  Quantum harmonic oscillators are central to many modern quantum technologies.
We introduce a method to determine the frequency noise spectrum of oscillator
modes through coupling them to a qubit with continuously driven
qubit-state-dependent displacements. We reconstruct the noise spectrum using a
series of different drive phase and amplitude modulation patterns in
conjunction with a data-fusion routine based on convex optimization. We apply
the technique to the identification of intrinsic noise in the motional
frequency of a single trapped ion with sensitivity to fluctuations at the
sub-Hz level in a spectral range from quasi-DC up to 50 kHz.
