Various digital pre-distortion systems for use in transmitters are disclosed. The digital pre-distortion system comprises an observing path, which performs either undersampling or radio frequency sampling of the output of a power amplifier. Undersampling may be performed at a rate, which causes aliasing to occur in the undersampled frequency domain. Both undersampling and radio frequency sampling reduces the complexity of the digital pre-distortion system by removing any down mixing modules or anti-aliasing modules, while maintaining reasonable performance of the digital pre-distortion systems.