Over-sampling improves signal-to-noise ratio

Increasing the sampling frequency can improve the SNR of the system because the quantization noise power remains the same when the sampling frequency increases (quantization noise is only related to the word length), and the quantization error can be modeled as irrelevant between the sample and the sample, which results in a flat frequency response, The result is a single-sided power spectral density: PSD equals twice times the quantization noise power compared to the sampling frequency. Thus, while the total quantization noise power remains constant, the PSD of the quantization noise decreases as the sampling frequency increases, i.e. the signal-to-noise ratio increases by about 3 decibels per increase in the sampling frequency. There are two ways to improve the signal-to-noise ratio: one is to increase the quantization word length, the word-to-noise ratio increases by 6 decibels, and the other is to increase the sampling frequency. As the quantization noise is uniformly distributed white noise, when the sampling frequency increases by one time, the noise energy does not change, and the noise distribution range increases by one times, therefore, the signal-to-noise ratio increases the "square root 2" one.

The formula in "Software radio Principles and Applications" translated by Yang Calf:

Snr=6.02n+1.76+10*log (FS/2B)

where n is the quantization bit, where the sampling rate of fs,b is the bandwidth, the obvious FS is the sample rate increases, can improve the SNR. The book explains that B is fixed, FS improves, and the effect is equivalent to extending the quantization noise over a wider frequency range, thereby increasing the SNR.

The ADC quantization noise is white noise within the FS/2, the signal frequency is equal to the FS/2 condition, i.e. Nequist sampling, at this time snr=6.02n+1.76.
When the signal frequency is less than FS/2, the quantization noise is still evenly distributed in FS/2, but the quantization noise in the "useful" signal bandwidth concerned is small, so the SNR is increased. The higher the sampling frequency, the more dispersed the quantization noise distribution becomes oversampling.

At the same time, add: When the use of over-sampling technology and believe that the SNR has improved, it is by default to the ADC output signal digital LPF/BPF operation to extract a useful signal, that is, the subsequent addition of a digital filter to achieve increased SNR.

Over-sampling improves signal-to-noise ratio