A polynomial generator and memory compensator module is provided that includes: a first bank of delay filters for generating current and delayed versions of the envelope for an RF input signal and for the square of the envelope, a polynomial generator for generating polynomials using the current and delayed versions of the envelope, each polynomial being weighted according to pre-distortion weights; an adder for adding the polynomials to provide a pre-distortion signal for pre-distorting the RF input signal to provide a pre-distorted RF input signal such that a power amplifier amplifying the pre-distorted RF input signal provides an amplified RF output signal that reduces a non-linearity of the power amplifier; and a second bank of delay filters for generating delayed versions of the output signal, wherein the adder further adds the delayed versions of the output signal to the polynomials to provide the pre-distortion signal.