Signals and Systems, 2nd Edition
- Length: 1100 pages
- Edition: 2
- Language: English
- Publisher: Springer
- Publication Date: 2021-08-27
- ISBN-10: 3030757412
- ISBN-13: 9783030757410
- Sales Rank: #24726363 (See Top 100 Books)
The book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Electrical Engineering. The first edition of this book was published in 2014. As there is a demand for the next edition, it is quite natural to take note of the several advances that have occurred in the subject over the past five years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book presents a clear and comprehensive introduction to signals and systems. For easier comprehension, the course contents of all the chapters are in sequential order. Analysis of continuous-time and discrete-time signals and systems are done separately for easy understanding of the subjects. The chapters contain over seven hundred numerical examples to understand various theoretical concepts. This textbook also includes numerical examples that were appeared in recent examinations and presented in a graded manner. The topics such as the representation of signals, convolution, Fourier Series and Fourier Transform, Laplace transform, Z-transform, and state-space analysis are explained with a large number of numerical examples in the book. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in electrical engineering and related courses.
Preface to Second Edition Preface to First Edition The notable features of this book includes the following: Contents About the Author 1 Representation of Signals 1.1 Introduction 1.2 Terminologies Related to Signals and Systems 1.2.1 Signal 1.2.2 System 1.3 Continuous and Discrete Time Signals 1.4 Basic Continuous Time Signals 1.4.1 Unit Impulse Function 1.4.2 Unit Step Function 1.4.3 Unit Ramp Function 1.4.4 Unit Parabolic Function 1.4.5 Unit Rectangular Pulse (or Gate) Function 1.4.6 Unit Area Triangular Function 1.4.7 Unit Signum Function 1.4.8 Unit Sinc Function 1.4.9 Sinusoidal Signal 1.4.10 Real Exponential Signal 1.4.11 Complex Exponential Signal 1.5 Basic Discrete Time Signals 1.5.1 The Unit Impulse Sequence 1.5.2 The Basic Unit Step Sequence 1.5.3 The Basic Unit Ramp Sequence 1.5.4 Unit Rectangular Sequence 1.5.5 Sinusoidal Sequence 1.5.6 Discrete Time Real Exponential Sequence 1.6 Basic Operations on Continuous Time Signals 1.6.1 Addition of CT Signals 1.6.2 Multiplications of CT Signals 1.6.3 Amplitude Scaling of CT Signals 1.6.4 Time Scaling of CT Signals 1.6.5 Time Shifting of CT Signals 1.6.6 Signal Reflection or Folding 1.6.7 Inverted CT Signal 1.6.8 Multiple Transformation 1.7 Basic Operations on Discrete Time Signals 1.7.1 Addition of Discrete Time Sequence 1.7.2 Multiplication of DT Signals 1.7.3 Amplitude Scaling of DT Signal 1.7.4 Time Scaling of DT Signal 1.7.5 Time Shifting of DT Signal 1.7.6 Multiple Transformation 1.8 Classification of Signals 1.8.1 Deterministic and Non-deterministic Continuous Signals 1.8.2 Periodic and Non-periodic Continuous Signals 1.8.3 Fundamental Period of Two Periodic Signals 1.8.4 Odd and Even Functions of Continuous Time Signals 1.8.5 Energy and Power of Continuous Time Signals 1.9 Classification of Discrete Time Signals 1.9.1 Periodic and Non-Periodic DT Signals 1.9.2 Odd and Even DT Signals 1.9.3 Energy and Power of DT Signals 2 Continuous and Discrete Time Systems 2.1 Introduction 2.2 Linear Time Invariant Continuous (LTIC) Time System 2.3 Linear Time Invariant Discrete (LTID) Time System 2.4 Properties (Classification) of Continuous Time System 2.4.1 Linear and Non-linear Systems 2.4.2 Time Invariant and Time Varying Systems 2.4.3 Static and Dynamic Systems (Memoryless and System with Memory) 2.4.4 Causal and Non-causal Systems 2.4.5 Stable and Unstable Systems 2.4.6 Invertibility and Inverse System 2.5 Discrete Time System 2.6 Properties of Discrete Time System 2.6.1 Linear and Non-linear Systems 2.6.2 Time Invariant and Time Varying DT Systems 2.6.3 Causal and Non-causal DT Systems 2.6.4 Stable and Unstable Systems 2.6.5 Static and Dynamic Systems 2.6.6 Invertible and Inverse Discrete Time Systems 3 Time Domain Analysis of Continuous and Discrete Time Systems 3.1 Introduction 