Calculating Quantization Error
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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 maximum quantization error coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1
Quantization Error Formula
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 how to calculate quantization error in adc 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 Definition
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 example 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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Quantization Error Matlab
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Quantization Error Of A/d Converter
of 8 How do I solve quantization errors in ADC system? LinkBack LinkBack URL About LinkBacks Thread quantization error in analog to digital conversion Tools Show Printable Version Download This Thread Subscribe to this Thread… Search Thread Advanced Search 22nd June 2005,16:25 #1 KrisUK Newbie level 4 Join Date May 2005 Posts http://www.skillbank.co.uk/SignalConversion/snr.htm 7 Helped 0 / 0 Points 1,398 Level 8 How do I solve quantization errors in ADC system? How do I work out quantization error in a ADC system? I looked around on different sites from a recommendation from another user and came to the conclusion it is the max voltage divided by the number of bits. Is this http://www.edaboard.com/thread40731.html correct? Thank you. 22nd June 2005,16:25 22nd June 2005,16:52 #2 Kral Advanced Member level 4 Join Date Mar 2005 Location USA Posts 1,326 Helped 278 / 278 Points 11,626 Level 25 Re: Quantization Error The weighting of the LSB is equal to the (Reference Voltage)/2^n, where n is the number of bits. The Quantization error = 1/2 LSB. If the ADC is bipolar (can represent both positive and negative values, then the LSB weighting is 2X the above value. The quantization error is still 1/2 LSB. The total error includes the quantization error plus scale factor (gain) error, non-linearity errors. Regards, Jon 22nd June 2005,17:22 #3 banh Advanced Member level 1 Join Date Dec 2004 Posts 458 Helped 17 / 17 Points 3,856 Level 14 Quantization Error quantization error/noise is the difference between the actual sampled value and the quantized value. 2 cases: if the the actual sampled value is between 2 quantized levels -> it will either be rounded off or truncated. rounding -> take the nearest quantized level.
Quantization Error Barry Van Veen SubscribeSubscribedUnsubscribe10,40310K Loading... Loading... Working... Add to Want to watch this again later? Sign in to add this https://www.youtube.com/watch?v=RxHNQLLsnVc video to a playlist. Sign in Share More Report Need to report the video? Sign in to report inappropriate content. Sign in Transcript Statistics 8,928 views 44 Like this video? Sign in to make your opinion count. Sign in 45 0 Don't like this video? Sign in to make your opinion count. quantization error Sign in 1 Loading... Loading... Transcript The interactive transcript could not be loaded. Loading... Loading... Rating is available when the video has been rented. This feature is not available right now. Please try again later. Published on Dec 31, 2012http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB quantization error in and data files.Modeling quantization error as uncorrelated noise. Signal to quantization noise ratio as a function of the number of bits used to represent the signal. Category Education License Standard YouTube License Show more Show less Loading... Advertisement Autoplay When autoplay is enabled, a suggested video will automatically play next. Up next DSP Lecture 23: Introduction to quantization - Duration: 1:03:51. Rich Radke 7,727 views 1:03:51 Quantization and Coding in A/D Conversion - Duration: 8:31. Barry Van Veen 10,242 views 8:31 Basics of sampling and quantization - Duration: 1:31:04. Satish Kashyap 6,399 views 1:31:04 Linear Phase FIR Filters - Duration: 13:12. Barry Van Veen 13,615 views 13:12 Frequency Sampling FIR Filter Design - Duration: 14:11. Barry Van Veen 13,952 views 14:11 TSP #32 - Tutorial on the Theory, Design and Measurement of Delta-Sigma Analog to Digital Converters - Duration: 1:01:58. The Signal Path 28,209 views 1:01:58 Digital Audio 102 - PCM, Bit-Rate, Quantisat