Calculate The Variance Of The Quantization Error
Contents |
Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation Toggle navigation Trial Software Product Updates Documentation how to calculate quantization error in adc Home Fixed-Point Designer Examples Functions and Other Reference Release Notes
Quantization Noise Calculation
PDF Documentation Fixed-Point Design for MATLAB Code Fixed-Point Functions Math Statistics Fixed-Point Designer Functions errvar On this quantization error definition page Syntax Description Examples See Also errvarVariance of quantization error Syntaxv = errvar(q)
Descriptionv = errvar(q) returns the variance of a uniformly distributed random quantization error that
Quantization Step Size
arises from quantizing a signal by quantizer object q. Note The results are not exact when the signal precision is close to the precision of the quantizer.ExamplesFind v, the variance of the quantization error for quantizer object q:q = quantizer; v = errvar(q) v = 7.761021455128987e-011Now compare v to v_est, the sample variance from quantization error formula a Monte Carlo experiment:r = realmax(q); u = 2*r*rand(1000,1)-r; % Original signal y = quantize(q,u); % Quantized signal e = y - u; % Error v_est = var(e) % Estimate of the error variance v_est = 7.520208858166330e-011 See Alsoerrmean | errpdf | quantize Was this topic helpful? × Select Your Country Choose your country to get translated content where available and see local events and offers. Based on your location, we recommend that you select: . You can also select a location from the following list: Americas Canada (English) United States (English) Europe Belgium (English) Denmark (English) Deutschland (Deutsch) España (Español) Finland (English) France (Français) Ireland (English) Italia (Italiano) Luxembourg (English) Netherlands (English) Norway (English) Österreich (Deutsch) Portugal (English) Sweden (English) Switzerland Deutsch Français United Kingdom (English) Asia Pacific Australia (English) India (English) New Zealand (English) 中国 (简体中文) 日本 (日本語) 한국 (한국어) See all countries Trial Software Product Updates Fixed-Point Designer Documentation Examples Functions and Other Reference Release Notes
Quantization Error Barry Van Veen SubscribeSubscribedUnsubscribe10,40310K Loading... Loading... Working... Add to Want to watch this again later? Sign in to add this video to a playlist. Sign
Quantization Example
in Share More Report Need to report the video? Sign in
Quantization Step Size Formula
to report inappropriate content. Sign in Transcript Statistics 8,928 views 44 Like this video? Sign in to quantization error in pcm make your opinion count. Sign in 45 0 Don't like this video? Sign in to make your opinion count. Sign in 1 Loading... Loading... Transcript The interactive transcript http://www.mathworks.com/help/fixedpoint/ref/errvar.html 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 and data files.Modeling quantization error as uncorrelated noise. Signal to quantization noise ratio as https://www.youtube.com/watch?v=RxHNQLLsnVc 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 signal to quantization noise ratio derivation - Duration: 18:44. Signals Systems 454 views 18:44 Quantization and Coding in A/D Conversion - Duration: 8:31. Barry Van Veen 10,242 views 8:31 Quantization Part 2: Quantization Understanding - Duration: 4:08. Madhan Mohan 14,581 views 4:08 Digital Audio 102 - PCM, Bit-Rate, Quantisation, Dithering, Nyquists Sampling Theorum - PB15 - Duration: 6:06. Production Bytes 60,048 views 6:06 Signal-to-Noise Ratio - Duration: 13:17. Darryl Morrell 84,581 views 13:17 Quantization Part 1: What is quantization - Duration: 4:03. Madhan Mohan 26,956 views 4:03 Lecture - 2 Sampling - Duration: 53:17. nptelhrd 186,266 views 53:17 QUANTIZER - Duration: 9:06. GATE ACHIEVERS 1,511 views 9:06 GATE 2001 ECE Resolution, Mean Squared Qua
ComparedOEMs traditionally used DSP-based hardware, plugged into a PC, for motion control. But new software-based solutions have challenged this approach, claiming equal or better performance at lower cost.View Free Books https://www.dsprelated.com/freebooks/mdft/Round_Off_Error_Variance.html Mathematics of the DFT Round-Off Error Variance This appendix shows how to derive that the noise power of amplitude quantization error is , where is the quantization step size. This is an example of a topic in statistical signal processing, which is beyond the scope of this book. (Some good textbooks in this area include [27,51,34,33,65,32].) However, since the main quantization error result is so useful in practice, it is derived below anyway, with needed definitions given along the way. The interested reader is encouraged to explore one or more of the above-cited references in statistical signal processing.G.10 Each round-off error in quantization noise is modeled as a uniform random variable between and . It therefore has the following probability density function (pdf) quantization error in [51]:G.11 Thus, the probability that a given roundoff error lies in the interval is given by assuming of course that and lie in the allowed range . We might loosely refer to as a probability distribution, but technically it is a probability density function, and to obtain probabilities, we have to integrate over one or more intervals, as above. We use probability distributions for variables which take on discrete values (such as dice), and we use probability densities for variables which take on continuous values (such as round-off errors). The mean of a random variable is defined as In our case, the mean is zero because we are assuming the use of rounding (as opposed to truncation, etc.). The mean of a signal is the same thing as the expected value of , which we write as . In general, the expected value of any function of a random variable is given by Since the quantization-noise signal is modeled as a series of independent, identically distributed (iid) random variables, we can estimate the mean by averaging the signal over time. Such an estim