3.2 Time Response of Continuous Time System 3.3 The Unit Impulse Response 3.4 Unit Impulse Response and the Convolution Integral 3.5 Step by Step Procedure to Solve Convolution 3.6 Properties of Convolution 3.6.1 The Commutative Property 3.6.2 The Distributive Property 3.6.3 The Associative Property 3.6.4 The Shift Property 3.6.5 The Width Property 3.7 Analytical Method of Convolution Operation 3.7.1 Convolution Operation of Non-causal Signals 3.8 Causality of an Linear Time Invariant Continuous Time System 3.9 Stability of a Linear Time Invariant System 3.10 Step Response from Impulse Response 3.11 Representation of Discrete Time Signals in Terms of Impulses 3.12 The Discrete Time Unit Impulse Response 3.13 The Convolution Sum 3.14 Properties of Convolution Sum 3.14.1 Distributive Property 3.14.2 Associative Property of Convolution 3.14.3 Commutative Property of Convolution 3.14.4 Shifting Property of Convolution 3.14.5 The Width Property of Convolution 3.14.6 Convolution with an Impulse 3.14.7 Convolution with Delayed Impulse 3.14.8 Convolution with Unit Step 3.14.9 Convolution with Delayed Step 3.14.10 System Causality from Convolution 3.14.11 BIBO Stability from Convolution 3.14.12 Step Response in Terms of Impulse Response of a LTDT System 3.15 Response Using Convolution Sum 3.15.1 Analytical Method Using Convolution Sum 3.15.2 Convolution Sum of Two Sequences by Multiplication Method 3.15.3 Convolution Sum by Tabulation Method 3.15.4 Convolution Sum of Two Sequences by Matrix Method 3.16 Convolution Sum by Graphical Method 3.17 Deconvolution 3.18 Step Response of the System 3.19 Stability from Impulse Response 3.20 System Causality 4 Fourier Series Analysis of Continuous Time Signals 4.1 Introduction 4.2 Periodic Signal Representation by Fourier Series 4.3 Different Forms of Fourier Series Representation 4.3.1 Trigonometric Fourier Series 4.3.2 Complex Exponential Fourier Series 4.3.3 Polar or Harmonic Form Fourier Series 4.4 Properties of Fourier Series 4.4.1 Linearity 4.4.2 Time Shifting Property 4.4.3 Time Reversal Property 4.4.4 Time Scaling Property 4.4.5 Multiplication Property 4.4.6 Conjugation Property 4.4.7 Differentiation Property 4.4.8 Integration Property 4.4.9 Parseval's Theorem 4.5 Existence of Fourier Series—the Dirichlet Conditions 4.6 Convergence of Continuous Time Fourier Series 4.7 Fourier Series Spectrum 5 Fourier Series Analysis of Discrete Time Signals 5.1 Introduction 5.2 Periodicity of Discrete Time Signal 5.3 DT Signal Representation by Fourier Series 5.4 Fourier Spectra of x[n] 5.5 Properties of Discrete Time Fourier Series 5.5.1 Linearity Property 5.5.2 Time Shifting Property 5.5.3 Time Reversal Property 5.5.4 Multiplication Property 5.5.5 Conjugation Property 5.5.6 Difference Property 5.5.7 Parseval's Theorem 6 Fourier Transform Analysis of Continuous Time Signals 6.1 Introduction 6.2 Representation of Aperiodic Signal by Fourier Integral—The Fourier Transform 6.3 Convergence of Fourier Transforms—The Dirichlet Conditions 6.4 Fourier Spectra 6.5 Connection Between the Fourier Transform and Laplace Transform 6.6 Properties of Fourier Transform 6.6.1 Linearity 6.6.2 Time Shifting 6.6.3 Conjugation and Conjugation Symmetry 6.6.4 Differentiation in Time 6.6.5 Differentiation in Frequency 6.6.6 Time Integration 6.6.7 Time Scaling 6.6.8 Frequency Shifting 6.6.9 Duality 6.6.10 The Convolution 6.6.11 Parseval's Theorem (Relation) 6.7 Fourier Transform of Periodic Signal 6.7.1 Fourier Transform Using Differentiation and Integration Properties 7 Fourier Transform Analysis of Discrete Time Signals and Systems—DTFT, DFT and FFT 7.1 Introduction 7.2 Representation of Discrete Time Aperiodic Signals 7.3 Connection Between the Fourier Transform and the z-Transform 7.4 Properties of Discrete Time Fourier Transform 7.4.1 Linearity 7.4.2 Time Shifting Property 7.4.3 Frequency Shifting 7.4.4 Time Reversal 7.4.5 Time Scaling 7.4.6 Multiplication by n 7.4.7 Conjugation 7.4.8 Time Convolution 7.4.9 Parseval's Theorem 7.4.10 Modulation Property 7.5 Inverse Discrete Time Fourier Transform (IDTFT) 7.6 LTI System Characterized by Difference Equation 7.7 Discrete Fourier Transform (DFT) 7.7.1 The Discrete Fourier