Adaptive filters are self-designing systems for information extraction which rely for their operation on a recursive algorithm (Haykin, 2001). They find application in environments where the optimum filter cannot be applied because of lack of knowledge about the signal characteristics and/or the data to be processed. This a priori knowledge required for the design of the optimum filter is commonly based on stochastic signal models, which traditionally are stationary. However, the parameters of many signals found in communication, radar, telemetry and many other fields can be represented as periodic functions of time (Gardner, 1991). When this occurs, stationary signal models cannot exploit the signal periodicities, while cyclostationary models become more suitable since they represent more reliably the statistical signal properties.1 Firstly, let us review some of the key points of cyclostationary signals, while introducing some definitions that will be used throughout this chapter. We have said that most of signals used in many fields such as communication, radar, or telemetry exhibit statistical parameters which vary periodicallywith time. The periodicities of these parameters are related to the parameters of the signalmodulation, such as the carrier frequency or the chip rate among others (Gardner, 1986; 1994). Let the second-order2 auto-correlation function of a zero-mean stochastic signal be defined as: Rxx(t,λ) E {x(t) x (λ)} (1)