16-bit Quantization Error
Contents |
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
Quantization Error Formula
(red). The difference between the original signal and the reconstructed signal is quantization error adc the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in
Quantization Error Definition
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 quantization error example 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 quantization error matlab 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 output values may be f
iclicker Registration Check Grades Honors Section Step-By-Step Examples ECE110 BLOG Suggested Reading Online Flashcards Video Channel ECE 110 Course Notes Sampling and Quantization Learn
Quantization Error Of A/d Converter
It! Required Analog and Digital Signals Sampling Nyquist Sampling Rate Quantization quantization error in analog to digital conversion Unit Conversion Explore More Learn It! Analog and Digital SignalsDigital signals are more resilient against noise than
Quantization Error In Pcm
analog signals. An analog signal exists throughout a continuous interval of time and/or takes on a continuous range of values. A sinusoidal signal (also called a pure tone https://en.wikipedia.org/wiki/Quantization_(signal_processing) in acoustics) has both of these properties. Figure 1 Fig. 1: Analog signal. This signal $v(t)=\cos(2\pi ft)$ could be a perfect analog recording of a pure tone of frequency $f$ Hz. If $f=440 \text{ Hz}$, this tone is the musical note $A$ above middle $C$, to which orchestras often tune their instruments. The period $T=1/f$ is the https://courses.engr.illinois.edu/ece110/content/courseNotes/files/?samplingAndQuantization duration of one full oscillation. In reality, electrical recordings suffer from noise that unavoidably degrades the signal. The more a recording is transferred from one analog format to another, the more it loses fidelity to the original.
Figure 2 Fig. 2: Noisy analog signal. Noise degrades the sinusoidal signal in Fig. 1. It is often impossible to recover the original signal exactly from the noisy version. A digital signal is a sequence of discrete symbols. If these symbols are zeros and ones, we call them bits. As such, a digital signal is neither continuous in time nor continuous in its range of values. and, therefore, cannot perfectly represent arbitrary analog signals. On the other hand, digital signals are resilient against noise. Figure 3 Fig. 3: Analog transmission of a digital signal. Consider a digital signal $100110$ converted to an analog signal for radio transmission. The received signal suffers from noise, but given sufficient bit duration $T_b$, it is still easy to read off the original sequence $100110$ perfSoftware and Teaching http://www.dspguide.com/ch3/1.htm Aids Differences Between Editions Steven W. 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 quantization error TerminologyMean and 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 Antialias FilterMultirate Data ConversionSingle Bit Data Conversion4: DSP SoftwareComputer NumbersFixed Point quantization error in (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 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 Pha