{"product_id":"signals-and-systems-theory-and-practical-explorations-with-python-hardback-9781394215751","title":"Signals and Systems; Theory and Practical Explorations with Python (Hardback) 9781394215751","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSignals and Systems\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eTheory and Practical Explorations with Python\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eFatos Tunay Yarman Vural (Author), Emre Akbas (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781394215751, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 February 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e448 pages\u003cbr\u003e25.9 x 18.4 x 2.9 cm, 1.134 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eIntroductory course textbook on signals and systems with numerous examples and code snippets implemented in Python\u003c\/b\u003e \u003c\/p\u003e\n\u003cp\u003eSupported by code examples, \u003ci\u003eSignals and Systems: Theory and Practical Explorations with Python\u003c\/i\u003e is a textbook resource for a complete introductory course in systems and signals, enabling readers to run Python programs for convolution, discrete time Fourier transforms and series, sampling, and interpolation for a wide range of functions. Readers are guided step-by-step through basic differential equations, basic linear algebra, and calculus to ensure full comprehension of the exercises. \u003c\/p\u003e\n\u003cp\u003eThis book is supported by a companion website, hosting interactive material to draw functions, and run programs in Python; it is enriched with audiovisual material via linking to related videos. Links to resources that provide a deeper explanation about the important concepts in the book, such as the systems approach, complex numbers, harmony, the Euler equation, and Hilbert spaces, are also included. \u003c\/p\u003e\n\u003cp\u003eWritten by two highly qualified academics, topics covered include: \u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eSystems approach for modeling the natural and manmade systems and some application areas\u003c\/li\u003e \u003cli\u003eRepresentation of complex and real signals by basic functions, such as real and complex exponentials, unit step and unit impulse functions\u003c\/li\u003e \u003cli\u003eProperties of signals, such as symmetry, harmony, energy, power, continuity and discreteness\u003c\/li\u003e \u003cli\u003eConvolution and correlation operations for continuous time and discrete time signals and systems\u003c\/li\u003e \u003cli\u003eRepresentation of systems by impulse response, frequency response, transfer function, block diagram, differential and difference equations \u003c\/li\u003e \u003cli\u003eProperties of systems, such as linearity, time invariance, memory, invertibility, stability and causality\u003c\/li\u003e \u003cli\u003eContinuous time and discrete time Fourier analysis in Hilbert space and their extension to Laplaca transform and z-transform \u003c\/li\u003e \u003cli\u003eFiltering by Linear Time Invariant systems in time and frequency domains, covering low pass, high pass band pass and band reject filters\u003c\/li\u003e \u003cli\u003eSampling theorems for continuous time and discrete time systems, covering A\/D and D\/A conversion, sampling and interpolation\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eSignals and Systems \u003c\/i\u003eis an ideal textbook resource for a one semester introductory course on signals and systems for upper level undergraduate and graduate students in computer science, electrical engineering and data science. It is also a useful reference for professionals working in bioinformatics, robotics, remote sensing, and related fields.