The control technique based on infinite-gain resonators also called Adaptive Feedforward Cancellation (AFC) has been used for some years, mainly in continuous time. In this article, finite-gain resonators in discrete time are analyzed and the advantages for their use in practical applications are discussed, from the perspectives of dynamical behavior and computational implementation. The existing design rules for optimizing system robustness are generalized to any kind of resonator, whether of infinite or finite gain. Nowadays, because most practical implementations are carried out by means of digital systems, such as Digital Signal Processors (DSPs), working directly in discrete time is justified, avoiding any problems that may appear when the resonant controllers are discretized by means of approximations from continuous time.