3.8.6 What Is Quantization Noise?
- What Causes Quantization Noise?
- Why Is Quantization Necessary?
- Why Does Quantization Noise Resemble Random Noise?
- How Large Can Quantization Error Become?
- What Is Signal-to-Quantization-Noise Ratio (SQNR)?
- Why Does Increasing the Number of Bits Improve Quality?
- Why Does Each Additional Bit Improve SQNR by About 6 dB?
- How Good Is 8-Bit Quantization?
- Why Does Audio Equipment Use 16 Bits or More?
- Is Quantization Noise Always Audible?
- Why Are Small Signals More Affected by Quantization Noise?
- What Is Companding?
- Can Quantization Noise Be Eliminated Completely?
- What Is Dithering?
- How Does Quantization Noise Affect Communications Systems?
- Why Is Quantization Noise Important?
One of the most important steps in converting an analog signal into digital form is quantization. During this process, each sample of the analog signal is assigned to the nearest available quantization level so that it can be represented using a finite number of binary digits.
Quantization makes digital communications possible, but it introduces an unavoidable consequence: quantization noise.
Whenever a continuous range of values is replaced by a finite set of discrete levels, a small error is introduced. This error appears as a noise-like distortion in the reconstructed signal and limits the fidelity that can be achieved by a digital system.
Quantization noise is present in virtually every digital communications system, including digital telephony, audio recording, digital television, satellite communications, and multimedia systems. Understanding its causes and effects helps explain why some systems use 8-bit quantization, others use 16 bits or more, and why increasing the number of bits generally improves signal quality.
What Causes Quantization Noise?
Consider an analog signal whose amplitude varies continuously. At a particular instant, the signal may have a value of 4.63. Suppose the quantizer can represent only the values: 4.5; 5.0; 5.5;6.0. The actual value of 4.63 cannot be represented exactly.
Instead, the quantizer assigns the sample to the nearest available level 4.5. The resulting error is 4.63 – 4.5=0.13. This difference is known as the quantization error.
Because every sample may contain a small error, the reconstructed signal differs slightly from the original waveform. The collection of these errors appears as a noise-like disturbance known as quantization noise.
Why Is Quantization Necessary?
Digital systems can process only a finite number of values. Without quantization, each sample would require an infinite number of bits for exact representation.
Quantization converts a continuous range of amplitudes into a finite set of discrete levels that can be represented using binary numbers. For example:
| Bits per Sample | Quantization Levels |
|---|---|
| 2 | 4 |
| 4 | 16 |
| 8 | 256 |
| 12 | 4096 |
| 16 | 65,536 |
The greater the number of quantization levels, the more accurately the signal can be represented. Quantization therefore involves a trade-off between:
- Signal quality.
- Data rate.
- Equipment complexity.
- Storage requirements.
Why Does Quantization Noise Resemble Random Noise?
Although quantization error arises from a deterministic process, the errors associated with successive samples often appear random. Some samples are rounded upward. Others are rounded downward. The resulting error sequence fluctuates in a seemingly random manner.
For many practical analyses, quantization noise can therefore be modeled as a random noise source. This approximation greatly simplifies the analysis of digital communications systems and is widely used in engineering practice.
How Large Can Quantization Error Become?
For a uniform quantizer, the maximum quantization error is half of the quantization step size. If the spacing between adjacent levels is Δ then the maximum error is Δ/2. No sample can be more than half a step away from the nearest quantization level.
This simple relationship allows engineers to estimate quantization-noise performance and compare different quantization schemes.
What Is Signal-to-Quantization-Noise Ratio (SQNR)?
The effect of quantization noise is commonly measured using the signal-to-quantization-noise ratio (SQNR) which compares the power of the desired signal with the power of the quantization noise: SQNR = Signal Power / Quantization Noise Power. SQNR is usually expressed in decibels: SQNRdB = 10log10(S/Nq) where S is the signal power and Nq is the quantization-noise power.
A higher SQNR indicates better signal quality because the quantization noise is smaller relative to the signal.
Why Does Increasing the Number of Bits Improve Quality?
Adding more bits increases the number of available quantization levels.
This reduces the spacing between adjacent levels and therefore reduces the quantization error. For example:
| Bits | Levels |
|---|---|
| 4 | 16 |
| 8 | 256 |
| 12 | 4096 |
| 16 | 65,536 |
As the number of levels increases:
- Quantization error decreases.
- Quantization-noise power decreases.
- SQNR increases.
- Signal fidelity improves.
The improvement can be substantial. An 8-bit system provides far better quality than a 4-bit system, while a 16-bit system provides dramatically better performance than an 8-bit system.
Why Does Each Additional Bit Improve SQNR by About 6 dB?
