A standard mathematical model of the glycemia/insulinemia dynamics is in continuous time and goes with discrete time measurements of the subcutaneous glycemia delivered by a continuously glucose monitor (CGM). An ad hoc observer for linear models with discrete output measurements is experimented for such biomedical systems. It is based on the impulsively observability over a finite-time horizon and its corresponding Kalman - like criterion to check asymptotic convergence. The method depends on the allocation of eigenvalues of an impulsive system and the Hautus criterion for an underlying discrete-time system. Finally, the performance of the impulsive observer is tested through 50 hours estimation on 3 patients using their clinical data. These preliminary results motivate an extensive study of this class of observers for biomedical processes, in particular, for the case of T1DM patients. It represents an economical way to estimate the states such as blood glucose, insulin and carbohydrates concentration. Their estimates may eventually be used in a closed-loop for the design of an artificial pancreas.