Quantization Error Analysis
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) and the difference between the original signal and the reconstructed signal (red). The difference between the quantization error formula original signal and the reconstructed signal is the quantization error and, in this simple quantization of signals quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process quantization noise in pcm of mapping a large set of input values to a (countable) smaller set. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, what is quantization as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Contents 1 Basic
Quantization Error Example
properties of quantization 2 Basic types of quantization 2.1 Analog-to-digital converter (ADC) 2.2 Rate–distortion optimization 3 Rounding example 4 Mid-riser and mid-tread uniform quantizers 5 Dead-zone quantizers 6 Granular distortion and overload distortion 7 The additive noise model for quantization error 8 Quantization error models 9 Quantization noise model 10 Rate–distortion quantizer design 11 Neglecting the entropy constraint: Lloyd–Max quantization 12 Uniform quantization and the 6 dB/bit approximation 13 Other fields 14 See also 15 Notes 16 References 17 External links Basic properties of quantization[edit] Because quantization is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible in general to recover the exact input value when given only the output value). The set of possible input values may be infinitely large, and may possibly be continuous and therefore uncountable (such as the set of all real numbers, or all real numbers within some limited range). The set of possible output values may be finite or countably infinite. The input and output sets involved in quantization can be defined in a rather general way. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input
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How To Reduce Quantization Error
Factor:2.489 | Ranking:Robotics 4 out of 25 Source:2016 Release quantization example of Journal Citation Reports with Source: 2015 Web of Science Data A more recent version quantization error in analog to digital conversion of this article was published on [07-18-2016] Stability and quantization-error analysis of haptic rendering of virtual stiffness and damping Nick Colonnese⇑ Allison Okamura Mechanical https://en.wikipedia.org/wiki/Quantization_(signal_processing) Engineering Department, Stanford University, USA Nick Colonnese, Mechanical Engineering Department, Stanford University, 424 Panama Mall, Bld. 560 Stanford, California, USA. Email: ncolonnese{at}stanford.edu Abstract The stable, quantization-error noise-free, rendering of high-stiffness dynamics can be challenging using impedance-type haptic displays. In this paper we examine a canonical, one degree of freedom, http://ijr.sagepub.com/content/early/2015/09/21/0278364915596234 haptic display rendering a virtual spring and damper, including the effects of the device and human dynamics, sampling, position quantization, time delay, and the low-pass filter operating on the device velocity estimate. We construct various stability and quantization-error regions as a function of the system parameters and show the necessary trade-offs that occur between them. Although we apply the quantization-error analysis to virtual spring and damper rendering, it applies to a general virtual environment. We present sufficiency for quantization-error passivity, necessity for no malicious-touch limit cycles, and necessity for no uncoupled-touch limit cycles. Using these results, aided by the presented supplementary code, we find control parameters to render the largest, renderable, virtual stiffness for a given haptic display. The analytical results are experimentally verified using a Phantom Premium 1.5 haptic device. Haptics and haptic interfaces simulation interfaces and virtual reality physical human–robot interaction m
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