Expected Value Of Quantization Error
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Please help to improve this article by introducing more precise citations. (August 2016) (Learn how and when to remove this template message) Mean square quantization error (MSQE) is a figure of merit quantization error formula for the process of analog to digital conversion. In this conversion process, analog quantization error adc signals in a continuous range of values are converted to a discrete set of values by comparing them with quantization error definition a sequence of thresholds. The quantization error of a signal is the difference between the original continuous value and its discretization, and the mean square quantization error (given some probability distribution on the quantization error example input values) is the expected value of the square of the quantization errors. Mathematically, suppose that the lower threshold for inputs that generate the quantized value q i {\displaystyle q_{i}} is t i − 1 {\displaystyle t_{i-1}} , that the upper threshold is t i {\displaystyle t_{i}} , that there are k {\displaystyle k} levels of quantization, and that the probability density function for the input
Quantization Error Matlab
analog values is p ( x ) {\displaystyle p(x)} . Let x ^ {\displaystyle {\hat {x}}} denote the quantized value corresponding to an input x {\displaystyle x} ; that is, x ^ {\displaystyle {\hat {x}}} is the value q i {\displaystyle q_{i}} for which t i − 1 ≤ x < t i {\displaystyle t_{i}-1\leq x von GoogleAnmeldenAusgeblendete FelderBooksbooks.google.de - This new, fully-revised edition covers all the major topics of digital signal processing (DSP) design and analysis in a single, all-inclusive volume, interweaving theory with real-world examples and design trade-offs. Building quantization error in analog to digital conversion on the success of the original, this edition includes new material on random...https://books.google.de/books/about/Digital_Signal_Processing.html?hl=de&id=-ClPeHVI9ZEC&utm_source=gb-gplus-shareDigital Signal ProcessingMeine quantization error in pcm BücherHilfeErweiterte BuchsucheE-Book kaufen - 46,65 €Nach Druckexemplar suchenCambridge University PressAmazon.deBuch.deBuchkatalog.deLibri.deWeltbild.deIn Bücherei suchenAlle Händler»Digital Signal Processing: System Analysis and DesignPaulo S. R. Diniz, Eduardo A. B. da https://en.wikipedia.org/wiki/Mean_square_quantization_error Silva, Sergio L. NettoCambridge University Press, 02.09.2010 1 Rezensionhttps://books.google.de/books/about/Digital_Signal_Processing.html?hl=de&id=-ClPeHVI9ZECThis new, fully-revised edition covers all the major topics of digital signal processing (DSP) design and analysis in a single, all-inclusive volume, interweaving theory with real-world examples and design trade-offs. Building on the success of the original, this edition includes new material https://books.google.com/books?id=-ClPeHVI9ZEC&pg=PA691&lpg=PA691&dq=expected+value+of+quantization+error&source=bl&ots=C-kUC3kjx3&sig=Is-GQ0jbCKSJjVAghLZpxTGOPoo&hl=en&sa=X&ved=0ahUKEwiXw7LckNXPAhXoxYMKHVP0CyQQ6AEIPTAF on random signal processing, a new chapter on spectral estimation, greatly expanded coverage of filter banks and wavelets, and new material on the solution of difference equations. Additional steps in mathematical derivations make them easier to follow, and an important new feature is the do-it-yourself section at the end of each chapter, where readers get hands-on experience of solving practical signal processing problems in a range of MATLAB experiments. With 120 worked examples, 20 case studies, and almost 400 homework exercises, the book is essential reading for anyone taking DSP courses. Its unique blend of theory and real-world practical examples also makes it an ideal reference for practitioners. Voransicht des Buches » Was andere dazu sagen-Rezension schreibenEs wurden keine Rezensionen gefunden.Ausgewählte SeitenTitelseiteInhaltsverzeichnisIndexVerweiseInhaltIntroduction 1 The z and Fourier transforms 75 Discrete transforms 143 Digital filters 222 FIR filter approximations 277 IIR filter approximations 349 Spectral estimation 409 Multir Data Conversion Website Quantization Error and Signal-to-Noise Ratio (SNR) Whenever we convert between digital and analog domains we introduce small errors that degrade the accuracy of the data. One way of analysing this is to look at what happens when we try to measure a sine wave. This diagram shows a http://www.skillbank.co.uk/SignalConversion/quanterror.htm true sine wave in gray, and in blue the wave you get if you try to generate a sine wave using 36 samples. You can think of this as a true sine wave plus an error signal called quantization error. The green line shows the size of this error signal. Another way of looking at this is to suppose that the gray wave is a signal you are measuring with an ADC. The stepped blue line then represents the data values of your readings. quantization error The question we need to address is how accurately the blue and gray lines must match. This is dealt with in the next section. Here you see a slightly different method for generating values. The value generated is that for the mid-point between the current and next time points. Because of this the error signal is simpler. However in both cases you can see that the total error over one cycle is twice the peak to peak amplitude of the wave (or four times quantization error in the peak value). The errors form a staircase to the top, down to the bottom and back to the middle. The total error is 4 * Vpk so for n samples per wave the average peak error size Vpke is 4 * Vpk / n Here the analysis begins, to find the frequency and size of components of the whole signal. The error signal is nearly a triangle wave; and the rms voltage for a triangle wave is Vrmse = Vpke / sqrt 3 whence Vrmse = 4 * Vpk / n sqrt 3 but the rms value for the sine wave is Vpk / sqrt 2 i.e. Vrms = Vpk / sqrt 2 so the error signal expressed as a fraction of the sine wave signal is e = Vrmse / Vrms = 4 * sqrt 2 / n * sqrt 3 = 3.266 / n Now, fourier analysis shows a sawtooth wave of period T = 2 / w and amplitude A ( = 3.266 / n ) can be made up from a series of sine waves ewave = ( 2A / ) * ( sin wt - 0.5 sin 2wt + 0.33 sin 3wt - ...) ewave = ( 2.08 / n ) * ( sin wt - 0.5 sin 2wt + 0.33 sin 3wt - ...) and we can see that the error signal amplitudes (ignoring shape and phase) are |ewave| = ( 2.08 / n ) * (1 at nfo +0.5 at 2nfo +0.33 at Quantization Error Of A/d Converter