8 Bit Quantization Error
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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 quantization error formula signal and the reconstructed signal is the quantization error and, in this simple quantization quantization error adc scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process of
Quantization Error Definition
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
Quantization Error Example
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 quantization error matlab 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 data.[1] Basic types of qu
Data Conversion Website Quantization Error and Signal - to - Noise Ratio calculations The signal to noise ratio of a quantized signal is 2+6*(no of bits), as shown in the following table. Resolution and Signal to Noise Ratio for signals
Quantization Error Of A/d Converter
coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1 quantization error in analog to digital conversion 2 0.5 8 2 4 0.25 14 3 8 0.125 20 4 16 0.0625 26 5 32 0.03125 32 6 64 0.01563 quantization error in pcm 38 7 128 0.00781 44 8 256 0.00391 50 9 512 0.00195 56 10 1024 0.00098 62 11 2048 0.00048 68 12 4096 0.00024 74 13 8192 0.00012 80 14 16384 0.00006 86 15 32768 0.00003 https://en.wikipedia.org/wiki/Quantization_(signal_processing) 92 16 65536 0.00001 98 These values are for a signal matched to the full-scale range of the converter. If a signal with a range of 5V is measured by an 8 bit ADC with a range of 10V then only 7 bits are effectively in use, and a signal to noise ratio of 44 rather than 50 will apply. Proof: Suppose that the instantaneous value of the input voltage is measured http://www.skillbank.co.uk/SignalConversion/snr.htm by an ADC with a Full Scale Range of Vfs volts, and a resolution of n bits. The real value can change through a range of q = Vfs / 2n volts without a change in measured value occurring. The value of the measured signal is Vm = Vs - e, where Vm is the measured value, Vs is the actual value, and e is the error. The maximum value of error in the measured signal is emax = (1/2)(Vfs / 2n) or emax = q/2 since q = Vfs / 2n The RMS value of quantization error voltage is whence The Signal to Noise Ratio (SNR) is defined as It is normally quoted on a logarithmic scale, in deciBels ( dB ). or The RMS signal voltage is then The error, or quantization noise signal is Thus the signal - to - noise ratio in dB. is since Vfs = 2n q, then which simplifies to N.B. This equation is true only if the input signal is exactly matched to the Full Scale Range of the converter. For signals whose amplitude is less than the FSR the Signal - to - Noise Ratio will be reduced. Download a .pdf file of the analysis of quantization error and signal to noise
Software and Teaching Aids Differences Between Editions Steven W. http://www.dspguide.com/ch3/1.htm SmithBlogContact Book Search Download this chapter in PDF format Chapter3.pdf Table of contents 1: The Breadth and Depth of DSPThe Roots of DSPTelecommunicationsAudio ProcessingEcho LocationImage Processing2: Statistics, Probability and NoiseSignal and Graph TerminologyMean and Standard DeviationSignal vs. Underlying ProcessThe Histogram, Pmf and PdfThe Normal DistributionDigital quantization error 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 PrecisionExecution Speed: Program LanguageExecution Speed: HardwareExecution Speed: Programming Tips5: Linear SystemsSignals and SystemsRequirements for quantization error in 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 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 th
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