Fast radio bursts (FRBs) are millisecond-duration radio transients with extremely high brightness temperatures at cosmological distances, and the physical origin and the radiation mechanism of FRBs are still unknown. The observed spectral bandwidth of some FRBs appeared narrow compared with their peak frequencies, which could be used to constrain the radiation mechanism and the astrophysical environment of FRBs. In this work, we investigate some of the possible physical origins of the narrow spectra from the perspectives of intrinsic radiation mechanisms, coherent processes, radiative transfers, and interference processes. We find that: (1) If the observed narrow spectra of FRBs are attributed to the intrinsic radiation mechanism by a single charged particle, the particle's deflection angle should be much smaller than the radiation beaming angle. (2) Coherent process can cause narrow spectra. For the bunching mechanism, the narrow spectra might arise from the radiating bunches with a quasiperiodic distribution. For the maser mechanism, the negative absorption process can naturally cause a narrow spectrum. (3) Most absorption and scattering processes seem not to significantly change the observed spectra based on the current observation of some FRB repeaters. (4) Scintillation and plasma lensing in the FRB source environment can modulate the spectra, leading to the narrow spectra and the burst-to-burst variation of spectra. A planet-like object can generate the spectral modulation via gravitational lensing at the gigahertz band, but the observed burst-to-burst variation of the spectra does not support this scenario.
