{"product_id":"essentials-of-signals-and-systems-isbn-9781119909217","title":"Essentials of Signals and Systems","description":"\u003cp\u003e\u003cb\u003eNovel approach to the theory of signals and systems in an introductory, accessible textbook\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eSignals and Systems have the reputation of being a difficult subject. \u003ci\u003eEssentials of Signals and Systems \u003c\/i\u003eis a standalone textbook aiming to change this reputation with a novel approach to this subject, teaching the essential concepts of signals and systems in a clear, friendly, intuitive, and accessible way.  \u003c\/p\u003e\u003cp\u003eThe overall vision of the book is that traditional approaches to signals and systems are unnecessarily convoluted, and that students’ learning experiences are much improved by making a clear connection between the theory of representation of signal and systems, and the theory of representation of vectors and matrices in linear algebra. The author begins by reviewing the theory of representation in linear algebra, emphasizing that vectors are represented by different coordinates when the basis is changed, and that the basis of eigenvectors is special because it diagonalizes the operator. Thus, in each step of the theory of representation of signals and systems, the author shows the analogous step in linear algebra. With such an approach, students can easily understand that signals are analogous to vectors, that systems are analogous to matrices, and that Fourier transforms are a change to the basis that diagonalizes LTI operators. \u003c\/p\u003e\u003cp\u003eThe text emphasizes the key concepts in the analysis of linear and time invariant systems, demonstrating both the algebraic and physical meaning of Fourier transforms. The text carefully connects the most important transforms (Fourier series, Discrete Time Fourier Transform, Discrete Fourier Transforms, Laplace and z-transforms), emphasizing their relationships and motivations. The continuous and discrete time domains are neatly connected, and the students are shown step-by-step how to use the fft function, using simple examples.  \u003c\/p\u003e\u003cp\u003eIncorporating learning objectives and problems, and supported with simple Matlab codes to illustrate concepts, the text presents to students the foundations to allow the reader to pursue more advanced topics in later courses.  \u003c\/p\u003e\u003cp\u003eDeveloped from lecture notes already tested with more than 600 students over six years, \u003ci\u003eEssentials of Signals and Systems \u003c\/i\u003ecovers sample topics such as: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eBasic concepts of linear algebra that are pertinent to signals and systems. \u003c\/li\u003e \u003cli\u003eTheory of representation of signals, with an emphasis on the notion of Fourier transforms as a change of basis, and on their physical meaning. \u003c\/li\u003e \u003cli\u003eTheory of representation of linear and time invariant systems, emphasizing the role of Fourier transforms as a change to the basis of eigenvectors, and the physical meaning of the impulse and frequency responses. \u003c\/li\u003e \u003cli\u003eWhat signals and systems have to do with phasors and impedances, and the basics of filter design.\u003c\/li\u003e \u003cli\u003eThe Laplace transform as an extension of Fourier transforms.\u003c\/li\u003e \u003cli\u003eDiscrete signals and systems, the sampling theorem, the Discrete Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT), and how to use the fast fourier transform (fft).\u003c\/li\u003e \u003cli\u003eThe z-transform as an extension of the Discrete Time Fourier Transform.