Using the geometric approach, a solution is given to the problem of detecting faults in linear periodic discrete- time 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.