Code division multiple access (CDMA) schemes allow a number of asynchronous users to share a transmission medium with minimum cooperation among them. However sophisticated signal processing algorithms are needed at the receiver to combat interference from other users and multipath effects. In this paper a discrete-time multirate formulation is introduced for asynchronous CDMA systems which can incorporate multipath effects. This formulation reveals interesting links between CDMA receivers and array processing problems. In this framework linear receivers are derived that can completely suppress multiuser interference (decorrelating receivers). A criterion is introduced which guarantees the decorrelating property while providing optimal solutions in the presence of noise. Parametric FIR designs as well as nonparametric solutions are delineated and their performance is analyzed. The proposed receivers are resistant to near-far effects and do not require the estimation of the users' and noise powers.