Principles of Signals and Systems

Description

Preface Contents Abbreviations Chapter 1: Introduction to Signals and Systems 1.1 System Chapter 2: Basic Signal Functions and Their Manipulations 2.1 Continuous-Time Signals 2.2 Discrete-Time Signals 2.3 Manipulation of Signals 2.3.1 Manipulation of Continuous-Time Signals Manipulation of Periodic Signals (Functions) 2.3.2 Manipulation of Digital Signals 2.4 Sampling 2.5 Basic Signals Used in Communication and Signal Processing 2.5.1 Representation of Signals with Mathematical Functions 2.5.2 Continuous-Time Basic Signal Functions Unit Step Function Unit Delta Step Function Unit Delta Impulse Function Unit Impulse Function 2.5.3 Properties of the Impulse Function Ramp Function Exponential Function Sinusoidal Function Exponentially Damped Sinusoidal Function Complex Exponential Function 2.5.4 Basic Digital Signal Functions Unit Step Function Unit Impulse Function Ramp Function Digital Exponential Function 2.6 Electronic Circuits Used in Signal Generation 2.6.1 Passive Circuit Elements Inductor Capacitor Resistor Unit Step Function Impulse Function Sinusoidal Function 2.6.2 Exponential Function 2.6.3 Exponentially Damped Sinusoidal Function 2.6.4 Linear and Time-Invariant Systems 2.6.5 Representation of Linear and Time-Invariant System with Differential Equations Problems Chapter 3: Energy, Power, Convolution, and Systems 3.1 Energy and Power in Signals 3.1.1 Energy and Power in Continuous-Time Signals Instantaneous Power Total Energy Average Power 3.1.2 Energies and Powers of Discrete-Time Signals Instantaneous Power Total Energy Average Power 3.2 Convolution 3.2.1 Convolution of Continuous-Time Signals 3.2.2 Impulse Function and Convolution 3.2.3 Convolution of Digital Signals 3.2.4 Convolution of Digital Signals 3.2.5 Digital Impulse Signal (Function) and Convolution Operation 3.3 Systems and Their Features 3.3.1 Mathematical Expressions of the Systems 3.3.2 Causality 3.3.3 Memory 3.3.4 Stability 3.3.5 Invertibility 3.3.6 Linearity 3.3.7 Time Invariance 3.3.8 Time Domain Representations of Linear and Time-Invariant Systems 3.3.9 The Relationship Between Impulse and Unit Step Responses of a Linear and Time-Invariant System 3.3.10 The Response of a Linear and Time-Invariant System to an Exponential Signal 3.3.11 Determining the Properties of a Linear and Time-Invariant System from Impulse Response Memory Causality Stability 3.3.12 Representation of Linear and Time-Invariant Systems with Differential and Difference Equations Continuous-Time Systems Digital Systems 3.3.13 Solving Differential and Difference Equations of Linear and Time-Invariant Systems Differential Equation Solution Solving Difference Equations Problems Chapter 4: Fourier Analysis of Continuous-Time Signals 4.1 Fourier Series Representations of Continuous-Time Periodic Signals 4.2 Fourier Integral and Fourier Transform 4.2.1 Fourier Cosine and Sine Transforms 4.2.2 Fourier Transform Summary Problems Chapter 5: Fourier Analysis of Digital Signals 5.1 Fourier Series Representations of Digital Signals 5.1.1 Periodic Digital Signal 5.1.2 Fourier Series Representations of Digital Signals 5.1.3 Properties for the Fourier Series Representation of Discrete-Time Periodic Signals (Digital Signals) 5.1.4 Convolution of Periodic Digital Signals 5.2 Fourier Transform of Digital Signals 5.2.1 Fourier Transform of Digital Periodic Signals 5.2.2 Properties of the Fourier Transform Summary Problems Chapter 6: Laplace Transform 6.1 Laplace Transform 6.1.1 Convergence Region 6.2 Inverse Laplace Transform 6.3 Laplace Transforms of Derivatives and Integrals of Functions Summary Problems Chapter 7: Z Transform 7.1 Transform 7.1.1 Properties of the Convergence Region 7.2 Inverse Transform 7.3 Z Transform of Linear and Time-Invariant Digital Systems 7.4 Solving the Discrete-Time Difference Equations of Causal Systems Using Z Transform Summary Problems Chapter 8: Practical Applications 8.1 Computational Complexity of the Discrete Fourier Transform Algorithm and Complexity Reduction 8.2 GoertzelAlgorithm 8.3 Dual-Tone Multi-frequency (DTMF) Detection Using Goertzel Algorithm 8.4 Fast Fourier Transform (FFT) Appendix A: Frequently Used Mathematical Expressions Appendix B: Fourier, Laplace, and Z Transform Pairs Bibliography Index