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We advance theoretical methods for studying propagation effects in the FastRadio Burst (FRB) spectra. We derive their autocorrelation function in themodel with diffractive lensing and strong Kolmogorov-type scintillations andanalytically obtain the spectra lensed on different plasma density profiles.With these tools, we reanalyze the highest frequency 4-8 GHz data of Gajjar etal. (2018) for the repeating FRB 20121102A (FRB 121102). In the data wediscover, first, a remarkable spectral structure of almost equidistant peaksseparated by $95\pm 16$ MHz. We suggest that it can originate from diffractivelensing of the FRB signals on a compact gravitating object of mass $10^{-4}\,M_\odot$ or on a plasma underdensity near the source. Second, the spectrainclude erratic interstellar, presumably Milky Way scintillations. We extracttheir decorrelation bandwidth $3.3\pm 0.6$ MHz at reference frequency 6 GHz.The third feature is a GHz-scale pattern which, as we find, linearly driftswith time and presumably represents a wide-band propagation effect, e.g.GHz-scale scintillations. Fourth, many spectra are dominated by a narrow peakat 7.1 GHz. We suggest that it can be caused by a propagation through a plasmalens, e.g., in the host galaxy. Fifth, separating the propagation effects, wegive strong arguments that the intrinsic progenitor spectrum has narrow GHzbandwidth and variable central frequency. This confirms expectations from theprevious observations. We discuss alternative interpretations of the abovespectral features.

Propagation effects in the FRB 20121102A spectra