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This paper presents a direct digital synthesizer (DDS) that has no ROM, but produces low-spurious square waves. The main feature is the interpolation of the analog-converted signal of the accumulator and the extraction of the timing when the interpolated signal is identical with a hypothetical continuous sawtooth waveform. Experimental results confirm successful frequency synthesizer operation. The spurious signal is successfully reduced in comparison with the raw analog-converted signal of the accumulator.