Using the geometric approach, a solution is given to the problem of detecting faults in linear periodic discretetime systems. The existing conditions are provided in terms of the new geometric notion of outer observable subspace. Making use of this notion, a residual generator is developed, such that the residual is made independent of unknown input disturbance, and its output free response goes asymptotically to zero. When different faults affect the system, a bank of observers solve the problem, generating a residual for each input fault