In crystalline nanoparticles, the Raman peak is downshifted with respect to the bulk material and has asymmetric broadening. These effects are straightly related to the finite size of nanoparticles, giving the perspective to use Raman spectroscopy as the size probe. By combining the dynamical matrix method (DMM) and the bond polarization model (BPM), we develop a new (DMM-BPM) approach for the description of Raman spectra of nanoparticle powders. The numerical variant of this approach is suitable for the description of small particles, whereas its analytical version is simpler to implement and allows one to obtain the Raman spectra of arbitrary-sized particles. Focusing on nanodiamond powders, the DMM BPM theory is shown to fit the most recent experimental data much better than the commonly used phonon confinement model.