A pre-distorter that both accurately compensates for the non-linearities of a radio frequency transmit chain, and that imposes as few computation requirements in terms of arithmetic operations, uses a diverse set of real-valued signals that are derived from separate band signals that make up the input signal. The derived real signals are passed through configurable non-linear transformations, which may be adapted during operation, and which may be efficiently implemented using lookup tables. The outputs of the non-linear transformations serve as gain terms for a set of complex signals, which are functions of the input, and which are summed to compute the pre-distorted signal. A small set of the complex signals and derived real signals may be selected for a particular system to match the classes of non-linearities exhibited by the system, thereby providing further computational savings, and reducing complexity of adapting the pre-distortion through adapting of the non-linear transformations.