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eAbout the Authors xiii\u003c\/p\u003e \u003cp\u003ePreface xiv\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Systems and Signals 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Example Applications 2\u003c\/p\u003e \u003cp\u003e1.1.1 Three-Dimensional World Models by LIDAR Signals 3\u003c\/p\u003e \u003cp\u003e1.1.2 Modeling the Brain Networks from the Brain Signals 3\u003c\/p\u003e \u003cp\u003e1.1.3 Detecting the Buildings from the Remote-Sensed Satellite Images 4\u003c\/p\u003e \u003cp\u003e1.1.4 Noise Reduction in Old Records 4\u003c\/p\u003e \u003cp\u003e1.2 Relationship Between Signals and Systems 4\u003c\/p\u003e \u003cp\u003e1.3 Mathematical Representation of Signals and Systems 5\u003c\/p\u003e \u003cp\u003e1.3.1 Signals Represented by Functions 6\u003c\/p\u003e \u003cp\u003e1.3.2 Types of Signals 6\u003c\/p\u003e \u003cp\u003e1.3.3 Energy of a Signal 9\u003c\/p\u003e \u003cp\u003e1.3.4 Power of a Signal 10\u003c\/p\u003e \u003cp\u003e1.4 Operations on the Time Variable of Signals 10\u003c\/p\u003e \u003cp\u003e1.4.1 Time Shift 11\u003c\/p\u003e \u003cp\u003e1.4.2 Time Reverse 12\u003c\/p\u003e \u003cp\u003e1.4.3 Time Scale 13\u003c\/p\u003e \u003cp\u003e1.4.4 Time Scale and Shift 15\u003c\/p\u003e \u003cp\u003e1.5 Signals with Symmetry Properties 19\u003c\/p\u003e \u003cp\u003e1.5.1 Periodic Signals 21\u003c\/p\u003e \u003cp\u003e1.5.1.1 Continuous Time Periodic Signals 22\u003c\/p\u003e \u003cp\u003e1.5.1.2 Discrete Time Periodic Signals 23\u003c\/p\u003e \u003cp\u003e1.5.2 Even and Odd Signals 24\u003c\/p\u003e \u003cp\u003e1.6 Complex Signals Represented by Complex Functions 28\u003c\/p\u003e \u003cp\u003e1.6.1 Complex Numbers Represented in Cartesian Coordinate System 28\u003c\/p\u003e \u003cp\u003e1.6.2 Complex Numbers Represented in Polar Coordinate System and Euler’s Number 30\u003c\/p\u003e \u003cp\u003e1.6.3 Complex Functions 33\u003c\/p\u003e \u003cp\u003e1.7 Chapter Summary 35\u003c\/p\u003e \u003cp\u003eProblems 36\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basic Building Blocks of Signals 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 LEGO Functions of Signals 43\u003c\/p\u003e \u003cp\u003e2.2 King of the Functions: Exponential Function 44\u003c\/p\u003e \u003cp\u003e2.2.1 Real Exponential Function 44\u003c\/p\u003e \u003cp\u003e2.2.1.1 Continuous Time Real Exponential Function 44\u003c\/p\u003e \u003cp\u003e2.2.1.2 Discrete Time Real Exponential Function 46\u003c\/p\u003e \u003cp\u003e2.2.2 Complex Exponential Function 47\u003c\/p\u003e \u003cp\u003e2.2.2.1 Continuous Time Complex Exponential Functions 48\u003c\/p\u003e \u003cp\u003e2.2.2.2 Harmonically Related Complex Exponential 49\u003c\/p\u003e \u003cp\u003e2.2.2.3 Complex Exponential Function for Discrete Time Signals 53\u003c\/p\u003e \u003cp\u003e2.3 Unit Impulse Function 55\u003c\/p\u003e \u003cp\u003e2.3.1 Discrete Time Unit Impulse Function or Dirac-Delta Function 55\u003c\/p\u003e \u003cp\u003e2.3.2 Continuous Time Unit Impulse Function 56\u003c\/p\u003e \u003cp\u003e2.3.3 Comparison of Discrete Time and Continuous Time Unit Impulse Functions 57\u003c\/p\u003e \u003cp\u003e2.4 Unit Step Function 58\u003c\/p\u003e \u003cp\u003e2.4.1 Discrete Time Unit Step Function 58\u003c\/p\u003e \u003cp\u003e2.4.2 Relationship Between the Discrete Time Unit Step and Unit Impulse Functions 58\u003c\/p\u003e \u003cp\u003e2.4.3 Continuous Time Unit Step Function 60\u003c\/p\u003e \u003cp\u003e2.4.4 Comparison of Discrete Time and Continuous Time Unit Step functions 61\u003c\/p\u003e \u003cp\u003e2.4.4.1 Relationship Between the Continuous Time Unit Step and Unit Impulse Functions 61\u003c\/p\u003e \u003cp\u003e2.5 Chapter Summary 65\u003c\/p\u003e \u003cp\u003eProblems 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Basic Building Blocks and Properties of Systems 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Representation of Systems by Equations 69\u003c\/p\u003e \u003cp\u003e3.2 Interconnection of Basic Systems: Series, Parallel, Hybrid, and Feedback Control Systems 70\u003c\/p\u003e \u003cp\u003e3.2.1 Series Systems 70\u003c\/p\u003e \u003cp\u003e3.2.2 Parallel Systems 71\u003c\/p\u003e \u003cp\u003e3.2.3 Hybrid Systems 71\u003c\/p\u003e \u003cp\u003e3.2.3.1 Feedback Control Systems 72\u003c\/p\u003e \u003cp\u003e3.2.3.2 An Example of System Modeling: Neurons as a Subsystem of Human Brain 73\u003c\/p\u003e \u003cp\u003e3.3 Properties of Systems 74\u003c\/p\u003e \u003cp\u003e3.3.1 Memory 75\u003c\/p\u003e \u003cp\u003e3.3.2 Causality 76\u003c\/p\u003e \u003cp\u003e3.3.3 Invertibility 77\u003c\/p\u003e \u003cp\u003e3.3.4 Stability 79\u003c\/p\u003e \u003cp\u003e3.3.5 Time Invariance 80\u003c\/p\u003e \u003cp\u003e3.3.6 Linearity and Superposition Property 81\u003c\/p\u003e \u003cp\u003e3.4 Basic Building Blocks of Systems and Their Properties 85\u003c\/p\u003e \u003cp\u003e3.4.1 Scalar Multiplier 85\u003c\/p\u003e \u003cp\u003e3.4.2 Adder 85\u003c\/p\u003e \u003cp\u003e3.4.3 Multiplier 85\u003c\/p\u003e \u003cp\u003e3.4.4 Integrator 86\u003c\/p\u003e \u003cp\u003e3.4.5 Differentiator 86\u003c\/p\u003e \u003cp\u003e3.4.6 Unit Delay Operator 87\u003c\/p\u003e \u003cp\u003e3.4.7 Unit Advance Operator 87\u003c\/p\u003e \u003cp\u003e3.5 Chapter Summary 89\u003c\/p\u003e \u003cp\u003eProblems 89\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Representation of Linear Time-Invariant Systems by Impulse Response and Convolution Operation 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Representation of LTI Systems by Impulse Response 96\u003c\/p\u003e \u003cp\u003e4.1.1 Representation of Discrete Time Linear Time-Invariant Systems by Impulse Response 97\u003c\/p\u003e \u003cp\u003e4.1.2 Representation of Continuous Time Linear Time-Invariant System 98\u003c\/p\u003e \u003cp\u003e4.1.3 Convolution Operation in Continuous Time 101\u003c\/p\u003e \u003cp\u003e4.1.4 Convolution Operation in Discrete Time Systems 105\u003c\/p\u003e \u003cp\u003e4.1.5 Cross-correlation and Autocorrelation Operations 107\u003c\/p\u003e \u003cp\u003e4.2 Properties of Impulse Response for LTI Systems 110\u003c\/p\u003e \u003cp\u003e4.2.1 Impulse Response of Memoryless LTI Systems 110\u003c\/p\u003e \u003cp\u003e4.2.2 Impulse Response of Causal LTI Systems 110\u003c\/p\u003e \u003cp\u003e4.2.3 Inverse of Impulse Response for LTI Systems 111\u003c\/p\u003e \u003cp\u003e4.2.4 Impulse Response of Stable LTI Systems 114\u003c\/p\u003e \u003cp\u003e4.2.5 Unit Step Response 115\u003c\/p\u003e \u003cp\u003e4.3 An Application of Convolution in Machine Learning 116\u003c\/p\u003e \u003cp\u003e4.4 Chapter Summary 118\u003c\/p\u003e \u003cp\u003eProblems 118\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Representation of LTI Systems by Differential and Difference Equations 