Coherent Raman vibrations in solid, liquid and gas phase samples, excited by impulsive stimulated Raman scattering, are probed via optical spectral interferometry. High vibrational spectral resolution is possible with a synthetic temporal aperture technique and we investigate the effects of this approach numerically. Measured spectra are determined either by direct Fourier transform or by linear prediction. This new Raman spectroscopy technique is shown to be well-suited to strongly damped as well as polarized and depolarized vibrational modes. (C) 2008 Elsevier B.V. All rights reserved.