Gate Commutated Thyristors (GCTs) are critical components in modern HVDC and FACTS devices. This paper presents a comprehensive harmonic and transient analysis of a GCT-based 12-pulse rectifier using Discrete Fourier Transform (DFT) methodologies implemented in the DFT Pro software environment. The study focuses on turn-off commutation characteristics, snubber circuit design, and total harmonic distortion (THD) under varying firing angles. Results indicate that DFT Pro's frequency-domain analysis accurately predicts voltage overshoot (12-15%) and reduces computation time by 40% compared to time-domain simulators.