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A novel identification and digital predistortion scheme of weakly nonlinear passband systems such as RF power amplifiers (PA) is presented. It is well known that for the identification of weakly nonlinear systems, despite the spectral regrowth, it suffices to sample the input-output (I/O) data of the system at the Nyquist rate of the input signal. Many applications such as linearization (digital predistortion) and mixed signal simulations require system models at a higher sampling rate than Nyquist. Up to now the construction of such high-rate predistorters has been done by oversampling the corresponding I/O data. This leads to high computational complexity, ill-posedness of the estimation, and high demand on the analog-to-digital converter (ADC) sampling rate for the implementation. This paper discusses an efficient way to obtain high-rate predistorters from low-rate system models and shows the validity of the proposed scheme for a 5th-order complex baseband PA model, where adjacent channel power suppression of 20 dB is achieved.