There is a well-developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller. This theory describes limitations on achievable performance present when the plant has non-minimum phase zeros, unstable poles, and/or time delays. The parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants. This paper develops a theory of design limitations for sampled-data feedback systems wherein the response of the analogue system output is considered. This is done using the fact that the steady-state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental. This fact allows fundamental sensitivity and complementary sensitivity functions that relate the fundamental component of the response to the input signal to be defined. These sensitivity and complementary sensitivity functions must satisfy integral relations analogous to the Bode and Poisson integrals for purely analogue systems. The relations shaw, for example, that design limitations due to non-minimum phase zeros of the analogue plant constrain the response of the sampled-data feedback system regardless of whether the discretized system is minimum phase and independently of the choice of hold function.