An exact theory is developed with the aim of assessing the properties of the harmonics spectrum of the dynamic magnetization originating from superparamagnetic nanoparticles submitted to a high-frequency driving field. The magnetization is assumed to be always close to equilibrium at the frequencies of interest, so that it can still be described by the anhysteretic Langevin function. The theory, valid for an extended range of values of physical properties and sizes of particles, is aimed at interpreting typical results of mag-netic particle spectroscopy and imaging. The analytical framework is exploited to get a deeper knowledge of the spectral properties of nanoparticle magnetization and to assess the persistence of the superpara-magnetic behavior at the operating frequencies. The spectral properties of the time-dependent Langevin function are analyzed in detail and compared with experimental results on polydisperse, immobilized nanoparticles. The system function usually exploited in magnetic particle imaging is calculated with precision as a function of both particle size and driving field's amplitude.