123\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Linear Constant-Coefficient Differential Equations 123\u003c\/p\u003e \u003cp\u003e5.2 Representation of a Continuous Time LTI System by Differential Equations 124\u003c\/p\u003e \u003cp\u003e5.3 Solving the Linear Constant Coefficient Differential Equations That Represent LTI Systems 126\u003c\/p\u003e \u003cp\u003e5.3.1 Finding the Particular Solution 127\u003c\/p\u003e \u003cp\u003e5.3.2 Finding the Homogeneous Solution 128\u003c\/p\u003e \u003cp\u003e5.3.3 Finding the General Solution 129\u003c\/p\u003e \u003cp\u003e5.3.4 Transfer Function of a Continuous Time LTI System 134\u003c\/p\u003e \u003cp\u003e5.4 Linear Constant Coefficient Difference Equations 136\u003c\/p\u003e \u003cp\u003e5.4.1 Representation of a Discrete Time LTI Systems by Difference Equations 136\u003c\/p\u003e \u003cp\u003e5.4.2 Solution to Linear Constant Coefficient Difference Equations 137\u003c\/p\u003e \u003cp\u003e5.4.3 Transfer Function of a Discrete Time LTI System 139\u003c\/p\u003e \u003cp\u003e5.5 Relationship Between the Impulse Response and Difference or Differential Equations 140\u003c\/p\u003e \u003cp\u003e5.6 Block Diagram Representation of Differential Equations for LTI Systems 144\u003c\/p\u003e \u003cp\u003e5.7 Chapter Summary 147\u003c\/p\u003e \u003cp\u003eProblems 148\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Fourier Series Representation of Continuous Time Periodic Signals 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 History 156\u003c\/p\u003e \u003cp\u003e6.2 Mathematical Representation of Waves and Harmony 157\u003c\/p\u003e \u003cp\u003e6.3 Dirichlet Conditions 160\u003c\/p\u003e \u003cp\u003e6.4 Fourier Theorem 162\u003c\/p\u003e \u003cp\u003e6.4.1 Proof Sketch for the Fourier Theorem 162\u003c\/p\u003e \u003cp\u003e6.4.2 Terminology 163\u003c\/p\u003e \u003cp\u003e6.5 Frequency Domain and Hilbert Spaces 164\u003c\/p\u003e \u003cp\u003e6.6 Response of a Linear Time-Invariant System to the Continuous Time Complex Exponential Input Signal 170\u003c\/p\u003e \u003cp\u003e6.6.1 Eigenfunctions and Eigenvalues of a Continuous Time LTI Systems 171\u003c\/p\u003e \u003cp\u003e6.7 Convergence of the Fourier Series and Gibbs Phenomenon 173\u003c\/p\u003e \u003cp\u003e6.8 Properties of Fourier Series for Continuous Time Functions 174\u003c\/p\u003e \u003cp\u003e6.8.1 Linearity Property 174\u003c\/p\u003e \u003cp\u003e6.8.2 Time Shifting Property 174\u003c\/p\u003e \u003cp\u003e6.8.3 Time Scale Property 175\u003c\/p\u003e \u003cp\u003e6.8.4 Time Reversal Property 175\u003c\/p\u003e \u003cp\u003e6.8.5 Convolution Property 175\u003c\/p\u003e \u003cp\u003e6.8.6 Multiplication Property 176\u003c\/p\u003e \u003cp\u003e6.8.7 Conjugate Symmetry 176\u003c\/p\u003e \u003cp\u003e6.8.8 Parseval’s Equality 177\u003c\/p\u003e \u003cp\u003e6.8.9 Differentiation Property 177\u003c\/p\u003e \u003cp\u003e6.9 Trigonometric Fourier Series for Continuous Time Functions 180\u003c\/p\u003e \u003cp\u003e6.10 Trigonometric Fourier Series for Continuous Time Even and Odd Functions 182\u003c\/p\u003e \u003cp\u003e6.11 Chapter Summary 185\u003c\/p\u003e \u003cp\u003eProblems 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Fourier Series Representation of Discrete Time Periodic Signals 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Fourier Series Theorem for Discrete Time Functions 191\u003c\/p\u003e \u003cp\u003e7.2 Discrete Time Fourier Series Representation in Hilbert Space 193\u003c\/p\u003e \u003cp\u003e7.3 