This paper shows that digital predistortion (DPD) used to linearize an RF power amplifier (PA) can achieve wide bandwidth distortion cancellation using measurements obtained from a narrow bandwidth observation path. The DPD module creates a correction signal using a set of nonlinear basis waveforms, weighted by adjustable coefficients. The coefficients are optimized using a closed-loop estimator. It is shown using superposition that the basis waveform sets used in the DPD module and closed-loop estimator can differ by a linear transformation, which includes filtering. By filtering the waveforms presented to the estimator, coefficients are optimized for distortion cancellation in a specific part of the spectrum corresponding to the observed bandwidth. The narrow bandwidth coefficient estimate provides wide bandwidth distortion cancellation when used by a DPD module having the unfiltered basis waveform set. Success of the approach relies on further filtering within the estimator to attenuate (notch) the input signal bandwidth, thereby reducing biases in the closed-loop estimation.