\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eEssentials of Signals and Systems \u003c\/i\u003eis an immensely helpful textbook on the subject for undergraduate students of electrical and computer engineering. The information contained within is also pertinent to those in physics and related fields involved in the understanding of signals and system processing, including those working on related practical applications. \u003c\/p\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAbout the Author xv\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Review of Linear Algebra 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Vectors, Scalars, and Bases 2\u003c\/p\u003e \u003cp\u003eWorked Exercise: Linear Combinations on the Left-hand Side of the Scalar Product 3\u003c\/p\u003e \u003cp\u003e1.3 Vector Representation in Different Bases 7\u003c\/p\u003e \u003cp\u003e1.4 Linear Operators 12\u003c\/p\u003e \u003cp\u003e1.5 Representation of Linear Operators 14\u003c\/p\u003e \u003cp\u003e1.6 Eigenvectors and Eigenvalues 18\u003c\/p\u003e \u003cp\u003e1.7 General Method of Solution of a Matrix Equation 21\u003c\/p\u003e \u003cp\u003e1.8 The Closure Relation 23\u003c\/p\u003e \u003cp\u003e1.9 Representation of Linear Operators in Terms of Eigenvectors and Eigenvalues 24\u003c\/p\u003e \u003cp\u003e1.10 The Dirac Notation 25\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Bra of the Action of an Operator on a Ket 28\u003c\/p\u003e \u003cp\u003e1.11 Exercises 30\u003c\/p\u003e \u003cp\u003eInterlude: Signals and Systems: What is it About? 35\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Representation of Signals 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 37\u003c\/p\u003e \u003cp\u003e2.2 The Convolution 38\u003c\/p\u003e \u003cp\u003eWorked Exercise: First Example of Convolution 42\u003c\/p\u003e \u003cp\u003eWorked Exercise: Second Example of Convolution 44\u003c\/p\u003e \u003cp\u003e2.3 The Impulse Function, or Dirac Delta 46\u003c\/p\u003e \u003cp\u003e2.4 Convolutions with Impulse Functions 50\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Convolution with δ(t − a) 52\u003c\/p\u003e \u003cp\u003e2.5 Impulse Functions as a Basis: The Time Domain Representation of Signals 53\u003c\/p\u003e \u003cp\u003e2.6 The Scalar Product 60\u003c\/p\u003e \u003cp\u003e2.7 Orthonormality of the Basis of Impulse Functions 62\u003c\/p\u003e \u003cp\u003eWorked Exercise: Proof of Orthonormality of the Basis of Impulse Functions 64\u003c\/p\u003e \u003cp\u003e2.8 Exponentials as a Basis: The Frequency Domain Representation of Signals 65\u003c\/p\u003e \u003cp\u003e2.9 The Fourier Transform 72\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Fourier Transform of the Rectangular Function 74\u003c\/p\u003e \u003cp\u003e2.10 The Algebraic Meaning of Fourier Transforms 75\u003c\/p\u003e \u003cp\u003eWorked Exercise: Projection on the Basis of Exponentials 78\u003c\/p\u003e \u003cp\u003e2.11 The Physical Meaning of Fourier Transforms 80\u003c\/p\u003e \u003cp\u003e2.12 Properties of Fourier Transforms 85\u003c\/p\u003e \u003cp\u003e2.12.1 Fourier Transform and the DC level 85\u003c\/p\u003e \u003cp\u003e2.12.2 Property of Reality 86\u003c\/p\u003e \u003cp\u003e2.12.3 Symmetry Between Time and Frequency 88\u003c\/p\u003e \u003cp\u003e2.12.4 Time Shifting 88\u003c\/p\u003e \u003cp\u003e2.12.5 Spectral Shifting 90\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Property of Spectral Shifting and AM Modulation 91\u003c\/p\u003e \u003cp\u003e2.12.6 Differentiation 92\u003c\/p\u003e \u003cp\u003e2.12.7 Integration 93\u003c\/p\u003e \u003cp\u003e2.12.8 Convolution in the Time Domain 96\u003c\/p\u003e \u003cp\u003e2.12.9 Product in the Time Domain 97\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Fourier Transform of a Physical Sinusoidal Wave 98\u003c\/p\u003e \u003cp\u003e2.12.10 The Energy of a Signal and Parseval’s Theorem 101\u003c\/p\u003e \u003cp\u003e2.13 The Fourier Series 102\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Fourier Series of a Square Wave 108\u003c\/p\u003e \u003cp\u003e2.14 Exercises 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Representation of Systems 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction and Properties 113\u003c\/p\u003e \u003cp\u003e3.1.1 Linearity 114\u003c\/p\u003e \u003cp\u003e3.1.2 Time Invariance 114\u003c\/p\u003e \u003cp\u003eWorked Exercise: Example of a Time Invariant System 116\u003c\/p\u003e \u003cp\u003eWorked Exercise: An Example of a Time Variant System 117\u003c\/p\u003e \u003cp\u003e3.1.3 Causality 117\u003c\/p\u003e \u003cp\u003e3.2 Operators Representing Linear and Time Invariant Systems 118\u003c\/p\u003e \u003cp\u003e3.3 Linear Systems as Matrices 119\u003c\/p\u003e \u003cp\u003e3.4 Operators in Dirac Notation 121\u003c\/p\u003e \u003cp\u003e3.5 