  A growing number of experimental set-ups in cavity optomechanics exploit
periodically driven fields. However, such set-ups are not amenable to analysis
using simple, yet powerful, closed-form expressions of linearized
optomechanics, which have provided so much of our present understanding of
experimental optomechanics. In the present paper, we formulate a new method to
calculate quantum noise spectra in modulated optomechanical systems, which we
analyze, compare, and discuss with two other recently proposed solutions: we
term these (i) frequency-shifted operators (ii) Floquet and (iii) iterative
analysis. We prove that (i) and (ii) yield equivalent noise spectra, and find
that (iii) is an analytical approximation to (i) for weak modulations. We
calculate the noise spectra of a doubly-modulated system describing experiments
of levitated particles in hybrid electro-optical traps. We show excellent
agreement with Langevin stochastic simulations in the thermal regime and
predict squeezing in the quantum regime. Finally, we reveal how experimentally
inaccessible spectral components of a modulated system can be measured in
heterodyne detection through an appropriate choice of modulation frequencies.
