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A new technique to send a signal in m-th harmonic band with a harmonic-tuning digital predistortion (DPD) scheme is presented. A nonlinear relationship between an input complex envelope and an output complex envelope of m-th harmonic zone is theoretically analyzed. The AM/AMm and AM/PMm are defined and extracted. The suggested analysis is verified with a fundamental-fundamental and fundamental-third harmonic measurements for a InGaP power amplifier (PA). A novel numerical and look-up table (LUT) based DPD algorithm to linearize output signal on m-th harmonic zone is developed. For a 16-QAM input signal, a predistortion for third harmonic signal is implemented, and output spectrum and signal constellation are measured. The results show that a proposed harmonic-tuning DPD scheme works. The proposed nonlinear analysis and predistortion scheme can be applied to multiband software defined radio (SDR) / cognitive radio (CR) wireless system.