Quantization Error In Digital Communication
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 original signal and the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process 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, 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 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 outpu
Delta Modulation (DM) QUANTIZATION NOISE Adaptive Delta Modulation Coding Speech at Low Bit Rates Digital Multiplexers Light Wave Transmission QUANTIZATION NOISE Delta modulation systems are subject to two types of quantization error: (1) slope –overload distortion, and (2) granular noise. If we consider the maximum slope of the original input waveform x(t), it is clear that in order for the sequence of samples{u(nTs)} to increase as fast as the input sequence of samples {x(nTs)} in a region of https://en.wikipedia.org/wiki/Quantization_(signal_processing) maximum slope of x(t), we require that the condition in equation 3.45 be satisfied. Otherwise, we find that the step size = 2δ is too small for the stair case approximation u(t) to follow a steep segment of the input waveform x(t), with the result that u(t) falls behind x(t). This condition is called slope-overload, and the resulting quantization http://www.allsyllabus.com/aj/note/ECE/Digital%20Communication/unit3/QUANTIZATION%20NOISE.php error is called slope-overload distortion(noise). Since the maximum slope of the staircase approximation u(t) is fixed by the step size , increases and decreases in u(t) tend to occur along straight lines. For this reason, a delta modulator using a fixed step size is often referred ton as linear delta modulation (LDM). The granular noise occurs when the step size is too large relative to the local slope characteristics of the input wave form x(t), thereby causing the staircase approximation u(t) to hunt around a relatively flat segment of the input waveform; The granular noise is analogous to quantization noise in a PCM system. The e choice of the optimum step size that minimizes the mean-square value of the quantizing error in a linear delta modulator will be the result of a compromise between slope overload distortion and granular noise. Output SNR for Sinusoidal Modulation. Consider the sinusoidal signal, x(t) = A cos(2μfot) The maximum slope of the signal x(t) is given by When there is no slope-overload, the maximum quantization error ±δ. Assuming that
quantization noise in a digital communication system? Quantization Error/Noise. Topics Digital Communications × 239 Questions 8,769 Followers Follow Oct 9, 2013 Share https://www.researchgate.net/post/Anyone_understand_method_in_quantization_noise_in_a_digital_communication_system Facebook Twitter LinkedIn Google+ 0 / 0 All Answers (2) A. H Kattoush · Tafila Technical University The noise is the difference betwwen the samples and the quantized samples. It is assumed to be uniformly distributed. You can refere to may book Digital communications, chapter 3 for more details Oct 9, 2013 Shahriar Shirvani moghaddam quantization error · Shahid Rajaee University This noise is the difference between non-quantized and quantized samples. It is due to the limitations of memory, processing time constraints and other parameters. For communication systems, total signal to noise ratio is a function of signal to noise ratio of channel and signal to noise ratio of quantization. For more details quantization error in about this type of noise you can refer to Book: Digital Signal Processing by Proakis. Jan 8, 2014 Can you help by adding an answer? Add your answer Question followers (6) Xumin Pu University of Electronic Science and Technology of China A. H Kattoush Tafila Technical University Nornabila Md Nor Technical University of Malaysia Malacca Shahriar Shirvani moghaddam Shahid Rajaee University Biswajit Singh Tata Consultancy Services Limited Zhang Junhao Zhejiang University of Technology Views 343 Followers 6 Answers 2 © 2008-2016 researchgate.net. All rights reserved.About us · Contact us · Careers · Developers · News · Help Center · Privacy · Terms · Copyright | Advertising · Recruiting orDiscover by subject areaRecruit researchersJoin for freeLog in EmailPasswordForgot password?Keep me logged inor log in with ResearchGate is the professional network for scientists and researchers. Got a question you need answered quickly? Technical questions like the one you've just found usually get answered within 48 hours on ResearchGate. Sign up today to join our community of over 11+ million scientific professionals. Join for free An error occurred while rendering template. rgreq-36adb07223307d2563de78ed4
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