A wideband, linear, direct-digital RF modulator (DDRM) for a digitally-intensive transmitter (DTX) includes an interpolation filter and an in-phase/quadrature (I/Q)-interleaving RF digital-to-analog converter (RF-DAC). The interpolation filter suppresses sampling replicas in the DDRM's output RF spectrum. I/Q interleaving performed by the interleaving RF-DAC avoids problems associated with using two separate I- and Q-path RF-DACs. Each unit cell of the interleaving RF-DAC is capable of producing four unique non-overlapping waveforms covering all four quadrants of the I/Q signal plane. In one embodiment of the invention, the interleaving RF-DAC includes three parallel-connected RF-DACs operating in accordance with a multi-phase set of LO clocks to both cancel 3rd-order and 5th-order LO harmonics generated by the RF-DAC unit cells' interleaving logic and prevent 3rd-order intermodulation from occurring in the DTX's final stage RF power amplifier.