  Characterization and suppression of noise are essential for the control of
harmonic oscillators in the quantum regime. We measure the noise spectrum of a
quantum harmonic oscillator from low frequency to near the oscillator resonance
by sensing its response to amplitude modulated periodic drives with a qubit.
Using the motion of a trapped ion, we experimentally demonstrate two different
implementations with combined sensitivity to noise from 500 Hz to 600 kHz. We
apply our method to measure the intrinsic noise spectrum of an ion trap
potential in a previously unaccessed frequency range.
