Calculate Quantization Error
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Quantization Error Signal
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Maximum Quantization Noise
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Quantization Error Formula
I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation. It is defined as: $$Q = \dfrac {\Delta x}{2^{N+1}}$$ where $N$ is the number of bits used for quantization in a analog to digital conversion, and $\Delta x$ is, in portuguese "Faixa de Excursão do Sinal", I don't know what would be the correct translation, but I bet on something like "Signal Excursion how to calculate quantization error in adc Band". I know, its a strange name. Can someone help me with this? What is this $\Delta x$? Sorry for my bad english, it isnt my native language. adc quantization share|improve this question edited Apr 29 '14 at 17:07 jojek♦ 6,70341444 asked Apr 29 '14 at 15:19 Diedre 20115 Evidently you are learning the basics. Speaking as a retired EE; real designs are a lot more complicated. The answer below is idealized for discussion. While not wrong, there are large confounding terms in physical implementation. –rrogers Dec 30 '15 at 14:42 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote accepted When you quantize a signal, you introduce and error which can be defined as $$q[n] = x_q[n]-x[n]$$ where $q[n]$ is the quantization error, $x[n]$ the original signal, and $x_q[n]$ of the quantized signal. The maximum quantization error is simply $max(\left | q \right |)$, the absolute maximum of this error function. Dx in this definition seems to be the range of the input signal so we could rewrite this as $$Q = \frac{max(x)-min(x)}{2^{N+1}}$$ Let's look at a quick example. Let's assume you have a signal that's uniformly distributed between -1 and +1 and you want to quantize this with 3 bits. You have a total 8 of quantizaton steps which would map to [-1 -.75 -.5 -25 0 .25 .5 .75]. The difference between steps is 0.25. If you round during quantization the maxi
Help Rules Groups Blogs What's New? Teardown Videos Datasheets Advanced Search Forum EDA Theory Elementary Electronic Questions How do I solve quantization errors in ADC system? quantization error definition + Post New Thread Results 1 to 8 of 8 How do quantization error example I solve quantization errors in ADC system? LinkBack LinkBack URL About LinkBacks Thread Tools Show Printable Version Download This quantization error matlab Thread Subscribe to this Thread… Search Thread Advanced Search 22nd June 2005,16:25 #1 KrisUK Newbie level 4 Join Date May 2005 Posts 7 Helped 0 / 0 Points 1,398 Level http://dsp.stackexchange.com/questions/15925/what-is-maximum-quantization-error 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 correct? Thank you. 22nd June 2005,16:25 22nd June 2005,16:52 http://www.edaboard.com/thread40731.html #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. truncated -> take the level below it. hence: the error is - rounding off: - truncated where Q is the resolution. Last edite
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 more about Stack Overflow the company Business Learn more about hiring http://stackoverflow.com/questions/1989222/how-to-calculate-quantization-error-from-16bit-to-8bit developers or posting ads with us Stack Overflow Questions Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 4.7 million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up How to calculate quantization error from 16bit to 8bit? up vote 1 down vote favorite Does anyone know how to calculate the error of quantizing from 16bit to 8bit? I have quantization error looked at the Wikipedia article about Quantization, but it doesn't explain this. Can anyone explain how it is done? Lots of love, Louise Update: My function looks like this. unsigned char quantize(double d, double max) { return (unsigned char)((d / max) * 255.0); } c++ c math share|improve this question edited Jan 1 '10 at 18:27 asked Jan 1 '10 at 18:21 Louise 1,40472432 I think your function is close. It can use some error checking - calculate quantization error e.g max better not be zero, both values probably should be positive. I would suggest unit-testing it to be 100% sure. When do you expect the output to be zero? When 255? –Hamish Grubijan Jan 1 '10 at 18:28 3 A double isn't 16 bits... –Ori Pessach Jan 1 '10 at 18:29 It looks like max is intended to be the maximum value of the sample 'd'. The code doesn't enforce it, though - d can take very small negative values or very large positive values, resulting in output that isn't in the range 0-255 (which appears to be the intent.) Also, what's the output data supposed to be? Unsigned audio samples centered around 128? Any negative values will result in the return range being [-255, 255], which probably isn't what you intend. –Ori Pessach Jan 1 '10 at 18:38 1 By the way, from reading other questions you posted I get the impression that your 16 bit sample values aren't 16 bit sample values at all. If you start out with 16 bit PCM samples and run an FFT on them (which I wouldn't do without normalizing the samples first) you end up with FFT coefficients, which aren't 16 bit sample values. They're something else. Maybe you should just describe what you're trying to do. –Ori Pessach Jan 1 '10 at 19:05 @Ori: I use a