Tetraphenylphosphonium tetraphenylborate (TPTB) is a common reference electrolyte in physical chemistry of solutions allowing for a convenient partitioning of thermodynamic properties into single-ion contributions. Here, we compute on the basis of ab initio molecular dynamics simulations the infrared (IR) spectra for hydrated constituent ions of the TPTB assumption. Using spectral decomposition techniques, we extract important information pertaining to the state of the hydration water from the IR spectra. Within their physical radii, the ions manage to capture about a dozen H2O molecules, several of which penetrate deep into the grooves between the tetrahedrally oriented "sails" of the rotating ions. In accordance with previous IR and Raman experiments, we find a considerable blue shift of the ν OH stretching band of liquid water by 240 cm-1 for TB, due to the extensive O-H⋯π hydrogen bonding, which is much weaker for TP. On the other hand, both ions show a second prominent band in the ν OH vibration range, only mildly blue shifted with respect to bulk water and attributable to the general distortion of the hydrogen bond network of the neighboring solvent. Finally, spatially resolved IR spectra allow us to pinpoint the exact location around the solutes, from which different IR resonances of the solvent originate.