What are some common quantization errors and how can you avoid or minimize them?

Quantization is the process of converting a continuous signal into a discrete one by assigning a finite number of values to represent the signal amplitude. Quantization is essential for digital signal processing, but it also introduces errors that can affect the quality and accuracy of the signal. In this article, you will learn about some common quantization errors and how you can avoid or minimize them.

1 Uniform quantization

Uniform quantization is the most commonly used method of quantization, where the signal amplitude range is divided into equal intervals called quantization levels. Each level is assigned a binary code that represents the quantized value. However, uniform quantization has some drawbacks, such as quantization noise, granular distortion, and overload distortion. Quantization noise is caused by the difference between the original signal and the quantized signal, which reduces the signal-to-noise ratio (SNR). Granular distortion occurs when the signal amplitude is small or constant, resulting in a coarse effect. Overload distortion occurs when the signal amplitude exceeds the maximum or minimum quantization level. To reduce these drawbacks, one can increase the number of quantization levels or use a companding technique to compress and expand the signal before and after quantization. Alternatively, one can choose an appropriate quantization range or use a limiter or an adaptive quantizer to adjust the range according to the signal variations.

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Javier Enique Gonzalez Barajas

Advanced Image Processing Engineer at Honeywell
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In this article, we have to think that the option is not to change or upgrade the ADC IC. Maybe, using a amplitude threshold strategy can make contributions. Not all the time we need all the possible amplitudes. For example in thermostat, we need to watch a limited temperature range and check if it is in the optimal value.

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2 Non-uniform quantization

Non-uniform quantization is a method of quantization that uses unequal intervals to divide the signal amplitude range into quantization levels. This type of quantization is more suitable for signals with a non-uniform probability distribution or a high dynamic range, such as speech or audio signals, as it can reduce the quantization noise and improve the signal-to-noise ratio (SNR). There are two main types of non-uniform quantization: logarithmic, which is based on the Weber-Fechner law and can achieve a constant relative error and SNR, and Lloyd-Max, which minimizes the mean squared error (MSE) between the original signal and the quantized signal but requires prior knowledge of the signal statistics. Logarithmic quantization is often used in telephony systems, while Lloyd-Max quantization can achieve a lower MSE and higher SNR than uniform or logarithmic quantization.

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3 Quantization error metrics

Quantization error metrics are measures that evaluate the performance and quality of a quantizer by quantifying the amount and type of errors introduced by quantization. Some common examples include MSE, SNR, Signal-to-quantization-noise ratio (SQNR), and Peak signal-to-noise ratio (PSNR). MSE reflects the overall distortion and noise caused by quantization, but does not indicate the perceptual quality or the frequency distribution of the errors. SNR indicates how well the signal can be distinguished from the noise, while SQNR is a function of the number of quantization levels and the signal amplitude range. PSNR is often used for image or video signals, where it can be used to measure the visual quality or compression efficiency of a quantizer.

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4 Quantization error reduction techniques

Quantization error reduction techniques are methods that aim to reduce the amount or impact of quantization errors on the signal quality and accuracy. Dithering is one such technique, which adds a small amount of random noise to the signal before quantization, thus breaking up the granular distortion and spreading the quantization noise over a wider frequency range. However, it also increases the MSE and reduces the SNR. Noise shaping is another method that filters the quantization noise and shifts it to a frequency range where it is less noticeable or less harmful to the signal. Delta modulation is a technique that quantizes the difference between the current signal sample and the previous quantized sample, rather than the absolute value of the signal. This can reduce bit rate and overload distortion, but can also introduce slope overload distortion when the signal changes too rapidly for the quantizer to follow.

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5 Quantization error examples

Quantization error examples are practical cases that demonstrate how quantization errors can affect different types of signals and applications. Audio clipping is a form of overload distortion that occurs when an audio signal exceeds the maximum quantization level, resulting in a harsh and distorted sound. Image banding is a form of granular distortion that happens when an image has insufficient color depth or bit depth to represent smooth gradients or transitions. Speech recognition errors can be caused by background noise, accents, dialects, and quantization errors that degrade the speech signal quality and intelligibility. All of these issues can be addressed by using a limiter, compressor, higher bit rate, higher color depth, dithering technique, noise shaping technique, suitable quantization method, noise reduction technique, or feedback mechanism.

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Leandro Stefanazzi

FPGA/DSP development | Audio Products
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An interesting example of quantization is truncation. I mention this because most of the times when implementing DSP on FPGA or ASIC, this is the cheapest quantization possible. Truncation adds a negative bias into the quantized signal. If the DC component of the signal is important, this may lead to important errors. This is quite obvious but not always understood by engineers. Quantization can be further improved with some of the techniques described in this article.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are some common quantization errors and how can you avoid or minimize them?

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1 Uniform quantization

2 Non-uniform quantization

3 Quantization error metrics

4 Quantization error reduction techniques

5 Quantization error examples

6 Here’s what else to consider

Signal Processing

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