In various of particle accelerator designs, amplitude and phase modulation methods are commonly applied to shape the RF pulses for implementing pulse compressors or compensating for the fluctuations introduced by the high-power RF components and beam loading effects. Phase modulations are typically implemented with additional phase shifters that require drive or control electronics. With our recent next-generation LLRF (NG-LLRF) platform developed based on direct RF sampling technology of RF system-on-chip (RFSoC) devices, RF pulse shaping can be realized without the analogue phase shifters, which can significantly simplify the system architecture. We performed a range of high-power experiments in the C-band to evaluate the RF pulse-shaping capabilities of the NG-LLRF system at different stages of the RF circuits. In this paper, the high-power characterization results with the Cool Copper Collider (C3) structure driven by RF pulses with different modulation schemes will be described. With the pulse modulation and demodulation completely implemented in the digital domain, the RF pulse shaping schemes can be rapidly adapted for X-band structures simply by adding analogue mixers.