Table of Contents

Preface; Glossary of symbols; Acronyms and abbreviations; Part I. Background: 1. Introduction; 2. Sampling theory; 3. Probability density functions, characteristic functions, and moments; Part II. Uniform Quantization: 4. Statistical analysis of the quantizer output; 5. Statistical analysis of the quantization noise; 6. Crosscorrelations between quantization noise, quantizer input, and quantizer Output; 7. General statistical relations among the quantization noise, the quantizer input, and the quantizer output; 8. Quantization of two or more variables - statistical analysis of the quantizer; 9. Quantization of two or more variables - statistical analysis of quantization noise; 10. Quantization of two or more variables - general statistical relations between the quantization noises, and the quantizer inputs and outputs; 11. Calculation of the moments and correlation functions of quantized Gaussian variables; Part III. Floating-point Quantization: 12. Floating-point quantization; 13. More on floating-point quantization; 14. Cascades of fixed-point and floating-point quantizers; Part IV. Quantization in Signal Processing, Feedback Control, and Computations: 15. Roundoff noise in FIR digital filters and in FFT calculations; 16. Roundoff noise in IIR digital filters; 17. Roundoff noise in digital feedback control systems; 18. Roundoff errors in nonlinear dynamic systems - a chaotic example; Part V. Applications of Quantization Noise Theory: 19. Dither; 20. Spectrum of quantization noise and conditions of whiteness; Part VI.Quantization of system parameters; 21. Coefficient quantization; Appendices: A. Perfectly bandlimited characteristic functions; B. General expressions of the moments of the quantizer output, and of the errors of Sheppard's Corrections; C. Derivatives of the sinc function; D. Proofs of quantizing theorems III and IV; E. Limits of applicability of the theory - Caveat reader; F. Some properties of the Gaussian PDF and CF; G. Quantization of a sinusoidal input; H. Application of the methods of appendix G to distributions other than sinusoidal; I. A Few properties of selected distributions; J. Digital dither; K. Roundoff noise in scientific computations; L. Simulating arbitrary-precision fixed-point and floating-point roundoff in Matlab; M. A Few papers from the literature of quantization theory; Bibliography; Index; Appendices N-V (available online only): N. Comparison of the characteristic function method and Sheppard's approach; O. Interpolation of the cumulative distribution function from the histogram and numerical reconstruction of the Input PDF; P. Small bit-number correlation; Q. Noise shaping and sigma-delta modulation; R. Second-order statistical properties of a triangle-wave signal; S. Characteristic functions of quantities involved when using Dither; T. Kind corrections; U. Comparison of the engineers' Fourier transform and definition of the characteristic function; V. A few more papers from the literature of quantization theory.

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An authoritative analysis of quantization (roundoff error), ideal for those working in digital signal processing, control or numerical analysis.

About the Author

Bernard Widrow, an internationally-recognised authority in the field of quantization, is a professor of electrical engineering at Stanford University, Californica. He pioneered the field and one of his papers on the topic is the standard reference. He is a Fellow of the IEEE and the AAAS, a member of the US National Academy of Engineering, and the winner of numerous prestigious awards. Istvan Kollar is a professor of electrical engineering at the Budapest University of Technology and Economics, Hungary. A Fellow of the IEEE, he is the recipient of numerous awards, the author of many publications and has been involved in several Industrial Development Projects.