| Preface | |
| Glossary of symbols | |
| Acronyms and abbreviations | |
| Background | |
| Introduction | |
| Sampling theory | |
| Probability density functions, characteristic functions, and moments | |
| Uniform Quantization | |
| Statistical analysis of the quantizer output | |
| Statistical analysis of the quantization noise | |
| Crosscorrelations between quantization noise, quantizer input, and quantizer Output | |
| General statistical relations among the quantization noise, the quantizer input, and the quantizer output | |
| Quantization of two or more variables - statistical analysis of the quantizer | |
| Quantization of two or more variables - statistical analysis of quantization noise | |
| Quantization of two or more variables - general statistical relations between the quantization noises, and the quantizer inputs and outputs | |
| Calculation of the moments and correlation functions of quantized Gaussian variables | |
| Floating-point Quantization | |
| Floating-point quantization | |
| More on floating-point quantization | |
| Cascades of fixed-point and floating-point quantizers | |
| Quantization in Signal Processing, Feedback Control, and Computations | |
| Roundoff noise in FIR digital filters and in FFT calculations | |
| Roundoff noise in IIR digital filters | |
| Roundoff noise in digital feedback control systems | |
| Roundoff errors in nonlinear dynamic systems - a chaotic example | |
| Applications of Quantization Noise Theory | |
| Dither | |
| Spectrum of quantization noise and conditions of whiteness | |
| Quantization of system parameters | |
| Coefficient quantization | |
| Appendices | |
| Perfectly bandlimited characteristic functions | |
| General expressions of the moments of the quantizer output, and of the errors of Sheppard's Corrections | |
| Derivatives of the sinc function | |
| Proofs of quantizing theorems III and IV | |
| Limits of applicability of the theory - Caveat reader | |
| Some properties of the Gaussian PDF and CF | |
| Quantization of a sinusoidal input | |
| Application of the methods of Appendix G to distributions other than sinusoidal | |
| A Few properties of selected distributions | |
| Digital | |
| Roundoff noise in scientific computations | |
| Simulating arbitrary-precision fixed-point and floating-point roundoff in Matlab | |
| A Few papers from the literature of quantization theory | |
| Bibliography | |
| Index | |
| Appendices N - V available online only | |
| Comparison of the characteristic function method and Sheppard's approach | |
| Interpolation of the cumulative distribution function from the histogram and numerical reconstruction of the Input PDF | |
| Small bit-number correlation W27 | |
| Noise shaping and sigma-delta modulation W31 | |
| Second-order statistical properties of a triangle-wave signal | |
| Characteristic functions of quantities involved when using Dither W45 | |
| Kind corrections W51 | |
| Comparison of the engineers' Fourier transform and definition of the characteristic function W75 | |
| A few more papers from the literature of quantization theory W79 | |
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