recursive digital pre - distortion techniques are provided . digital pre - distortion is performed by applying a signal to a recursive system to generate a state vector ; providing the state vector as a feedback value to the recursive non - linear system ; and applying the state vector to a second function to generate an output signal , wherein at least one of the recursive system and the second function comprise a non - linear function . the recursive non - linear system can be initialized to a known initial value . the recursive system is defined by a system of non - linear differential equations .