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A low-power, high speed direct digital frequency synthesizer (DDFS) is presented. Some approximations are used to avoid using a large ROM look-up table to store the trigonometric values in a conventional DDFS. Significant saving in power consumption, due to the compressed ROM, renders the design more suitable for portable wireless communication applications. To demonstrate the proposed technique, a DDFS has been implemented using useful trigonometric equations. The spurious-free dynamic range is about 60 dB at low synthesized frequencies.