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In this paper, we present a novel digital predistorter structure for joint mitigation of frequency-dependent power amplifier (PA) and in-phase and quadrature (I/Q) modulator impairments in direct-conversion radio transmitters. The predistorter is based on an extended parallel Hammerstein structure, yielding a predistorter that is fully linear in the parameters. In the parameter estimation stage, the indirect learning architecture is utilized. The proposed technique is the first technique in the literature to consider the joint estimation and mitigation of frequency-dependent PA and I/Q modulator impairments. Extensive simulation and measurement analysis is carried out to verify the operation and efficacy of the proposed predistortion structure. It is shown that the adjacent channel power ratio is increased by more than 20 dB in all experiments when using the proposed method, and that the performance of the reference techniques is clearly exceeded.