1. A linearized system comprising: an adaptive pre-distorter configured to pre-distort an input signal to generate a pre-distorted signal; a non-linear transmit path configured to generate an output signal from the pre-distorted signal; and a feedback path configured to generate a feedback signal based on the output signal, wherein the system is configured to adapt the adaptive pre-distorter by: (1) optimizing a filter that minimizes a cost function based on the input signal and the feedback signal; (2) applying the optimized filter to the input signal or the feedback signal to generate an aligned input signal and an aligned feedback signal; and (3) updating the adaptive pre-distorter based on the aligned input and feedback signals.