The linear optimal estimation problem of linear discrete time invariant processes is considered. Using a mixed z- and time-domain approach explicit expressions am obtained, in the case where the measurement record is infinitely long, for the constant Kalman gain and the minimum error covariance matrix of the filtered estimate in terms of the zero structure of the measurement power spectrum density matrix. These expressions are simple to obtain both conceptually and computationally and they provide a geometric insight to the structure of the solution. They are also applied to the filtering problems with finite number of measurements and to the optimal discrete smoothing problems where similar explicit results are obtained.