  We revisit the problem of full counting statistics of particles on a segment
of a one-dimensional gas of free fermions. Using a combination of analytical
and numerical methods, we study the crossover between the counting of discrete
particles and of the continuous particle density as a function of smoothing in
the counting procedure. In the discrete-particle limit, the result is given by
the Fisher--Hartwig expansion for Toeplitz determinants, while in the
continuous limit we recover the bosonization results. This example of full
counting statistics with smoothing is also related to orthogonality
catastrophe, Fermi-edge singularity and non-equilibrium bosonization.
