 For a system described by the transfer function

the final value theorem "appears" to predict the final value of the impulse response to be 0 and the final value of the step response to be 1.However, neither time-domain limit exists, and so the final value theorem predictions are not valid.In fact, both the impulse response and step response oscillate, and (in this special case) the final value theorem describes the average values around which the responses oscillate.