Properties of Discrete Time Fourier Series 199\u003c\/p\u003e \u003cp\u003e7.3.1 Difference Property 203\u003c\/p\u003e \u003cp\u003e7.3.2 Convolution Property 205\u003c\/p\u003e \u003cp\u003e7.3.3 Multiplication Property 208\u003c\/p\u003e \u003cp\u003e7.4 Discrete Time LTI Systems with Periodic Input and Output Pairs 211\u003c\/p\u003e \u003cp\u003e7.4.1 Eigenfunctions, Eigenvalues, and Transfer Functions of a Discrete Time LTI Systems 212\u003c\/p\u003e \u003cp\u003e7.4.2 Relationship Between the Fourier Series of Periodic Input and Output Pairs of Discrete Time LTI Systems 213\u003c\/p\u003e \u003cp\u003e7.5 Chapter Summary 215\u003c\/p\u003e \u003cp\u003eProblems 215\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Continuous Time Fourier Transform and Its Extension to Laplace Transform 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Fourier Series Extension to Aperiodic Functions 222\u003c\/p\u003e \u003cp\u003e8.2 Existence and Convergence of the Fourier Transforms: Dirichlet Conditions 224\u003c\/p\u003e \u003cp\u003e8.3 Fourier Transforms 225\u003c\/p\u003e \u003cp\u003e8.4 Comparison of Fourier Series and Fourier Transform 226\u003c\/p\u003e \u003cp\u003e8.5 Frequency Content of Fourier Transform 227\u003c\/p\u003e \u003cp\u003e8.6 Representation of LTI Systems in Frequency Domain by Frequency Response 232\u003c\/p\u003e \u003cp\u003e8.7 Relationship Between the Fourier Series and Fourier Transform of Periodic Functions 235\u003c\/p\u003e \u003cp\u003e8.8 Properties of Fourier Transform: For Continuous Time Signals and Systems 238\u003c\/p\u003e \u003cp\u003e8.8.1 Basic Properties of Continuous Time Fourier Transform 239\u003c\/p\u003e \u003cp\u003e8.8.2 Continuous Time Linear Time-Invariant Systems in Frequency Domain 256\u003c\/p\u003e \u003cp\u003e8.9 Laplace Transforms as an Extension of Continuous Time Fourier Transforms 259\u003c\/p\u003e \u003cp\u003e8.9.1 One-Sided Laplace Transform 260\u003c\/p\u003e \u003cp\u003e8.9.2 Region of Convergence in Laplace Transforms 261\u003c\/p\u003e \u003cp\u003e8.10 Inverse of Laplace Transform 265\u003c\/p\u003e \u003cp\u003e8.11 Continuous Time Linear Time-Invariant Systems in Laplace Domain 268\u003c\/p\u003e \u003cp\u003e8.11.1 Eigenvalues and Transfer Functions in s-Domain 269\u003c\/p\u003e \u003cp\u003e8.12 Chapter Summary 272\u003c\/p\u003e \u003cp\u003eProblems 273\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Discrete Time Fourier Transform and Its Extension to z-Transforms 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Fourier Series Extension to Discrete Time Aperiodic Functions 281\u003c\/p\u003e \u003cp\u003e9.1.1 Discrete Time Fourier Transform 282\u003c\/p\u003e \u003cp\u003e9.2 Dirichlet Conditions Are Relaxed for the Existence of Discrete Time Fourier Transform 284\u003c\/p\u003e \u003cp\u003e9.3 Fourier Transform of Discrete Time Periodic Functions 293\u003c\/p\u003e \u003cp\u003e9.4 Properties of Fourier Transforms for Discrete Time Signals and Systems 297\u003c\/p\u003e \u003cp\u003e9.4.1 Basic Properties of Discrete Time Fourier Transform 297\u003c\/p\u003e \u003cp\u003e9.5 Discrete Time Linear Time-Invariant Systems in Frequency Domain 307\u003c\/p\u003e \u003cp\u003e9.6 Representation of Discrete Time LTI Systems 310\u003c\/p\u003e \u003cp\u003e9.6.1 Impulse Response 311\u003c\/p\u003e \u003cp\u003e9.6.2 Unit Step Response 311\u003c\/p\u003e \u003cp\u003e9.6.3 Frequency Response 312\u003c\/p\u003e \u003cp\u003e9.6.4 Difference Equation 313\u003c\/p\u003e \u003cp\u003e9.6.5 