Contents Preface xiii 1 Sampling and Reconstruction 1 1.1 Introduction,I 1.2 Review of Analog Signals,1 1.3 Sampling Theorem,4 1.3.1 Sampling Theorem,6 1.3.2 Antialiasing Prefilters,7 1.3.3 Hardware Limits,8 1.4 Sampling of Sinusoids,9 1.4.1 Analog Reconstruction and Aliasing,10 1.4.2 Rotational Motion,27 1.4.3 DSP Frequency Units,29 1.5 Spectra of Sampled Signals*,29 1.5.1 Discrete-Time Fourier Transform,31 1.5.2 Spectrum Replication,33 1.5.3 Practical Antialiasing Prefilters,38 1.6 Analog Reconstructors*,42 1.6.1 Ideal Reconstructors,43 1.6.2 Staircase Reconstructors,45 1.6.3 Anti-Image Postfilters,46 1.7 Basic Components of DSP Systems,53 1.8 Problems,55 2 Quantization 61 2.1 Quantization Process,61 2.2 Oversampling and Noise Shaping*,65 2.3 D/A Converters,71 2.4 A/D Converters,75 2.5 Analog and Digital Dither*,83 2.6 Problems,90 3 Discrete-Time Systems 95 3.1 Input/Output Rules,96 3.2 Linearity and Time Invariance,100 3.3 Impulse Response,103 iContents Preface xiii 1 Sampling and Reconstruction 1 1.1 Introduction, 1 1.2 Review of Analog Signals, 1 1.3 Sampling Theorem, 4 1.3.1 Sampling Theorem, 6 1.3.2 Antialiasing Prefilters, 7 1.3.3 Hardware Limits, 8 1.4 Sampling of Sinusoids, 9 1.4.1 Analog Reconstruction and Aliasing, 10 1.4.2 Rotational Motion, 27 1.4.3 DSP Frequency Units, 29 1.5 Spectra of Sampled Signals∗, 29 1.5.1 Discrete-Time Fourier Transform, 31 1.5.2 Spectrum Replication, 33 1.5.3 Practical Antialiasing Prefilters, 38 1.6 Analog Reconstructors∗, 42 1.6.1 Ideal Reconstructors, 43 1.6.2 Staircase Reconstructors, 45 1.6.3 Anti-Image Postfilters, 46 1.7 Basic Components of DSP Systems, 53 1.8 Problems, 55 2 Quantization 61 2.1 Quantization Process, 61 2.2 Oversampling and Noise Shaping∗, 65 2.3 D/A Converters, 71 2.4 A/D Converters, 75 2.5 Analog and Digital Dither∗, 83 2.6 Problems, 90 3 Discrete-Time Systems 95 3.1 Input/Output Rules, 96 3.2 Linearity and Time Invariance, 100 3.3 Impulse Response, 103 vii