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Quantization Noise : Roundoff Error in Digital Computation, by Widrow B., Kollar I.

By Widrow B., Kollar I.

Grasp the fundamentals from first ideas: the physics of sound, rules of listening to and so on, then development onward to primary electronic rules, conversion, compression and coding after which onto transmission, electronic audio workstations, DAT and optical disks. wake up to hurry with how electronic audio is used inside DVD, electronic Audio Broadcasting, networked audio and MPEG shipping streams. all the key applied sciences are right here: compression, DAT, DAB, DVD, SACD, oversampling, noise shaping and blunder correction theories are handled in an easy but exact shape. completely researched, absolutely up to date and technically exact this can be the one ebook you would like at the topic Preface; word list of symbols; Acronyms and abbreviations; half I. historical past: 1. advent; 2. Sampling thought; three. likelihood density capabilities, attribute services, and moments; half II. Uniform Quantization: four. Statistical research of the quantizer output; five. Statistical research of the quantization noise; 6. Crosscorrelations among quantization noise, quantizer enter, and quantizer Output; 7. common statistical family members one of the quantization noise, the quantizer enter, and the quantizer output; eight. Quantization of 2 or extra variables - statistical research of the quantizer; nine. Quantization of 2 or extra variables - statistical research of quantization noise; 10. Quantization of 2 or extra variables - common statistical family members among the quantization noises, and the quantizer inputs and outputs; eleven. Calculation of the moments and correlation features of quantized Gaussian variables; half III. Floating-point Quantization: 12. Floating-point quantization; thirteen. extra on floating-point quantization; 14. Cascades of fixed-point and floating-point quantizers; half IV. Quantization in sign Processing, suggestions keep an eye on, and Computations: 15. Roundoff noise in FIR electronic filters and in FFT calculations; sixteen. Roundoff noise in IIR electronic filters; 17. Roundoff noise in electronic suggestions keep watch over structures; 18. Roundoff mistakes in nonlinear dynamic structures - a chaotic instance; half V. purposes of Quantization Noise concept: 19. Dither; 20. Spectrum of quantization noise and stipulations of whiteness; half VI.Quantization of method parameters; 21. Coefficient quantization; Appendices: A. completely bandlimited attribute features; B. basic expressions of the moments of the quantizer output, and of the mistakes of Sheppard's Corrections; C. Derivatives of the sinc functionality; D. Proofs of quantizing theorems III and IV; E. Limits of applicability of the idea - Caveat reader; F. a few homes of the Gaussian PDF and CF; G. Quantization of a sinusoidal enter; H. program of the equipment of appendix G to distributions except sinusoidal; I. a couple of homes of chosen distributions; J. electronic dither; ok. Roundoff noise in medical computations; L. Simulating arbitrary-precision fixed-point and floating-point roundoff in Matlab; M. a number of papers from the literature of quantization thought; Bibliography; Index; Appendices N - V to be had on-line merely: N. comparability of the attribute functionality process and Sheppard's strategy; O. Interpolation of the cumulative distribution functionality from the histogram and numerical reconstruction of the enter PDF; P. Small bit-number correlation; Q. Noise shaping and sigma-delta modulation; R. Second-order statistical houses of a triangle-wave sign; S. attribute capabilities of amounts concerned while utilizing Dither; T. type corrections; U. comparability of the engineers' Fourier rework and definition of the attribute functionality; V. a number of extra papers from the literature of quantization concept

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Additional info for Quantization Noise : Roundoff Error in Digital Computation, Signal Processing, Control, and Communications

Sample text

It should be mentioned here that Linvill’s approach makes use of an infinite series of Dirac delta functions. Such an impulse series is not a mathematical function, and conventional Laplace and Fourier theory does not apply to it. However, the whole derivation we are going to present can be rigorously justified by using distribution theory (Arsac, 1966; Bremermann, 1965; Lighthill, 1958; Zemanian, 1965). 1 LINVILL’S FREQUENCY DOMAIN DESCRIPTION OF SAMPLING A simple derivation of sampling theory follows.

What is the dynamic range1 if two decimal digits are used for representing the integer part? How many quantum steps are included in the dynamic range? Hint: look at the ratio of the largest and smallest representable positive values. 6 Number representations in digital systems, described by Oppenheim, Schafer and Buck (1998) and by other DSP texts, and by the world-wide web, correspond to certain quantizers. Draw the quantizer output vs. quantizer input for the following number representations: (a) two’s complement number representation,2 (b) one’s complement number representation,3 1 The dynamic range is a term used frequently in numerous fields to describe the ratio between the smallest and largest possible values of a changeable quantity, such as in sound and light.

Both sampling and quantizing degrade the quality of a signal and may irreversibly diminish our knowledge of it. A sampled quantized signal is discrete in both time and amplitude. Discrete systems behave very much like continuous systems in a macroscopic sense. 8 Sampling and quantization. ignoring the effects of sampling. In order to take into account these effects, however, use must be made of sampling theory. Quantized systems, on the other hand, behave in a macroscopic sense very much like systems without quantization.

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