Preface 1 DISCRETE SEQUENCES AND SYSTEMS 1.1 Discrete Sequences and Their Notation 1.2 Signal Amplitude, Magnitude, Power 1.3 Signal Processing Operational Symbols 1.4 Introduction to Discrete Linear Time-Invariant Systems 1.5 Discrete Linear Systems 1.6 Time-Invariant Systems 1.7 The Commutative Property of Linear Thne-Invariant Systems 1.8 Analyzing Linear Time-Invariant Systems 2 PERIODIC SAMPLING 2.1 Aliasing: Signal Ambiquity in the Frequency Domain 2.2 Sampling Low-Pass Signals 2.3 Sampling Bandpass Signals 2.4 Spectral Inversion in Bandpass Sampling 3 THE DISCRETE FOURIER TRANSFORM 3.1 Understanding the DFT Equation 3.2 DFT Symmetry 3.3 DFT Linearity 3.4 DFT Magnitudes 3.5 DFT Frequency Axis 3.6 DFT Shifting Theorem 3.7 Inverse DFT 3.8 DFT Leakage 3.9 Windows 3.10 DFT Scalloping Loss 3.11 DFT Resolution, Zero Stuffing, and Frequency-Domain Sampling 3.12 DFT Processing Gain 3.13 The DFT of Rectangular Functions 3.14 The DFT Frequency Response to a Complex Input 3.15 The DFT Frequency Response to a Real Cosine Input 3.16 The DFT Single-Bin Frequency Response to a Real Cosine Input 4 THE FAST FOURIER TRANSFORM 4.1 Relationship of the FFT to the DFT 4.2 Hints on Using FFTs in Practice 4.3 FFT Software Programs 4.4 Derivation of the Radix-2 FFT Algorithm 4.5 FFT Input/Output Data Index Bit Reversal 4.6 Radix-2 FFT Butterfly Structures 5 FINITE IMPULSE RESPONSE FILTERS 5.1 An Introduction to Finite Impulse Response FIR Filters 5.2 Convolution in FIR Filters 5.3 Low-Pass FIR Filter Design 5.4 Bandpass FIR Filter Design 5.5 Highpass FIR Filter Design 5.6 Remez Exchange FIR Filter Design Method 5.7 Half-Band FIR Filters 5.8 Phase Response of FIR Filters 5.9 A Generic Description of Discrete Convolution 6 INFINITE IMPULSE RESPONSE FILTERS 6.1 An Introduction to Infinite Impulse Response Filters 6.2 The Laplace Transform 6.3 The z-Transform 6.4 Impulse Invariance HR Filter Design Method 6.5 Bilinear Transform UR Filter Design Method 6.6 Optimized HR Filter Design Method 6.7 Pitfalls in Building ILR Digital Filters 6.8 Cascade and Parallel Combinations of Digital Filters 6.9 A Brief Comparison of UR and FIR Filters 7 ADVANCED SAMPLING TECHNIQUES 7.1 Quadrature Sampling 7.2 Quadrature Sampling with Digital Mixing 7.3 Digital Resampling 8 SIGNAL AVERAGING 8.1 Coherent Averaging 8.2 Incoherent Averaging 8.3 Averaging Multiple Fast Fourier Transforms 8.4 Filtering Aspects of Tune-Domain Averaging 8.5 Exponential Averaging 9 DIGITAL DATA FORMATS AND THEIR EFFECTS 9.1 Fixed-Point Binary Formats 9.2 Binary Number Precision and Dynamic Range 9.3 Effects of Finite Fixed-Point Binary Word Length 9.4 Floating-Point Binary Formats 9.5 Block Floating-Point Binary Format 10 DIGITAL SIGNAL PROCESSING TRICKS 10.1 Frequency Translation without Multiplication 10.2 High-Speed Vector-Magnitude Approximation 10.3 Data Windowing Tricks 10.4 Fast Multiplication of Complex Numbers 10.5 Efficiently Performing the FFT of Real Sequences 10.6 Calculating the Inverse FFT Using the Forward FFT 10.7 Fast FFT Averaging 10.8 Simplified FIR Filter Structure 10.9 Accurate A/D Converter Testing Technique 10.10 Fast FIR Filtering Using the FFT 10.11 Calculation of Sines and Cosines of Consecutive Angles 10.12 Generating Normally Distributed Random Data APPENDIX A. THE ARITHMETIC OF COMPLEX NUMBERS A.1 Graphical Representation of Real and Complex Numbers A.2 Arithmetic Representation of Complex Numbers A.3 Arithmetic Operations of Complex Numbers A.4 Some Practical Implications of Using Complex Numbers APPENDIX B. CLOSED FORM OF A GEOMETRIC SERIES APPENDIX C. COMPLEX SIGNALS AND NEGATIVE FREQUENCY C.1 Development of Imaginary Numbers C.2 Representing Real Signals Using Complex Phasors C.3 Representing Real Signals Using Negative Frequencies C.4 Complex Signals and Quadrature Mixing APPENDIX D. MEAN, VARIANCE, AND STANDARD DEVIATION D.1 Statistical Measures D.2 Standard Deviation, or RMS, of a Continuous Sinewave D.3 The Mean and Variance of Random Functions D.4 The Normal Probability Density Function APPENDIX E. DECIBELS (dB AND dBm) E.1 Using Logarithms to Determine Relative Signal Power E.2 Some Useful Decibel Numbers E.3 Absolute Power Using Decibels APPENDIX F. DIGITAL FILTER TERMINOLOGY Index
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