Coefficient Quantization Error
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Quantization Error Definition
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Quantization Error Of A/d Converter
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Quantization Error In Analog To Digital Conversion
Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Types of rounding in coefficients quantization up http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=778878 vote 3 down vote favorite Suppose we have create an IIR filter with matlab function "ellip", and then we want to quantize the coefficients using: \begin{align*} bq=Quantize('round',b,2^8); \cr aq=Quantize('round',a,2^8); \end{align*} I have read that there are 4 major types of rounding: truncate round convergent rounding round-to-zero What is the differences between of them and how i know which method is best to choose? filters filter-design share|improve this question edited Apr 9 '13 at 20:19 Jim Clay 9,3381437 asked http://dsp.stackexchange.com/questions/8571/types-of-rounding-in-coefficients-quantization Apr 9 '13 at 19:29 20317 18111 add a comment| 2 Answers 2 active oldest votes up vote 6 down vote accepted The various rounding methods have a computation vs. quantization error tradeoff. Truncate Truncation is the simplest method. Everything after the decimal point is simply lopped off. For instance, both 2.1 and 2.9 become 2. This is very simple, but is the worst method in terms of quantization error. It is particularly bad because when you are dealing with non-negative numbers it introduces a strong negative bias. In some algorithms that can be bad. Round/Convergent Rounding Simply saying "Round" doesn't tell you enough to know what is meant. What kind of rounding? People usually mean convergent rounding when they say "round", so I will assume that that is what is meant. Convergent rounding rounds down when the decimal place is $\le .499\overline{9}$ and rounds up when the decimal place is $\ge .500\overline{0}1$. The question remains- what to do when you have exactly $.5$? Some rounding algorithms always round down (this is called "round-to-zero"), but that introduces a very small amount of bias. Convergent rounding tries to eliminate the bias by rounding to the nearest even number, the assumption being that around half the time that will be up and half the time it will be down. This is the best algorithm in terms of quantization noise, but is the most computationally intense. I