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 non-linear and signal-dependent. It can be modeled in several different ways.

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) is defined as

$\mathrm {SNR_{ADC}} =20\log _{10}(2^{n})\approx 6.02\cdot n\ \mathrm {dB}$

This comes from a model of quantization noise equivalent to a uniform random fluctuation between two neighboring quantization levels. For instance, 16-bit audio has a quoted dynamic range of −96.33 dB.

Another equation is

$\mathrm {SNR_{ADC}} =\left(1.761+6.02\cdot Q\right)\ \mathrm {dB}$

See also

• Signal-to-noise ratio
• Bit resolution
• Quantization error

External links

• The Relationship of Dynamic Range to Data Word Size in Digital Audio Processing
• Round-Off Error Variance - derivation of noise power of q²/12 for round-off error