  Current fluctuations play an important role in non-equilibrium statistical
mechanics, and are a key object of interest in both theoretical studies and in
practical applications. So far, most of the studies were devoted to the
fluctuations in the time-averaged current -- the zero frequency Fourier
component of the time dependent current. However, in many practical
applications the fluctuations at other frequencies are of equal importance.
Here we study the full frequency dependence of current statistics in
periodically driven stochastic systems. First, we show a general method to
calculate the current statistics, valid even when the current's frequency is
incommensurate with the driving frequency, breaking the time periodicity of the
system. Somewhat surprisingly, we find that the cumulant generating function
(CGF), that encodes all the statistics of the current, is composed of a
continuous background at any frequency accompanied by either positive or
negative peaks at current's frequencies commensurate with the driving
frequency. We show that cumulants of increasing orders display peaks at an
increasing number of locations but with decreasing amplitudes that depend on
the commensurate ratio of frequencies. All these peaks are then transcribed in
the behaviour of the CGF. As the measurement time increases, these peaks become
sharper but keep the same amplitude and eventually lead to discontinuities of
the CGF at all the frequencies that are commensurate with the driving frequency
in the limit of infinitely long measurement. We demonstrate our formalism and
its consequences on three types of models: an underdamped Brownian particle in
a periodically driven harmonic potential; a periodically driven run-and-tumble
particle; and a two-state system.