Transform Pairs 7.7.2 Four Point, Six Point and Eight Point Twiddle Factors 7.7.3 Zero Padding 7.8 Properties of DFT 7.8.1 Periodicity 7.8.2 Linearity 7.8.3 Complex Conjugate Symmetry 7.8.4 Circular Time Shifting 7.8.5 Circular Frequency Shifting 7.8.6 Circular Correlation 7.8.7 Multiplication of Two DFTs 7.8.8 Parseval's Theorem 7.9 Circular Convolution 7.9.1 Circular Convolution—Circle Method 7.9.2 Circular Convolution-Matrix Multiplication Method 7.9.3 Circular Convolution-DFT-IDFT Method 7.10 Fast Fourier Transform 7.10.1 FFT Algorithm-Decimation in Time 7.10.2 FFT Algorithm-Decimation in Frequency 8 The Laplace Transform Method for the Analysis of Continuous Time Signals and Systems 8.1 Introduction 8.2 Definition and Derivations of the LT 8.2.1 LT of Causal and Non-causal Systems 8.3 The Existence of LT 8.4 The Region of Convergence 8.4.1 Properties of ROCs for LT 8.5 The Unilateral Laplace Transform 8.6 Properties of Laplace Transform 8.6.1 Linearity 8.6.2 Time Shifting 8.6.3 Frequency Shifting 8.6.4 Time Scaling 8.6.5 Frequency Scaling 8.6.6 Time Differentiation 8.6.7 Time Integration 8.6.8 Time Convolution 8.6.9 Complex Frequency Differentiation 8.6.10 Complex Frequency Shifting 8.6.11 Conjugation Property 8.6.12 Initial Value Theorem 8.6.13 Final Value Theorem 8.7 Laplace Transform of Periodic Signal 8.8 Inverse Laplace Transform 8.8.1 Graphical Method of Determining the Residues 8.9 Solving Differential Equation 8.9.1 Solving Differential Equation without Initial Conditions 8.9.2 Solving Differential Equation with the Initial Conditions 8.9.3 Zero Input and Zero State Response 8.9.4 Natural and Forced Response Using LT 8.10 Time Convolution Property of the Laplace Transform 8.11 Network Analysis Using Laplace Transform 8.11.1 Mathematical Description of R-L-C- Elements 8.11.2 Transfer Function and Pole-Zero Location 8.12 Connection Between Laplace Transform and Fourier Transform 8.13 Causality of Continuous Time Invariant System 8.14 Stability of Linear Time Invariant Continuous System 8.15 The Bilateral Laplace Transform 8.15.1 Representation of Causal and Anti-causal Signals 8.15.2 ROC of Bilateral Laplace Transform 8.16 System Realization 8.16.1 Direct Form-I Realization 8.16.2 Direct Form-II Realization 8.16.3 Cascade Form Realization 8.16.4 Parallel Structure Realization 8.16.5 Transposed Realization 9 The z-Transform Analysis of Discrete Time Signals and Systems 9.1 Introduction 9.2 The z-Transform 9.3 Existence of the z-Transform 9.4 Connection Between Laplace Transform, z-Transform and Fourier Transform 9.5 The Region of Convergence (ROC) 9.6 Properties of the ROC 9.7 Properties of z-Transform 9.7.1 Linearity 9.7.2 Time Shifting 9.7.3 Time Reversal 9.7.4 Multiplication by n 9.7.5 Multiplication by an Exponential 9.7.6 Time Expansion 9.7.7 Convolution Theorem 9.7.8 Initial Value Theorem 9.7.9 Final Value Theorem 9.8 Inverse z-Transform 9.8.1 Partial Fraction Method 9.8.2 Inverse z-Transform Using Power Series Expansion 9.8.3 Inverse z-Transform Using Contour Integration or the Method of Residue 9.9 The System Function of DT Systems 9.10 Causality of DT Systems 9.11 Stability of DT System 9.12 Causality and Stability of DT System 9.13 z-Transform Solution of Linear Difference Equations 9.13.1 Right Shift (Delay) 9.13.2 Left Shift (Advance) 9.14 Zero Input and Zero State Response 9.15 Natural and Forced Responses 9.16 Difference Equation from System Function 9.17 Discrete Time System Realization 9.17.1 Direct Form-I Realization 9.17.2 Direct Form-II Realization 9.17.3 Cascade Form Realization 9.17.4 Parallel Form Realization 9.17.5 The Transposed Form Realization 10 Sampling 10.1 Introduction 10.2 The Sampling Process 10.3 The Sampling Theorem 10.4 Signal Recovery 10.5 Aliasing 10.5.1 Sampling Rate ωs Higher than 2ωm 10.5.2 Anti-aliasing Filter 10.6 Sampling with Zero-Order Hold 10.7 Application of Sampling Theorem 10.8 Sampling of Band-Pass Signals Appendix Mathematical Formulae A.1 Summation Formulae A.2 Euler's Formula A.3 Power Series Expansion A.4 Trigonometric Identities A.5 Definite Integrals A.6 Indefinite Integrals A.7 Derivatives Appendix References Index
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