The vibrational properties of the hydrated proton and deuteron in bulk phase water and deuterated water are investigated spectroscopically and computationally. Mid-infrared spectra of aqueous acid solutions are measured by attenuated total reflectance-Fourier transform IR spectroscopy and compared with pure water and salt/counterion spectra to extract high-quality hydrated proton spectra at a series of concentrations. Multistate empirical valence bond simulations of the excess proton in bulk phase water are also performed, allowing the autocorrelation function of the time derivative of the dipole moment, and hence the power spectrum of the hydrated proton, to be evaluated. The experimental and theoretical spectra are found to be in very good agreement. Normal mode analysis of the bulk phase simulation data allows definitive assignment of the spectrum. The associated motions are found to be represented by both Eigen and Zundel forms of the hydrated proton.