This paper addresses the identification of source-sensor transfer functions from the measured space-time covariance matrix in the absence of any further side information about the source or the propagation environment. Using polynomial matrix decomposition techniques, the responses can be narrowed down to an indeterminacy of a common polynomial factor. If at least two different measurements for a source with constant power spectral density are available, this indeterminacy can be reduced to an ambiguity in the phase response of the source-sensor paths.