Quantization Error In Dsp
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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 original signal quantization error formula and the reconstructed signal is the quantization error and, in this simple quantization scheme, quantization of signals is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process of mapping a large
What Is Quantization
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
Quantization Error In Pcm
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 how to reduce quantization error 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 data.[1] Basic types of quantization[edit] 2-bit resolution with four levels of quantization compared
Software and Teaching Aids Differences
Quantization Error Example
Between Editions Steven W. SmithBlogContact Book Search quantization example Download this chapter in PDF format Chapter3.pdf Table of contents 1: The quantization error in analog to digital conversion Breadth and Depth of DSPThe Roots of DSPTelecommunicationsAudio ProcessingEcho LocationImage Processing2: Statistics, Probability and NoiseSignal and Graph TerminologyMean and Standard https://en.wikipedia.org/wiki/Quantization_(signal_processing) DeviationSignal vs. Underlying ProcessThe Histogram, Pmf and PdfThe Normal DistributionDigital Noise GenerationPrecision and Accuracy3: ADC and DACQuantizationThe Sampling TheoremDigital-to-Analog ConversionAnalog Filters for Data ConversionSelecting The Antialias FilterMultirate Data ConversionSingle Bit Data Conversion4: DSP SoftwareComputer NumbersFixed Point (Integers)Floating Point (Real Numbers)Number http://www.dspguide.com/ch3/1.htm PrecisionExecution Speed: Program LanguageExecution Speed: HardwareExecution Speed: Programming Tips5: Linear SystemsSignals and SystemsRequirements for LinearityStatic Linearity and Sinusoidal FidelityExamples of Linear and Nonlinear SystemsSpecial Properties of LinearitySuperposition: the Foundation of DSPCommon DecompositionsAlternatives to Linearity6: ConvolutionThe Delta Function and Impulse ResponseConvolutionThe Input Side AlgorithmThe Output Side AlgorithmThe Sum of Weighted Inputs7: Properties of ConvolutionCommon Impulse ResponsesMathematical PropertiesCorrelationSpeed8: The Discrete Fourier TransformThe Family of Fourier TransformNotation and Format of the Real DFTThe Frequency Domain's Independent VariableDFT Basis FunctionsSynthesis, Calculating the Inverse DFTAnalysis, Calculating the DFTDualityPolar NotationPolar Nuisances9: Applications of the DFTSpectral Analysis of SignalsFrequency Response of SystemsConvolution via the Frequency Domain10: Fourier Transform PropertiesLinearity of the Fourier TransformCharacteristics of the PhasePeriodic Nature of the DFTCompression and Expansion, Multirate meth
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack http://dsp.stackexchange.com/questions/15925/what-is-maximum-quantization-error Overflow the company Business Learn more about hiring developers or posting ads with us Signal Processing Questions Tags Users Badges Unanswered Ask Question _ Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers quantization error are voted up and rise to the top What is “Maximum Quantization Error”? up vote 2 down vote favorite 1 I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation. It is defined as: $$Q = \dfrac {\Delta x}{2^{N+1}}$$ where $N$ is the number of bits used for quantization in a analog to quantization error in digital conversion, and $\Delta x$ is, in portuguese "Faixa de Excursão do Sinal", I don't know what would be the correct translation, but I bet on something like "Signal Excursion Band". I know, its a strange name. Can someone help me with this? What is this $\Delta x$? Sorry for my bad english, it isnt my native language. adc quantization share|improve this question edited Apr 29 '14 at 17:07 jojek♦ 6,71041444 asked Apr 29 '14 at 15:19 Diedre 20115 Evidently you are learning the basics. Speaking as a retired EE; real designs are a lot more complicated. The answer below is idealized for discussion. While not wrong, there are large confounding terms in physical implementation. –rrogers Dec 30 '15 at 14:42 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote accepted When you quantize a signal, you introduce and error which can be defined as $$q[n] = x_q[n]-x[n]$$ where $q[n]$ is the quantization error, $x[n]$ the original signal, and $x_q[n]$ of the quantized signal. The maximum quantization error is simply $max(\left | q \right |)$, the absolute maximum of this error function. Dx in this definition seems to be the range of the input signal so we could rewrite this as $$Q = \f