We report an analytical model of signal formation in spectrometer-based two-beam spectral interferometry. Considering the pixel size, the optical resolution and the spectral resolution of the spectrometer, and dispersion, the model represents the signal recorded by a spectrometer based on a diffraction grating and linear detector array. The model is general, but degenerates to more familiar forms with simplifying assumptions. The model is validated by comparison with experimental measurements, where it is shown that the model can accurately predict both signal fall-off and axial resolution for Fourier-domain optical coherence tomography imaging. The model may be useful for determining design specifications and expected performance parameters for spectrometers for spectral interferometry.