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A major problem in oversampling digital-to-analog converters and fractional-N frequency synthesizers, which are ubiquitous in modern communication systems, is that the noise they introduce contains spurious tones. The spurious tones are the result of digitally generated, quantized signals passing through nonlinear analog components. This paper presents a new method of digital requantization called successive requantization, special cases of which avoids the spurious tone generation problem. Sufficient conditions are derived that ensure certain statistical properties of the quantization noise, including the absence of spurious tones after nonlinear distortion. A practical example is presented and shown to satisfy these conditions.