Quantisation Error In Volts
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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 formula coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1 quantization error example 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 definition 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 92 quantization error in analog to digital conversion 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 by
Quantization Error In Pcm
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 ratio
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How To Reduce Quantization Error
Notice Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math quantization noise in pcm community on the planet! Everyone who loves science is here! Quantization Error Voltage Aug 19, 2010 #1 kukumaluboy 1. The problem quantization noise power formula statement, all variables and given/known data Q1 A linear PCM system has an input signal 2cos6000PIt volt. Determine, (a) the minimum sampling rate required, (b) the number of bits per PCM codeword required for a http://www.skillbank.co.uk/SignalConversion/snr.htm signal to quantization noise ratio of at least 40 dB, (c) the maximum quantization error voltage, (d) the dynamic range in dB. (a) 6000 Hz (b) n = 7 (c) 15.63 mV (d) 42 dB 3. The attempt at a solution a) By Nyquist theorom , for a analog signal to be accurate reproduced, it should be sampled at a rate of not less than 2 times the highest https://www.physicsforums.com/threads/quantization-error-voltage.423079/ frequency. 2cos6000PIt = 2cosPIft therefore highest f= 6000/2 = 3000Hz Sample f= 2 x 3000Hz = 6kHz b)SNq = 6n (in dB) Therefore 40dB <=6n (bigger or equals to) n= 7 bits c) How to Do d)Dynamic Range = 6n = 6*7 = 42 dB kukumaluboy, Aug 19, 2010 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Aug 19, 2010 #2 Zryn Gold Member a) By Nyquist theorom , for a analog signal to be accurate reproduced, it should be sampled at a rate of not less than 2 times the highest frequency. This quote says that given the highest frequency component of B Hz, 2B Hz is sufficient a sampling rate to prevent aliasing. Nyquist requires a sampling frequency greater than twice the highest frequency component. Thus given the highest frequency component of B Hz, you must have 2B + 1 Hz sampling rate to prevent aliasing. c) How to Do Lets say you have an analogue sin wave with an amplitude of x, and you split that wave into 2^n different voltage levels for your digital
Software and Teaching Aids Differences http://www.dspguide.com/ch3/1.htm 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 TerminologyMean and Standard DeviationSignal quantization error 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 PrecisionExecution Speed: quantization error in 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 methodsMultiplying Signals (Amplitude Modulation)The Di