One of the most useful rules in digital communications is: Each additional bit of quantization improves SQNR by approximately 6 dB. For a full-scale sinusoidal signal, the relationship is approximately SQNRapprox = 6.02n+1.76 (dB) where n is the number of bits per sample. Examples include:
| Bits per Sample | Approximate SQNR |
|---|---|
| 4 | 26 dB |
| 8 | 50 dB |
| 12 | 74 dB |
| 16 | 98 dB |
This relationship explains why increasing quantizer resolution can dramatically improve signal quality.
How Good Is 8-Bit Quantization?
Traditional PCM telephony uses 8 bits per sample.
For a full-scale sinusoidal input, the theoretical SQNR is approximately 50 dB. This level of performance is generally adequate for intelligible and natural-sounding speech. However, it is not sufficient for high-fidelity music reproduction.
Consequently, telephone systems often employ additional techniques such as companding to improve perceived performance.
Why Does Audio Equipment Use 16 Bits or More?
Music reproduction places far greater demands on signal quality than ordinary speech communications.
Compact-disc audio employs 16 bits per sample which provides an SQNR approaching 98 dB which is sufficient for high-quality audio reproduction. Professional audio systems may use:
- 20-bit quantization.
- 24-bit quantization.
- Even higher internal precision.
These systems achieve extremely low quantization-noise levels and very high dynamic range.
Is Quantization Noise Always Audible?
Not necessarily.
Whether quantization noise is noticeable depends on:
- Signal amplitude.
- Signal content.
- Number of bits.
- Listener sensitivity.
- Application requirements.
In many communications systems, quantization noise is sufficiently small that users are unaware of its presence.
However, if too few bits are used, the resulting distortion may become obvious. Effects may include:
- Hiss.
- Graininess.
- Reduced clarity.
- Loss of low-level detail.
The objective of system design is usually to make quantization noise insignificant compared with other impairments.
Why Are Small Signals More Affected by Quantization Noise?
Quantization error is determined primarily by the spacing between quantization levels. For a large signal, a given error may represent only a tiny fraction of the signal amplitude. For a small signal, the same error may represent a much larger fraction.
Consequently, low-level signals often experience poorer SQNR than high-level signals.
This effect is particularly important in speech systems because speech amplitudes vary considerably which is one of the reasons why telephone systems employ companding.
What Is Companding?
Companding is a technique used to improve quantization performance for low-level signals.
The word is derived from:
- Compressing before quantization.
- Expanding after decoding.
The compressor reduces the dynamic range of the signal before quantization. This effectively provides:
- Finer quantization for weak signals.
- Coarser quantization for strong signals.
After transmission, an expander restores the original dynamic range. The result is improved perceived quality without increasing the number of bits per sample.
Companding is discussed in more detail in the next FAQ.
Can Quantization Noise Be Eliminated Completely?
No.
Whenever a finite number of quantization levels is used, some quantization error will occur.
The only way to eliminate quantization noise completely would be to use an infinite number of quantization levels, which would require an infinite number of bits. This is not physically possible.
Engineers therefore seek to make quantization noise sufficiently small that it does not significantly affect system performance.
What Is Dithering?
In some applications, a small amount of random noise is deliberately added before quantization.
This process is known as dithering. Although adding noise may seem counterintuitive, dithering can reduce undesirable quantization artifacts and make the resulting distortion less objectionable. Dithering is widely used in:
- Audio systems.
- Image processing.
- Digital graphics.
The technique improves subjective quality even though the total noise power may increase slightly.
How Does Quantization Noise Affect Communications Systems?
Quantization noise influences many aspects of communications-system design.
- Digital telephony. It affects speech quality and determines the number of bits required per sample.
- Audio systems. It influences fidelity, dynamic range, and perceived sound quality.
- Video systems. It affects image quality and visible artifacts.
- Satellite communications. It influences the performance of onboard and ground-based digital processing equipment.
- Measurement systems. It limits the accuracy of digital instruments and data-acquisition systems.
In every case, engineers must balance quality against bit rate and system complexity.
Why Is Quantization Noise Important?
Quantization noise represents one of the fundamental limits of digital representation. Even in a perfect communications channel with no thermal noise, interference, or distortion, quantization introduces an unavoidable error whenever analog signals are converted into digital form.
Understanding quantization noise helps explain why some systems use 8-bit samples, others use 16-bit samples, and still others use sophisticated techniques such as companding and dithering to improve performance.
It is therefore one of the most important concepts in source coding and digital communications.
Summary
Quantization noise is the error introduced when continuous signal amplitudes are rounded to discrete quantization levels during analog-to-digital conversion. The resulting quantization error appears as a noise-like distortion that limits the fidelity of the reconstructed signal.
Increasing the number of bits per sample reduces quantization noise by increasing the number of available quantization levels. For a full-scale sinusoidal signal, each additional bit improves the signal-to-quantization-noise ratio by approximately 6 dB. Although quantization noise can never be eliminated completely, careful system design, higher-resolution quantization, and techniques such as companding can reduce its effects to acceptable levels in practical communications systems.
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