Anomalous diffusion processes are usually detected by analyzing the time-dependent mean square displacement of the diffusing particles. The latter evolves asymptotically as W(t) approximately 2Dalphat(alpha), where Dalpha is the fractional diffusion constant and 0 < alpha < 2. In this article we show that both Dalpha and alpha can also be extracted from the low-frequency Fourier spectrum of the corresponding velocity autocorrelation function. This offers a simple method for the interpretation of quasielastic neutron scattering spectra from complex (bio)molecular systems, in which subdiffusive transport is frequently encountered. The approach is illustrated and validated by analyzing molecular dynamics simulations of molecular diffusion in a lipid POPC bilayer.