Cover -- Contents -- 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 Time-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 Padding, 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 -- 3.17 Interpreting the DFT -- 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 IIR Filter Design Method -- 6.5 Bilinear Transform IIR Filter Design Method -- 6.6 Optimized IIR Filter Design Method -- 6.7 Pitfalls in Building IIR Digital Filters -- 6.8 Improving IIR Filters with Cascaded Structures -- 6.9 A Brief Comparison of IIR and FIR Filters -- 7 SPECIALIZED LOWPASS FIR FILTERS -- 7.1 Frequency Sampling Filters: The Lost Art -- 7.2 Interpolated Lowpass FIR Filters -- 8 QUADRATURE SIGNALS -- 8.1 Why Care About Quadrature Signals -- 8.2 The Notation of Complex Numbers -- 8.3 Representing Real Signals Using Complex Phasors -- 8.4 A Few Thoughts on Negative Frequency -- 8.5 Quadrature Signals in the Frequency Domain -- 8.6 Bandpass Quadrature Signals in the Frequency Domain -- 8.7 Complex Down-Conversion -- 8.8 A Complex Down-Conversion Example -- 8.9 An Alternate Down-Conversion Method -- 9 THE DISCRETE HILBERT TRANSFORM -- 9.1 Hilbert Transform Definition -- 9.2 Why Care About the Hilbert Transform? -- 9.3 Impulse Response of a Hilbert Transformer -- 9.4 Designing a Discrete Hilbert Transformer -- 9.5 Time-Domain Analytic Signal Generation -- 9.6 Comparing Analytical Signal Generation Methods -- 10 SAMPLE RATE CONVERSION -- 10.1 Decimation -- 10.2 Interpolation -- 10.3 Combining Decimation and Interpolation -- 10.4 Polyphase Filters -- 10.5 Cascaded Integrator-Comb Filters -- 11 SIGNAL AVERAGING -- 11.1 Coherent Averaging -- 11.2 Incoherent Averaging -- 11.3 Averaging Multiple Fast Fourier Transforms -- 11.4 Filtering Aspects of Time-Domain Averaging -- 11.5 Exponential Averaging -- 12 DIGITAL DATA FORMATS AND THEIR EFFECTS -- 12.1 Fixed-Point Binary Formats.

12.2 Binary Number Precision and Dynamic Range -- 12.3 Effects of Finite Fixed-Point Binary Word Length -- 12.4 Floating-Point Binary Formats -- 12.5 Block Floating-Point Binary Format -- 13 DIGITAL SIGNAL PROCESSING TRICKS -- 13.1 Frequency Translation without Multiplication -- 13.2 High-Speed Vector-Magnitude Approximation -- 13.3 Frequency-Domain Windowing -- 13.4 Fast Multiplication of Complex Numbers -- 13.5 Efficiently Performing the FFT of Real Sequences -- 13.6 Computing the Inverse FFT Using the Forward FFT -- 13.7 Simplified FIR Filter Structure -- 13.8 Reducing A/D Converter Quantization Noise -- 13.9 A/D Converter Testing Techniques -- 13.10 Fast FIR Filtering Using the FFT -- 13.11 Generating Normally Distributed Random Data -- 13.12 Zero-Phase Filtering -- 13.13 Sharpened FIR Filters -- 13.14 Interpolating a Bandpass Signal -- 13.15 Spectral Peak Location Algorithm -- 13.16 Computing FFT Twiddle Factors -- 13.17 Single Tone Detection -- 13.18 The Sliding DFT -- 13.19 The Zoom FFT -- 13.20 A Practical Spectrum Analyzer -- 13.21 An Efficient Arctangent Approximation -- 13.22 Frequency Demodulation Algorithms -- 13.23 DC Removal -- 13.24 Improving Traditional CIC Filters -- 13.25 Smoothing Impulsive Noise -- 13.26 Efficient Polynomial Evaluation -- 13.27 Designing Very High-Order FIR Filters -- 13.28 Time-Domain Interpolation Using the FFT -- 13.29 Frequency Translation Using Decimation -- 13.30 Automatic Gain Control (AGC) -- 13.31 Approximate Envelope Detection -- 13.32 A Quadrature Oscillator -- 13.33 Dual-Mode Averaging -- 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. TIME REVERSAL AND THE DFT -- APPENDIX D. MEAN, VARIANCE, AND STANDANDARD 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 -- APPENDIX G. FREQUENCY SAMPLING FILTER DERIVATIONS -- G.1 Frequency Response of a Comb Filter -- G.2 Single Complex FSF Frequency Response -- G.3 Multisection Complex FSF Phase -- G.4 Multisection Complex FSF Frequency Response -- G.5 Real FSF Transfer Function -- G.6 Type-IV FSF Frequency Response -- APPENDIX H. FREQUENCY SAMPLING FILTER DESIGN TABLES -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z -- ABOUT THE AUTHOR.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.