The impedance condition in computational aeroacoustic applications is required in order to model acoustically treated walls. The application of this condition in time-domain methods, however, is extremely difficult because of the convolutions involved. In this paper, a time-domain method is developed which overcomes the computational difficulties associated with these convolutions. This method builds on the z-transform from control and signal processing theory and the z-domain model of the impedance. The idea of using the z-domain operations originates from the computational electromagnetics community. When the impedance is expressed in the z-domain with a rational function, the inverse z-transform of the impedance condition results in only infinite impulse response type, digital, recursive filter operations. These operations, unlike convolutions, require only limited past-time knowledge of the acoustic pressures and velocities on the surface. Examples of one-and two-dimensional problems with and without how indicate that the method promises success in aeroacoustic applications.