12 Bit Adc 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 quantization error formula adc and the reconstructed signal (red). The difference between the original signal and adc quantization noise the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic function of wiki adc 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 and truncation quantization noise power 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 referred to as
Quantization Noise In Pcm
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 and therefore uncountable (such as the s
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 Example
coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1 uniform quantization 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 reduce quantization error 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 https://en.wikipedia.org/wiki/Quantization_(signal_processing) 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 http://www.skillbank.co.uk/SignalConversion/snr.htm 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
tour help Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn http://electronics.stackexchange.com/questions/61596/quantization-noise-and-quantization-error more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Electrical Engineering Questions Tags Users Badges Unanswered Ask Question _ Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The quantization error best answers are voted up and rise to the top Quantization noise and Quantization error up vote 6 down vote favorite 1 What is the difference between the quantization noise and quantization error in ADC? I understood that the quantization error you get when you convert analog to digital and quantization noise when you convert from digital to analog. adc conversion share|improve this question asked Mar 20 '13 at 12 bit adc 10:08 Sam 13314 add a comment| 4 Answers 4 active oldest votes up vote 4 down vote accepted The quantization noise is an abstraction, meant to represent the quantization error as a signal (so it can be compared to other forms of noise. You consider the quantization noise as the difference between the (real) quantized signal and the (ideal) sampled one. Because of the loss of information due to quantization, a signal that is A/D and then D/A converted will show an additional noise due to quantization. A situation in which using quantization noise is useful is when determining the quantization depth (number of levels/bits) of a signal. By comparing the quantization noise to the other noise sources, it's possible to determine the maximum reasonable number of levels for the quantization, because additional bits would be absorbed by noise. This of course happens if the sampling rule is respected. share|improve this answer edited Mar 20 '13 at 10:24 answered Mar 20 '13 at 10:17 clabacchio♦ 11k42061 grazie per la risposta. –Sam Mar 20 '13 at 10:27 (English mode OFF) Prego :) (English mode ON) –clabacchio♦ Mar 20 '13 at 10:33 add a comment| up vote 3 down vote An
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