Quantization noise

Quantization noise is a noise error introduced by the analogue to digital conversion (ADC) process in telecommunication systems and signal processing. It is a rounding error between the analogue input voltage to the ADC and the output digitized value. The noise is additive and independent of the signal when the number of bits $Q$ is greater than 4, that is, more than 16 digitizing levels, $L=2^{Q}$.

It is expressed as a root-mean-square error as

$N_{Q}={\frac {\left({\frac {V_{\mathrm {AD} }}{2^{Q}}}\right)^{2}}{6\cdot T_{\mathrm {S} }\cdot R_{\mathrm {L} }^{2}}}$

where $V_{\mathrm {AD} }$ is the analogue voltage range of the converter (volts), $Q$ is the number of bits of the converter, that is, bit resolution of the converter, $T_{\mathrm {S} }$ is the sample interval of the converter (seconds), and $R_{\mathrm {L} }$ is the load resistance of the converter (ohms).

In an ideal analogue-to-digital converter, the signal-to-noise ratio (SNR) in defined as

$\mathrm {SNR_{ADC}} =\left(1.763+6.02\cdot Q\right)\ \mathrm {dB}$