QUANTIZATION ERROR

(Redirected from Quantization noise)

When converting from an analog signal to a digital signal, error is unavoidable. An analog signal is continuous, with ideally infinite accuracy, while the digital signal's accuracy is dependent on the quantization resolution, or number of bits of the analog to digital converter. The difference between the actual analog value and approximated digital value due to the "rounding" that occurs while converting is called 'quantization error'.
Many physical quantities are actually quantized by physical entities. Examples of fields where this limitation applies include electronics (due to electrons), optics (due to photons), biology (due to DNA), and chemistry (due to molecules). This is sometimes known as the "quantum noise limit" of systems in those fields. This is a different manifestation of "quantization error," in which theoretical models may be analog but physics occurs digitally. Around the quantum limit, the distinction between analog and digital quantities vanishes.

Contents

Quantization noise model of quantization error

See also

External links

Quantization noise model of quantization error

Quantization noise is a model of quantization error introduced by quantization in the analog-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
:
ight )^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 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) can be calculated from
:
For instance, 16-bit audio has a quoted dynamic range of 6.0206 · 16 = 96.33 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
:$mathrm\{SNR\_\{ADC\}\}\; =\; left\; (\; 1.761\; +\; 6.0206\; cdot\; Q$
ight ) mathrm{dB} ,!
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.

See also

★ Round-off error

★ Dither

★ Analog to digital converter

★ Quantization

★ Quantization noise

★ Discretization error

★ Signal-to-noise ratio

★ Bit resolution

★ Quantization error

★ SQNR

External links

★ Quantization noise in Digital Computation, Signal Processing, and Control, Bernard Widrow and István Kollár, 2007.

★ 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