Ошибка квантования шум квантования

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The difference between the actual analog value and quantized digital value due is called quantization error. This error is due either to rounding or truncation.

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.

Quantization noise model of quantization error[]

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Quantization noise. The difference between the blue and red signals in the upper graph is the quantization error, which is «added» to the original signal and is the source of noise.

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 modelled in several different ways.

In an ideal analog-to-digital converter, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, and the signal has a uniform distribution covering all quantization levels, the signal-to-noise ratio (SNR) can be calculated from

${displaystyle mathrm {SNR_{ADC}} =20log _{10}(2^{Q})approx 6.0206cdot Q mathrm {dB} ,!}$

The most common test signals that fulfil this are full amplitude triangle waves and sawtooth waves.

In this case a 16-bit ADC has a maximum signal-to-noise ratio of 6.0206 · 16=96.33 dB.

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

${displaystyle mathrm {SNR_{ADC}} =left(1.761+6.0206cdot Qright) mathrm {dB} ,!}$

Here, the quantization noise is once again assumed to be uniformly distributed. When the input signal has a high amplitude and a wide frequency spectrum this is the case.^[1]

In this case a 16-bit ADC has a maximum signal-to-noise ratio of 98.09 dB.

For complex signals in high-resolution ADCs this is an accurate model. For low-resolution ADCs, low-level signals in high-resolution ADCs, and for simple waveforms the quantization noise is not uniformly distributed, making this model inaccurate.^[2] In these cases the quantization noise distribution is strongly affected by the exact amplitude of the signal.

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References[]

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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

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