Statement of the Problem 123\u003c\/p\u003e \u003cp\u003e3.6 Eigenvectors and Eigenvalues of LTI Operators 123\u003c\/p\u003e \u003cp\u003e3.7 General Method of Solution 124\u003c\/p\u003e \u003cp\u003e3.7.1 Step 1: Defining the Problem 124\u003c\/p\u003e \u003cp\u003e3.7.2 Step 2: Finding the Eigenvalues 125\u003c\/p\u003e \u003cp\u003e3.7.3 Step 3: The Representation in the Basis of Eigenvectors 126\u003c\/p\u003e \u003cp\u003e3.7.4 Step 4: Solving the Equation and Returning to the Original Basis 129\u003c\/p\u003e \u003cp\u003eWorked Exercise: Input is an Eigenvector 130\u003c\/p\u003e \u003cp\u003eWorked Exercise: Input is an Explicit Linear Combination of Eigenvectors 131\u003c\/p\u003e \u003cp\u003eWorked Exercise: An Arbitrary Input 132\u003c\/p\u003e \u003cp\u003e3.8 The Physical Meaning of Eigenvalues: The Impulse and Frequency Responses 133\u003c\/p\u003e \u003cp\u003eWorked Exercise: Impulse and Frequency Responses of a Harmonic Oscillator 136\u003c\/p\u003e \u003cp\u003eWorked Exercise: How can the Frequency Response be Measured? 139\u003c\/p\u003e \u003cp\u003eWorked Exercise: The Transient of a Harmonic Oscillator 142\u003c\/p\u003e \u003cp\u003eWorked Exercise: Charge and Discharge in an RC Circuit 145\u003c\/p\u003e \u003cp\u003e3.9 Frequency Conservation in LTI Systems 147\u003c\/p\u003e \u003cp\u003e3.10 Frequency Conservation in Other Fields 148\u003c\/p\u003e \u003cp\u003e3.10.1 Snell’s Law 149\u003c\/p\u003e \u003cp\u003e3.10.2 Wavefunctions and Heisenberg’s Uncertainty Principle 150\u003c\/p\u003e \u003cp\u003e3.11 Exercises 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Electric Circuits as LTI Systems 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Electric Circuits as LTI Systems 157\u003c\/p\u003e \u003cp\u003e4.2 Phasors, Impedances, and the Frequency Response 158\u003c\/p\u003e \u003cp\u003eWorked Exercise: An RLC Circuit as a Harmonic Oscillator 163\u003c\/p\u003e \u003cp\u003e4.3 Exercises 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Filters 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Ideal Filters 165\u003c\/p\u003e \u003cp\u003e5.2 Example of a Low-pass Filter 167\u003c\/p\u003e \u003cp\u003e5.3 Example of a High-pass Filter 170\u003c\/p\u003e \u003cp\u003e5.4 Example of a Band-pass Filter 171\u003c\/p\u003e \u003cp\u003e5.5 Exercises 172\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Introduction to the Laplace Transform 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Motivation: Stability of LTI Systems 175\u003c\/p\u003e \u003cp\u003e6.2 The Laplace Transform as a Generalization of the Fourier Transform 179\u003c\/p\u003e \u003cp\u003e6.3 Properties of Laplace Transforms 181\u003c\/p\u003e \u003cp\u003e6.4 Region of Convergence 182\u003c\/p\u003e \u003cp\u003e6.5 Inverse Laplace Transform by Inspection 185\u003c\/p\u003e \u003cp\u003eWorked Exercise: Example of Inverse Laplace Transform by Inspection 185\u003c\/p\u003e \u003cp\u003eWorked Exercise: Impulse Response of a Harmonic Oscillator 187\u003c\/p\u003e \u003cp\u003e6.6 Zeros and Poles 188\u003c\/p\u003e \u003cp\u003eWorked Exercise: Finding the Zeros and Poles 189\u003c\/p\u003e \u003cp\u003eWorked Exercise: Poles of a Harmonic Oscillator 190\u003c\/p\u003e \u003cp\u003e6.7 The Unilateral Laplace Transform 191\u003c\/p\u003e \u003cp\u003e6.7.1 The Differentiation Property of the Unilateral Fourier Transform 193\u003c\/p\u003e \u003cp\u003eWorked Exercise: Differentiation Property of the Unilateral Fourier Transform Involving Higher Order Derivatives 195\u003c\/p\u003e \u003cp\u003eWorked Exercise: Example of Differentiation Using the Unilateral Fourier Transform 196\u003c\/p\u003e \u003cp\u003eWorked Exercise: Discharge of an RC Circuit 197\u003c\/p\u003e \u003cp\u003e6.7.2 Generalization to the Unilateral Laplace Transform 198\u003c\/p\u003e \u003cp\u003e6.8 Exercises 199\u003c\/p\u003e \u003cp\u003eInterlude: Discrete Signals and Systems: Why do we Need Them? 