In this sampled digital signal, because the number of quantization bits has not changed, the total quantization noise power has not changed, but at this time, the spectral distribution of quantization noise has changed, that is, the quantization noise that was originally evenly distributed in the ~ fs/2 frequency band has been dispersed to the ~ Rfs/2 frequency band. The figure on the right shows the power spectrum of quantization noise when oversampling.

if R> > 1, then Rfs/2 is much larger than the highest frequency fm of the audio signal, which makes the quantization noise mostly distributed in the high-frequency area outside the audio frequency band, while the quantization noise distributed in the audio frequency band will be reduced accordingly. Therefore, the signal-to-noise ratio of the system can be improved by filtering out the noise components above fm through the low-pass filter. At this time, the maximum quantization signal-to-noise ratio of the oversampling system is as shown in the formula on the right.

In the formula, fm is the highest frequency of the audio signal, Rfs is the oversampling frequency, and n is the quantization bit number. As can be seen from the above formula, when oversampling, every time the sampling frequency is doubled, the signal-to-noise ratio of the system is improved by 3dB, in other words, the number of quantization bits is increased by .5 bits. It can be seen that increasing the oversampling ratio can improve the accuracy of A/D converter.

However, the effect of improving the signal-to-noise ratio only by this oversampling method is not obvious, so noise shaping technology must be combined.