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Quantization noise
From Wikipedia, the free encyclopedia
Quantization noise is a noise error introduced by quantization in 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
where VAD 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, TS is the sample interval of the converter (seconds), and RL is the load resistance of the converter (ohms).
In an ideal analogue-to-digital converter, the signal-to-noise ratio (SNR) can be calculated from
For instance, 16-bit audio has a quoted dynamic range of 6.02 · 16 = 96.3 dB.
This comes from a model of quantization noise in an ideal ADC where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB. The signal is also assumed to have a uniform distribution covering all quantization levels, and the most common test signals that fulfill this are full amplitude triangle waves and sawtooth waves.
When the input signal is a full-amplitude sine wave the distribution of the signal is no longer uniform, and the corresponding equation is instead
Here, the quantization noise is once again assumed to be uniformly distributed. This is very close to the truth for high resolution ADCs, but does not accurately model the noise in low resolution ADCs (e.g. ~4 bits) where the quantization noise distribution is strongly affected by the exact amplitude of the signal.
- Quantization Noise (file info) — play in browser (beta)
- An example of audio with progressively worsening quantization noise.
- Problems listening to the file? See media help.
- 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
- Dynamic Evaluation of High-Speed, High Resolution D/A Converters Outlines HD, IMD and NPR measurements, also includes a derivation of quantization noise
- Signal to quantization noise in quantized sinusoidal