1. A machine-implemented method for generating a linearized output signal from an input signal, the method comprising: (1) applying the input signal to an adaptive pre-distorter to generate a pre-distorted signal; (2) applying the pre-distorted signal to a non-linear amplifier to generate the linearized output signal; (3) generating a feedback signal based on the linearized output signal; and (4) adapting the adaptive pre-distorter based on the input signal and the feedback signal by: (a) time aligning, at a waveform level, a feedback waveform corresponding to the feedback signal with a reference waveform corresponding to the input signal; (b) dividing the time-aligned feedback waveform in time into a plurality of feedback sub-waveforms, wherein each feedback sub-waveform has a shorter time interval than the feedback waveform; (c) dividing the reference waveform in time into a plurality of reference sub-waveforms, wherein each reference sub-waveform has a shorter time interval than the reference waveform and each reference sub-waveform corresponds to a different feedback sub-waveform; (d) independently phase-aligning each feedback sub-waveform to its corresponding reference sub-waveform at a sub-waveform level to form a plurality of independently phase-aligned feedback sub-waveforms; (e) combining the plurality of independently phase-aligned feedback sub-waveforms in time to form a hybrid-aligned feedback waveform; and (f) updating the adaptive pre-distorter based on the hybrid-aligned feedback waveform.