CHAPTER 1 Fundamentals of Signals and Systems 1.1 Signals 1 1.2 Systems 17 1.3 Fourier Analysis of Discrete Time Signals 42 1.4 Fourier Analysis of Continuous Time Signals 55 CHAPTER 2 Discrete Time Processing of Continuous Time Signals 2.1 Introduction 83 2.2 Structure of a Digital Filter 84 2.3 Frequency Domain Analysis of a Digital Filter 85 2.4 Quantization Errors 92 2.5 Prediction-Based Sampling Methods: Sigma and Sigma-Delta Modulation 98 CHAPTER Fourier Analysis of Discrete Time Signals 3.1 Introduction 107 3.2 Discrete Time Fourier Transform (DTFT) 107 3.3 Discrete Fourier Transform (DFT) 111 3.4 The DFT as an Estimate of the DTFT 117 3.5 DFT for Spectral Estimation 123 3.6 DFT for Convolution 130 3.6 DFT/DCT for Compression 134 3.7 The Fast Fourier Transform (FFT) 140 CHAPTER 4 Digital Filters 4.1 Introduction 151 4.2 Ideal Versus Nonideal Filters 152 4.3 Finite Impulse Response (FIR) Filters 157 4.4 Infinite Impulse Response (IIR) Filters 172 CHAPTER 5 Digital Filters Implementation 5.1 Introduction 199 5.2 Elementary Operations 199 5.3 State Space Realization of Digital Filters 203 5.4 Robust Implementation of Digital Filters 213 5.5 Robust Implementation of Equiripple FIR Filters 227 CHAPTER 6 Multirate Digital Signal Processing: Fundamentals 234 6.1 Introduction 234 6.2 Statement of the Problem and Definitions 235 6.3 Analysis of Downsampling and Upsampling 238 6.4 Sampling Rate Conversion by a Rational Factor 250 6.5 Multistage Implementation of Digital Filters 253 6.6 Efficient Implementation of Multirate Systems 256 6.7 Application of Multirate DSP: Digital-to-Analog Conversion 260 6.8 Sampling Frequency and Quanfization Error 264 CHAPTER 7 DFT Filter Banks and Transmultiplexers 7.1 Introduction 270 7.2 DFT Filter Banks 272 7.3 Maximally Decimated DFT Filter Banks and Transmultiplexers 279 7.4 Transmultiplexers 284 7.5 Application of Transmultiplexers to Digital Communications Modulation 291 CHAPTER 8 Maximally Decimated Filter Banks 8.1 Introduction 302 8.2 Vector Spaces 303 8.3 Two-Channel Perfect Reconstruction Conditions 311 8.4 Design of Perfect Reconstruction Filter Banks with Real Coefficients 320 8.5 Lattice Implementation of Orthonormal Filter Banks 328 8.6 Application to an Audio Signal 333 CHAPTER 9 Time Frequency Expansion: An Introdudion 9.1 Introduction 337 9.2 The Short Time Fourier Transform (STFT) 340 9.3 The Gabor Transform (GT) 345 9.4 The Wavelet Transform 351 9.5 Recursive Multiresolution Decomposition 360 APPENDIXES 372 INDEX 375
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