Devices, systems and methods for optical spectroscopy using a Fourier transform that improve measurement speed, and relax the sampling rate and dynamic range requirements compared to conventional techniques, are described. One exemplary method for optical Fourier transform spectroscopy includes receiving a broadband signal, spectrally partitioning the broadband signal to generate a plurality of spectral channel interferograms, computing a one-dimensional Fourier transform of a function of each of the plurality of spectral channel interferograms to generate each of a plurality of channel spectrums, and reconstructing a spectrum of the broadband signal based on the plurality of channel spectrums. Embodiments of the disclosed technology include a free-space channel dispersed Fourier transform spectrometer and an integrated silicon-on-insulator Fourier transform spectrometer.