Abstract Two techniques are developed for approximating a given three-dimensional ( 3-D) digital filter by a 3-D rational function. The one is by a general 3-D rational function and the other by a 3-D rational function which is separable in the denominator. Each technique relies on the use of mixed first and second information, in the form of a finite portion of the impulse response and its autocorrelation sequence. The approximation is performed by solving a set of linear equations. The separable-denominator approximation is more advantageous due to the guaranteed stability and reduced amount of calculations.