| 1 Introduction 1-1 Mathematical Representation of Signals 1-2 Mathematical Representation of Systems 1-3 Thinking About Systems 1-4 The Next Step 2 Sinusoids 2-1 Tuning Fork Experiment 2-2 Review of Sine and Cosine Functions 2-3 Sinusodal Signals 2-4 Sampling and Plotting Sinusoids 2-5 Complex Exponentials and Phasors 2-6 Phasor Addition 2-7 Physics of the Tuning Fork 2-8 Time Signals:More Than Formulas 2-9 Summary and Links 2-10 Problems 3 Spectrum Representation 3-1 The Spectrum of a Sum of Sinusoids 3-2 Beat Notes 3-3 Periodic Waveforms 3-4 Fourier Series 3-5 Spectrum of the Fourier Series 3-6 Fourier Analysis of Periodic Signals 3-7 Time-Frequency Spectrum 3-8 Frequency Modulation:Chirp Signals 3-9 Summary and Links 3-10 Problems 4 Sampling and Aliasing 4-1 Sampling 4-2 Spectrum View of Sampling and Reconstruction 4-3 Strobe Demonstration 4-4 Discrete-to-Continuous Conversion 4-5 The Sampling Theorem 4-6 Summary and Links 4-7 Problems 5 FIR Filters 5-1 Discrete-Time Systems 5-2 The Running-Average Filter 5-3 The General FIR Filter 5-4 Implementation of FIR Filters 5-5 Linear Time-Invariant(LTI)Systems 5-6 Convolution and LTI Systems 5-7 Cascaded LTI Systems 5-8 Example of FIR Filtering 5-9 Summary and Links 5-10 Problems 6 Frequency Response of FIR Filters 6-1 Sinusoidal Response of FIR Systems 6-2 Superposition and the Frequency Response 6-3 Steady-State and Transient Response 6-4 Properties of the Frequency Response 6-5 Graphical Representation of the Frequency Response 6-6 Cascaded LTI Systems 6-7 Running-Average Filtering 6-8 Filtering Sampled Continuous-Time Signals 6-9 Summary and Links 6-10 Problems 7 z-Transforms 7-1 Definition of the z-Transform 7-2 The z-Transform and Linear Systems 7-3 Properties of the z-Transform 7-4 The z-Transform as an Operator 7-5 Convolution and the z-Transform 7-6 Relationship Between the z-Domain and the ω-Domain 7-7 Useful Filters 7-8 Practical Bandpass filter Design 7-9 Properties of Linear-Phase Filters 7-10 Summary and Links 7-11 Problems 8 IIR Filters 8-1 The General IIR Difference Equation 8-2 Time-Domain Response 8-3 System Function of an IIR Filter 8-4 Poles and Zeros 8-5 Frequency Response of an IIR Filter 8-6 Three Domains 8-7 The Inverse z-Transform and Some Applications 8-8 Steady-State Response and Stability 8-9 Second-Order Filters 8-10 Frequency Response of Second-Order IIR Filter 8-11 Example of an IIR Lowpass Filter 8-12 Problems 9 Continuous-Time Signals and LTI Systems 9-1 Continuous-Time Signals 9-2 The Unit Impulse 9-3 Continuous-Time Systems 9-4 Linear Time-Invariant Systems 9-5 Impulse Responses of Basic LTI Systems 9-6 Convolution of Impulses 9-7 Evaluating Convolution Integrals 9-8 Properties of LTI Systems 9-9 Using Convolution to Remove Multipath Distortion 9-10 Summary 9-11 Problems 10 Frequency Response 10-1 The Frequency Response Function for LTI Systems 10-2 Response to Real Sinusoidal Signals 10-3 Ideal Filters 10-4 Application of Ideal Filters 10-5 Time-Domain of Frequency-Domain? 10-6 Summary/Future 10-7 Problems 11 Continuous-Time Fourier Transform 11-1 Definition of the Fourier Transform 11-2 Fourier Transoform and the Spectrum 11-3 Existence and Convergence of the Fourier Transform 11-4 Examples of Fourier Transform Pairs 11-5 Properties of Fourier Transform Pairs 11-6 The Convolution Property 11-7 Basic LTI Systems 11-8 The Multiplication Property 11-9 Table of Fourier Transform Properties and Pairs 11-10 Using the Fourier Transform for Multipath Analysis 11-11 Summary 11-12 Problems 12 Filtering,Modulation,and Sampling 12-1 Linear Time-Invariant Systems 12-2 Sinewave Amplitude Modulation 12-3 Sampling and Reconstruction 12-4 Summary 12-5 Problems 13 Computing the Spectrum 13-1 Finite Fourier Sum 13-2 Too Many Fourier Transforms? 13-3 Time-Windowing 13-4 Analysis of a Sum of Sinusoids 13-5 Discrete Fourier Transform 13-6 Spectrum Analysis of Finite-Length Signals 13-7 Spectrum Analysis of Periodic Signals 13-8 The Spectrogram 13-9 The Fast Fourier Transform(FFT) 13-10 Summary and Links 13-11 Problems A Complex Numbers A-1 Introduction A-2 Notation for Complex Numbers A-3 Euler's Formula A-4 Algebraic Rules for Complex Numbers A-5 Geometric Views of Complex Operations A-6 Powers and Roots A-7 Summary and Links A-8 Problems B Programming in MATLAB B-1 MATLAB Help B-2 Matrix Operations and Variables B-3 Plots and Graphics B-4 Programming Constructs B-5 MATLAB Scripts B-6 Writing a MATLAB Function B-7 Programming Tips C Laboratory Projects C-1 Introduction to MATLAB C-2 Encoding and Decoding Touch-Tone Signals C-3 Two Convolution GUIs D CD-ROM Demos Index |
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