  We present a technique for recovering the spectrum of a non-Markovian bosonic
bath and/or non-Markovian noises coupled to an harmonic oscillator. The
treatment is valid under the conditions that the environment is large and hot
compared to the oscillator, and that its temporal auto-correlation functions
are symmetric with respect to time translation and reflection -- criteria which
we consider fairly minimal. We model a demonstration of the technique as
deployed in the experimental scenario of a nanosphere levitated in a Paul trap,
and show that it would effectively probe the spectrum of an electric field
noise source from $10^2\,-\,10^6$ Hz with a resolution inversely proportional
to the measurement time. This technique may be deployed in quantum sensing,
metrology, computing, and in experimental probes of foundational questions
