Quantization Noise NOTE
Quantization noise is
a model of quantization error introduced by quantization in the ADC in
telecommunication systems and signal processing.
Property :
- A rounding error between the analog input voltage to the ADC and the output digitized value.
- Non-linear and signal-dependent.
In an ideal ADC, where the quantization error is uniformly distributed in [−1/2 LSB , +1/2 LSB], and the signal has a uniform distribution covering all quantization levels,the Signal-to-quantization-noise ratio (SQNR) can be calculated as SQNR = 1.76 + 6.02*Q , where Q equals quantization bit number.
Quantization (A/D conversion) at a sample rate Fs and a certain number of bits N produces a total noise power Pn that is a function of N but not a function of Fs.
Therefore for any given N, we will get Pn watts of noise power no matter what the sample rate is. The next thing to understand is
that the quantization noise power Pn is
spread evenly across all frequencies in the digital signal. So if you're
sampling at Fs samples per second, the noise will be Pn/(Fs/2)
watts per Hertz.Property :
- A rounding error between the analog input voltage to the ADC and the output digitized value.
- Non-linear and signal-dependent.
In an ideal ADC, where the quantization error is uniformly distributed in [−1/2 LSB , +1/2 LSB], and the signal has a uniform distribution covering all quantization levels,the Signal-to-quantization-noise ratio (SQNR) can be calculated as SQNR = 1.76 + 6.02*Q , where Q equals quantization bit number.
Quantization (A/D conversion) at a sample rate Fs and a certain number of bits N produces a total noise power Pn that is a function of N but not a function of Fs.
If we have total signal power in the bandwidth of
interest is Ps, the total noise power due to quantization is Pn, and the
signal bandwidth is B Hz.
Assume that we sample at 2*B samples/second, then the amount of quantization noise power Pnb in the signal bandwidth B is Pnb = B * (Pn / (Fs/2)) = B * (Pn / B) = Pn and
SNR = Ps / Pnb = Ps / Pn
How can we improve SNR in this case ?
Assume that we sample at 2*B samples/second, then the amount of quantization noise power Pnb in the signal bandwidth B is Pnb = B * (Pn / (Fs/2)) = B * (Pn / B) = Pn and
SNR = Ps / Pnb = Ps / Pn
How can we improve SNR in this case ?
We can do oversampling by
some amount, say, Fs = M*2*B samples per second, where M > 1, where B is the
bandwidth of interest, then the amount of quantization noise power Pnb in the
signal bandwidth B is Pnb = B * (Pn / (Fs/2)) = B * (Pn / M*B) =
Pn / M and SNR = Ps / Pnb = M * Ps
/ Pn.
We can improve SNR by a factor of M in this way at cost of higher sampling rate which means cost more current consumption. So, if M = 2, you improve the SNR by 3 dB; if M = 4, you improve the SNR by 6 dB (or 1 bit), etc.
Related article : http://clearningn.blogspot.tw/2015/11/delta-sigma-adc.html
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