in observations. The intrinsic radiation mechanisms are more likely to generate the observed narrow spectra of FRBs, rather than the absorption effects. [ABSTRACT FROM AUTHOR]