The study of the spectral-spatial anisotropy of the high-latitude mm-wave sky is a powerful tool of cosmology. It can be used to provide deep insight in the Sunyaev-Zeldovich (SZ) effect, the Cosmic Infrared Background, the anisotropy of the CMB, using the spectral dimension to provide substantially increased information with respect to what is achievable by means of standard multiband photometry. Here we focus on spectral measurements of the SZ effect. Large mm-wave telescopes are now routinely mapping photometrically the SZ effect in a number of clusters, estimating the comptonisation parameter and using them as cosmological probes. Low-resolution spectroscopic measurements of the SZ effect would be very effective in removing the degeneracy between parameters inevitable in photometric measurements. We describe a real-world implementation of this measurement strategy, based on an imaging, efficient, differential Fourier transform spectrometer (FTS). The instrument is based on a Martin-Puplett interferometer (MPI) configuration. We combined two MPIs working synchronously to use the entire input power. In our implementation the observed sky field is divided into two halves along the meridian. Each half-field corresponds to one of the two input ports of the MPI. Each detector in the FTS focal planes measures the difference in brightness between two sky pixels, symmetrically located with respect to the meridian. Exploiting the high common mode rejection of the MPI, tiny sky brightness gradients embedded in an overwhelming isotropic background might be measured. We investigate experimentally the common-mode rejection achievable in the MPI at mm wavelengths, and discuss the use of such an instrument to measure the spectrum of cosmic microwave background (CMB) anisotropy and the SZ effect.