A spatial heterodyne spectrometer may employ an integrated computational element (ICE) to obtain a measure of one or more fluid properties without requiring any moving parts, making it particularly suitable for use in a downhole environment. One illustrative method embodiment includes: directing light from a light source to illuminate a sample; transforming light from the sample into spatial fringe patterns using a dispersive two-beam interferometer; adjusting a spectral weighting of the spatial fringe patterns using an integrated computation element (ICE); focusing spectral-weight-adjusted spatial fringe patterns into combined fringe intensities; detecting the combined fringe intensities; and deriving at least one property of the sample.