Direct Digital Synthesizers (DDS) are known to be very spurious due to the use of Digital-to-Analog Convertors (DAC). This thesis presents the phase behaviour of spurs of the commercial AD9912 DDS and its SpurKiller cancellation system. A great variation in spur phase and a large variation in its Spurious-Free Dynamic Range (SFDR) was observed. As a result, an adaptive system is proposed using a Double Quadrature Mixer and a variable phase Local Oscillator (LO). The system is tested at an Intermediate Frequency (IF) of 1.2 GHz, simulating the input of an Ultra-Wideband (UWB) radio. In simulation, an increase in SFDR of 29 dB resulted. In system prototype, an increase in SFDR of 10 dB was achieved. The spur-carrier phase offset was found to be unrelated to the phase of the Double Quad LO to achieve maximum spur reduction, and to be with great variation.