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The error feedback (EF) technique is used to suppress phase and amplitude spurs in direct digital synthesisers (DDSs). It allows the reduction of wordlengths of the phase-to-amplitude converter and the D/A converter. The drawback of the conventional phase EF technique is that it reduces the phase spurs only at DDS output frequencies, which are near DC or half the sampling frequency. New phase EF structures with arbitrary centre frequency for cosine and quadrature output DDSs are introduced. The cosine and quadrature DDS with tunable phase and amplitude EF were designed and implemented on a programmable logic device. The experimental results show their desired operation and performance.