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 The Sampling Theorem and the Discrete Time Fourier Transform (DTFT) 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Discrete Signals 205\u003c\/p\u003e \u003cp\u003e7.2 Fourier Transforms of Discrete Signals and the Sampling Theorem 207\u003c\/p\u003e \u003cp\u003e7.3 The Discrete Time Fourier Transform (DTFT) 216\u003c\/p\u003e \u003cp\u003eWorked Exercise: Example of a Matlab Routine to Calculate the Dtft 218\u003c\/p\u003e \u003cp\u003eWorked Exercise: Fourier Transform from the DTFT 221\u003c\/p\u003e \u003cp\u003e7.4 The Inverse DTFT 223\u003c\/p\u003e \u003cp\u003e7.5 Properties of the DTFT 224\u003c\/p\u003e \u003cp\u003e7.5.1 ‘Time’ shifting 225\u003c\/p\u003e \u003cp\u003e7.5.2 Difference 226\u003c\/p\u003e \u003cp\u003e7.5.3 Sum 228\u003c\/p\u003e \u003cp\u003e7.5.4 Convolution in the ‘Time’ Domain 229\u003c\/p\u003e \u003cp\u003e7.5.5 Product in the Time Domain 230\u003c\/p\u003e \u003cp\u003e7.5.6 The Theorem that Should not be: Energy of Discrete Signals 231\u003c\/p\u003e \u003cp\u003e7.6 Concluding Remarks 235\u003c\/p\u003e \u003cp\u003e7.7 Exercises 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The Discrete Fourier Transform (DFT) 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Discretizing the Frequency Domain 239\u003c\/p\u003e \u003cp\u003e8.2 The DFT and the Fast Fourier Transform (fft) 246\u003c\/p\u003e \u003cp\u003eWorked Exercise: Getting the Centralized DFT Using the Command fft 250\u003c\/p\u003e \u003cp\u003eWorked Exercise: Getting the Fourier Transform with the fft 254\u003c\/p\u003e \u003cp\u003eWorked Exercise: Obtaining the Inverse Fourier Transform Using the ifft 256\u003c\/p\u003e \u003cp\u003e8.3 The Circular Time Shift 258\u003c\/p\u003e \u003cp\u003e8.4 The Circular Convolution 259\u003c\/p\u003e \u003cp\u003e8.5 Relationship Between Circular and Linear Convolutions 264\u003c\/p\u003e \u003cp\u003e8.6 Parseval’s Theorem for the DFT 269\u003c\/p\u003e \u003cp\u003e8.7 Exercises 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Discrete Systems 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction and Properties 275\u003c\/p\u003e \u003cp\u003e9.1.1 Linearity 276\u003c\/p\u003e \u003cp\u003e9.1.2 ‘Time’ invariance 276\u003c\/p\u003e \u003cp\u003e9.1.3 Causality 276\u003c\/p\u003e \u003cp\u003e9.1.4 Stability 276\u003c\/p\u003e \u003cp\u003e9.2 Linear and Time Invariant Discrete Systems 277\u003c\/p\u003e \u003cp\u003eWorked Exercise: Further Advantages of Frequency Domain 279\u003c\/p\u003e \u003cp\u003e9.3 Digital Filters 283\u003c\/p\u003e \u003cp\u003e9.4 Exercises 285\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Introduction to the z-transform 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Motivation: Stability of LTI Systems 287\u003c\/p\u003e \u003cp\u003e10.2 The z-transform as a Generalization of the DTFT 289\u003c\/p\u003e \u003cp\u003eWorked Exercise: Example of z-transform 290\u003c\/p\u003e \u003cp\u003e10.3 Relationship Between the z-transform and the Laplace Transform 292\u003c\/p\u003e \u003cp\u003e10.4 Properties of the z-transform 293\u003c\/p\u003e \u003cp\u003e10.4.1 ‘Time’ shifting 294\u003c\/p\u003e \u003cp\u003e10.4.2 Difference 294\u003c\/p\u003e \u003cp\u003e10.4.3 Sum 294\u003c\/p\u003e \u003cp\u003e10.4.4 Convolution in the Time Domain 294\u003c\/p\u003e \u003cp\u003e10.5 The Transfer Function of Discrete LTI Systems 295\u003c\/p\u003e \u003cp\u003e10.6 The Unilateral z-transform 295\u003c\/p\u003e \u003cp\u003e10.7 Exercises 297\u003c\/p\u003e \u003cp\u003eReferences with Comments 299\u003c\/p\u003e \u003cp\u003eAppendix A: Laplace Transform Property of Product in the Time Domain 301\u003c\/p\u003e \u003cp\u003eAppendix B: List of Properties of Laplace Transforms 303\u003c\/p\u003e \u003cp\u003eIndex 305\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eEmiliano R. Martins\u003c\/b\u003e majored in electrical engineering at the University of São Paulo (Brazil), then obtained a master’s degree in electrical engineering from the same university, another master’s degree in photonics from the Erasmus Mundus Master in Photonics (European consortium), and a PhD in physics from the University of St. Andrews (UK). He has been teaching signals and systems in the Department of Electrical and Computer Engineering of the University of São Paulo (Brazil) since 2016. He is also the author of \u003ci\u003eEssentials of Semiconductor Device Physics.