The discrete-time stationary Kalman filter problem is solved in the z-domain for nth-order systems with>moutputs, where 0 ≤>k≤>mmeasurements are noise-free. The design equations are very similar to the continuous-time cage, and they can be solved by spectral factorization, giving the polynomial matrix D¯∼( z) which parametrizes the reduced-order optimal estimator in the frequency domain. By solving a single linear equation the equivalent time-domain representation for the optimal filter can also be obtained. A simple example demonstrates the filter design in the frequency domain.