  We introduce an extension of the periodogram concept to time-resolved
spectroscopy. USuRPER -- Unit Sphere Representation PERiodogram -- is a novel
technique which opens new horizons in the analysis of astronomical spectra. It
can be used to detect a wide range of periodic variability of the spectrum
shape. Essentially, the technique is based on representing spectra as unit
vectors in a multidimensional hyperspace, hence its name. It is an extension of
the phase-distance correlation (PDC) periodogram we had introduced in previous
papers, to very high-dimensional data like spectra. USuRPER takes into account
the overall shape of the spectrum, sparing the need to reduce it into a single
quantity like radial velocity or temperature. Through simulations we
demonstrate its performance in various types of spectroscopic variability --
single-lined and double-lined spectroscopic binary stars and pulsating stars.
We also show its performance on actual data of a rapidly oscillating Ap (roAp)
star. USuRPER is a new tool to explore large time-resolved spectroscopic
databases, e.g. APOGEE, LAMOST and the RVS spectra of Gaia. We have made
available to the community a public GitHub repository with a Python
implementation of USuRPER, to experiment with it and apply it to a wide range
of spectroscopic time series.
