A new method for high-speed photonic arbitrary waveform generation using optical sinc-pulse sequences and Mach-Zehnder modulators is presented, enabling a three- to four-fold increase in sampling rate compared to the bandwidth of the used modulator for generating the pulses and an <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-fold increase compared to the bandwidth of the incorporated electronics, with <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> as the number of parallel branches. Proof of concept experimental results, using conventional off-the-shelf fiber components have been presented in this study. Due to its simplicity and the possibility to achieve high sampling rates with low bandwidth photonic and electronic equipment, this method is beneficial for integration on a silicon photonics platform.