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 feedback signal has multiple different types of linear distortions including a first linear distortion that is not a linear time distortion, and the system is configured to adapt the adaptive pre-distorter by: (1) optimizing complex filter coefficients of a linear finite impulse response (FIR) filter to minimize a cost function based on the filter, the input signal, and the feedback signal; (2) applying the optimized linear FIR filter to the input signal or the feedback signal to generate an aligned input signal and an aligned feedback signal, wherein the optimized linear FIR filter aligns the input and feedback signals with respect to all of the multiple different types of linear distortions in the feedback signal including the first linear distortion; and (3) updating the adaptive pre-distorter based on the aligned input and feedback signals.