Block Diagram Representation 314\u003c\/p\u003e \u003cp\u003e9.7 z-Transforms as an Extension of Discrete Time Fourier Transforms 317\u003c\/p\u003e \u003cp\u003e9.7.1 One-Sided z-Transform 319\u003c\/p\u003e \u003cp\u003e9.7.2 Region of Convergence in z-Transforms 320\u003c\/p\u003e \u003cp\u003e9.8 Inverse of z-Transform 325\u003c\/p\u003e \u003cp\u003e9.9 Discrete Time Linear Time-Invariant Systems in z-Domain 329\u003c\/p\u003e \u003cp\u003e9.9.1 Eigenvalues and Transfer Functions in z-Domain 329\u003c\/p\u003e \u003cp\u003e9.10 Chapter Summary 333\u003c\/p\u003e \u003cp\u003eProblems 334\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Linear Time-Invariant Systems as Filters 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Filtering the Periodic Signals by Frequency Response 344\u003c\/p\u003e \u003cp\u003e10.2 Filtering the Aperiodic Signals by Frequency Response 345\u003c\/p\u003e \u003cp\u003e10.3 Frequency Ranges of Frequency Response 347\u003c\/p\u003e \u003cp\u003e10.4 Filtering with LTI Systems 347\u003c\/p\u003e \u003cp\u003e10.5 Ideal Filters for Discrete Time and Continuous Time LTI Systems 348\u003c\/p\u003e \u003cp\u003e10.5.1 Ideal Low-Pass Filters 349\u003c\/p\u003e \u003cp\u003e10.5.2 Ideal High-Pass Filters 349\u003c\/p\u003e \u003cp\u003e10.5.3 Ideal Band-Pass and Band-Reject Filters 350\u003c\/p\u003e \u003cp\u003e10.6 Discrete Time Real Filters 358\u003c\/p\u003e \u003cp\u003e10.6.1 Discrete Time Low-Pass and High-Pass Real Filters 358\u003c\/p\u003e \u003cp\u003e10.6.2 Band-Stop Filters for Filtering Well-Defined Frequency Bandwidths 363\u003c\/p\u003e \u003cp\u003e10.7 Continuous Time Real Filters 365\u003c\/p\u003e \u003cp\u003e10.8 Chapter Summary 370\u003c\/p\u003e \u003cp\u003eProblems 370\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Continuous Time Sampling 375\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Sampling 376\u003c\/p\u003e \u003cp\u003e11.2 Properties of the Sampled Signal in Time and Frequency Domains 377\u003c\/p\u003e \u003cp\u003e11.3 Reconstruction 382\u003c\/p\u003e \u003cp\u003e11.4 Aliasing 385\u003c\/p\u003e \u003cp\u003e11.5 Sampling Theorem 388\u003c\/p\u003e \u003cp\u003e11.6 Sampling with Zero-Order Hold 389\u003c\/p\u003e \u003cp\u003e11.7 Reconstruction with Zero-Order Hold 391\u003c\/p\u003e \u003cp\u003e11.8 Sampling and Reconstruction with First-Order Hold 393\u003c\/p\u003e \u003cp\u003e11.9 Chapter Summary 394\u003c\/p\u003e \u003cp\u003eProblems 395\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Discrete Time Sampling and Processing 403\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Time Normalization 404\u003c\/p\u003e \u003cp\u003e12.2 C\/D Conversion: x(t) → x[n] 405\u003c\/p\u003e \u003cp\u003e12.3 D\/C Conversion 407\u003c\/p\u003e \u003cp\u003e12.3.1 Band-Limited Digital Differentiator 409\u003c\/p\u003e \u003cp\u003e12.3.2 Digital Time Shift 413\u003c\/p\u003e \u003cp\u003e12.4 Sampling the Discrete Time Signals 415\u003c\/p\u003e \u003cp\u003e12.4.1 Discrete Time Impulse Train Sampling 415\u003c\/p\u003e \u003cp\u003e12.5 Reconstruction of Discrete Time Signal from Its Sampled Counterpart 418\u003c\/p\u003e \u003cp\u003e12.6 Discrete Time Decimation and Interpolation 419\u003c\/p\u003e \u003cp\u003e12.7 Chapter Summary 421\u003c\/p\u003e \u003cp\u003eProblems 421\u003c\/p\u003e \u003cp\u003eBibliography 425\u003c\/p\u003e \u003cp\u003eIndex 427\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" 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