\u003c\/i\u003e   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eNovel approach to the theory of signals and systems in an introductory, accessible textbook\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eSignals and Systems have the reputation of being a difficult subject. \u003ci\u003eEssentials of Signals and Systems \u003c\/i\u003eis a standalone textbook aiming to change this reputation with a novel approach to this subject, teaching the essential concepts of signals and systems in a clear, friendly, intuitive, and accessible way.  \u003c\/p\u003e\u003cp\u003eThe overall vision of the book is that traditional approaches to signals and systems are unnecessarily convoluted, and that students’ learning experiences are much improved by making a clear connection between the theory of representation of signal and systems, and the theory of representation of vectors and matrices in linear algebra. The author begins by reviewing the theory of representation in linear algebra, emphasizing that vectors are represented by different coordinates when the basis is changed, and that the basis of eigenvectors is special because it diagonalizes the operator. Thus, in each step of the theory of representation of signals and systems, the author shows the analogous step in linear algebra. With such an approach, students can easily understand that signals are analogous to vectors, that systems are analogous to matrices, and that Fourier transforms are a change to the basis that diagonalizes LTI operators. \u003c\/p\u003e\u003cp\u003eThe text emphasizes the key concepts in the analysis of linear and time invariant systems, demonstrating both the algebraic and physical meaning of Fourier transforms. The text carefully connects the most important transforms (Fourier series, Discrete Time Fourier Transform, Discrete Fourier Transforms, Laplace and z-transforms), emphasizing their relationships and motivations. The continuous and discrete time domains are neatly connected, and the students are shown step-by-step how to use the fft function, using simple examples.  \u003c\/p\u003e\u003cp\u003eIncorporating learning objectives and problems, and supported with simple Matlab codes to illustrate concepts, the text presents to students the foundations to allow the reader to pursue more advanced topics in later courses.  \u003c\/p\u003e\u003cp\u003eDeveloped from lecture notes already tested with more than 600 students over six years, \u003ci\u003eEssentials of Signals and Systems \u003c\/i\u003ecovers sample topics such as: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eBasic concepts of linear algebra that are pertinent to signals and systems. \u003c\/li\u003e \u003cli\u003eTheory of representation of signals, with an emphasis on the notion of Fourier transforms as a change of basis, and on their physical meaning. \u003c\/li\u003e \u003cli\u003eTheory of representation of linear and time invariant systems, emphasizing the role of Fourier transforms as a change to the basis of eigenvectors, and the physical meaning of the impulse and frequency responses. \u003c\/li\u003e \u003cli\u003eWhat signals and systems have to do with phasors and impedances, and the basics of filter design.\u003c\/li\u003e \u003cli\u003eThe Laplace transform as an extension of Fourier transforms.\u003c\/li\u003e \u003cli\u003eDiscrete signals and systems, the sampling theorem, the Discrete Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT), and how to use the fast fourier transform (fft).\u003c\/li\u003e \u003cli\u003eThe z-transform as an extension of the Discrete Time Fourier Transform.\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eEssentials of Signals and Systems \u003c\/i\u003eis an immensely helpful textbook on the subject for undergraduate students of electrical and computer engineering. The information contained within is also pertinent to those in physics and related fields involved in the understanding of signals and system processing, including those working on related practical applications.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989163098341,"sku":"NP9781119909217","price":58.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119909217.jpg?v=1761783049","url":"https:\/\/k12savings.com\/products\/essentials-of-signals-and-systems-isbn-9781119909217","provider":"K12savings","version":"1.0","type":"link"}