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