  Recent observations have shown that repeating Fast Radio Bursts (FRBs)
exhibit band-limited emission, whose frequency-dependent amplitude can be
modeled using a Gaussian function. In this analysis, we show that banded
emission of FRBs can lead to incompleteness across the observing band. This
biases the detected sample of bursts and can explain the various shapes of
cumulative energy distributions seen for repeating FRBs. We assume a Gaussian
shape of the burst spectra and used simulations to demonstrate the above bias
using an FRB 121102-like example. We recovered energy distributions that showed
a break in power-law and flattening of power-law at low energies, based on the
fluence threshold of the observations. We provide recommendations for
single-pulse searches and analysis of repeating FRBs to account for this
incompleteness. Primarily, we recommend that burst spectra should be modeled to
estimate the intrinsic fluence and bandwidth of the burst robustly. Also,
bursts that lie mainly within the observing band should be used for analyses of
energy distributions. We show that the bimodality reported in the distribution
of energies of FRB 121102 by Li et al. (2021) disappears when burst bandwidth,
instead of the center frequency of the observation, is used to estimate energy.
Sub-banded searches will also aid in detecting band-limited bursts. All the
analysis scripts used in this work are available in a Github repository.
