Spin-lattice relaxation rates of unentangled poly(dimethylsiloxane) (PDMS) melts of different M measured by field-cycling (FC) H-1 NMR are analyzed using a new approach. By fitting the time domain mode distribution of the Rouse model to the experimental data, interpolation of the latter is achieved and a mode separation is performed. The evolution of the Rouse relaxation spectrum with increasing M is studied. From the model parameters, the diffusion coefficient D, the Rouse time tau(R), and the statistical length are calculated, all in good agreement with literature values and the Rouse model. The new approach allows for a more accurate calculation of the segmental mean square displacement, removes previous discrepancies between FC and field-gradient NMR and verifies the relevant relaxation theory. Furthermore, for the first time, the analysis provides the radius of gyration R-G, the values of which are in agreement with literature values obtained by small-angle neutron scattering. The M-dependence R-G proportional to M-0.53 +/- 0.04 indicates ideal chain statistics down to M = 860 g/mol.