The recent advances of machine learning in MRSI have mainly been focused on predicting metabolite concentrations and denoising the metabolite-only spectra. Here, we present a deep neural network based on the AUTOMAP formalism to reconstruct metabolic cycle FIDs into the spectral domain. A density matrix formalism was used to generate up/down fields of 1H FIDs of 27 metabolites. B0 inhomogeneity was also included in the simulations. Non water-suppressed up/down field FIDs were fed to the trained network and the proposed reconstruction strategy was validated on simulated FIDs at different noise levels and on an in vivo cerebellum dataset at 3T.