Quantization Error 12 Bit
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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 quantization error formula signal and the reconstructed signal (red). The difference between the original signal
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and the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic quantization error example 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
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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 quantization of signals 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
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Quantization Error In Analog To Digital Conversion
format Chapter3.pdf Table of contents 1: The Breadth and Depth
Quantization Example
of DSPThe Roots of DSPTelecommunicationsAudio ProcessingEcho LocationImage Processing2: Statistics, Probability and NoiseSignal and Graph TerminologyMean and quantization step size formula Standard 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 https://en.wikipedia.org/wiki/Quantization_(signal_processing) Antialias FilterMultirate Data ConversionSingle Bit Data Conversion4: DSP SoftwareComputer NumbersFixed Point (Integers)Floating Point (Real Numbers)Number 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 http://www.dspguide.com/ch3/1.htm 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 methodsMultiplying Signals (Amplitude Modulation)The Discrete Time Fourier TransformParseval's Relation11: Fourier Transform PairsDelta Function PairsThe Sinc FunctionOther Transform PairsGibbs EffectHarmonicsChirp Signals12: The Fast Fourier TransformReal DFT Using the Complex DFTHow the FFT worksFFT ProgramsSpeed and Precision ComparisonsFurther Speed Increases13: Continuous Signal ProcessingThe Delta FunctionConvolutionThe Fourier TransformThe Fourier Series14: Introduction to Digital FiltersFilter BasicsHow Information is Represented in SignalsTime Domain ParametersFrequency Domain ParametersHigh-Pass, Band-Pass and Band-Reject FiltersFilter Classification15: Moving Average FiltersImplementation by ConvolutionNoise Reduction vs. Step ResponseFrequency Respons
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