We find conditions on the input signal of an output reachable possibly unstable linear system, under which the output is persistently exciting. The conditions are given in both frequency and in time domain versions. Interpreting these results in the context of controllable or observable state space realizations we obtain some interesting facts relating persistency of excitation of the input, state and output signals. To illustrate the importance of our results we propose an adaptive identification scheme with “least squares” update law for multivariable plants with proper transfer function. We conclude that parameter convergence is guaranteed for any stationary piecewise uniformly continuous input with nonzero minimum interdiscontinuity distance and at least 2n + 1 points of strong support of its spectral measure, where n is the McMillan degree of the plant. With covariance resetting the convergence rate is shown to be exponential. Without covariance resetting we prove, that the convergence rate is as 1 / t for sufficiently fast identifiers, and in any case at least as fast as 1 /√t.