# Book Title: LINEAR SYSTEMS AND SIGNALS > Author: B. P. Lathi and R. A. Green | Category: engineering | Pages: 1010 | Year: 2017 ## Overview & Metadata - Document ID: linear-systems-and-signals-3rd-edition-bp-lathi - Category: engineering - Tags: 3rd, and, lathi, linear, signals, systems - Primary Markdown Path: engineering/linear-systems-and-signals-3rd-edition-bp-lathi/linear-systems-and-signals-3rd-edition-bp-lathi.md - Original PDF Path: engineering/linear-systems-and-signals-3rd-edition-bp-lathi/linear-systems-and-signals-3rd-edition-bp-lathi.pdf - Layout Coordinates JSON: engineering/linear-systems-and-signals-3rd-edition-bp-lathi/linear-systems-and-signals-3rd-edition-bp-lathi.layout.json - Folder Name: linear-systems-and-signals-3rd-edition-bp-lathi - Starlight Content Route: /engineering/linear-systems-and-signals/ - Book LLM Text URL: /engineering/linear-systems-and-signals-3rd-edition-bp-lathi/llm.txt ## Table of Contents & Structure - Cover - Page 1 - Half title - Page 3 - Series page - Page 4 - Title page - Page 5 - Copyright page - Page 6 - CONTENTS - Page 7 - PREFACE - Page 17 - B BACKGROUND - Page 21 - B.1 COMPLEX NUMBERS - Page 21 - B.1-1 A Historical Note - Page 21 - B.1-2 Algebra of Complex Numbers - Page 25 - B.2 SINUSOIDS - Page 36 - B.2-1 Addition of Sinusoids - Page 38 - B.2-2 Sinusoids in Terms of Exponentials - Page 40 - B.3 SKETCHING SIGNALS - Page 40 - B.3-1 Monotonic Exponentials - Page 40 - B.3-2 The Exponentially Varying Sinusoid - Page 42 - B.4 CRAMER’S RULE - Page 43 - B.5 PARTIAL FRACTION EXPANSION - Page 45 - B.5-1 Method of Clearing Fractions - Page 46 - B.5-2 The Heaviside “Cover-Up” Method - Page 47 - B.5-3 Repeated Factors of Q(x) - Page 51 - B.5-4 A Combination of Heaviside “Cover-Up” and Clearing Fractions - Page 52 - B.5-5 Improper F(x) with m = n - Page 54 - B.5-6 Modified Partial Fractions - Page 55 - B.6 VECTORS AND MATRICES - Page 56 - B.6-1 Some Definitions and Properties - Page 57 - B.6-2 Matrix Algebra - Page 58 - B.7 MATLAB: ELEMENTARY OPERATIONS - Page 62 - B.7-1 MATLAB Overview - Page 62 - B.7-2 Calculator Operations - Page 63 - B.7-3 Vector Operations - Page 65 - B.7-4 Simple Plotting - Page 66 - B.7-5 Element-by-Element Operations - Page 68 - B.7-6 Matrix Operations - Page 69 - B.7-7 Partial Fraction Expansions - Page 73 - B.8 APPENDIX: USEFUL MATHEMATICAL FORMULAS - Page 74 - B.8-1 Some Useful Constants - Page 74 - B.8-2 Complex Numbers - Page 74 - B.8-3 Sums - Page 74 - B.8-4 Taylor and Maclaurin Series - Page 75 - B.8-5 Power Series - Page 75 - B.8-6 Trigonometric Identities - Page 75 - B.8-7 Common Derivative Formulas - Page 76 - B.8-8 Indefinite Integrals - Page 77 - B.8-9 L’Hôpital’s Rule - Page 78 - B.8-10 Solution of Quadratic and Cubic Equations - Page 78 - REFERENCES - Page 78 - PROBLEMS - Page 79 - 1 SIGNALS AND SYSTEMS - Page 84 - 1.1 SIZE OF A SIGNAL - Page 84 - 1.1-1 Signal Energy - Page 85 - 1.1-2 Signal Power - Page 85 - 1.2 SOME USEFUL SIGNAL OPERATIONS - Page 91 - 1.2-1 Time Shifting - Page 91 - 1.2-2 Time Scaling - Page 93 - 1.2-3 Time Reversal - Page 96 - 1.2-4 Combined Operations - Page 97 - 1.3 CLASSIFICATION OF SIGNALS - Page 98 - 1.3-1 Continuous-Time and Discrete-Time Signals - Page 98 - 1.3-2 Analog and Digital Signals - Page 98 - 1.3-3 Periodic and Aperiodic Signals - Page 99 - 1.3-4 Energy and Power Signals - Page 102 - 1.3-5 Deterministic and Random Signals - Page 102 - 1.4 SOME USEFUL SIGNAL MODELS - Page 102 - 1.4-1 The Unit Step Function u(t) - Page 103 - 1.4-2 The Unit Impulse Function δ(t) - Page 106 - 1.4-3 The Exponential Function e^{st} - Page 109 - 1.5 EVEN AND ODD FUNCTIONS - Page 112 - 1.5-1 Some Properties of Even and Odd Functions - Page 112 - 1.5-2 Even and Odd Components of a Signal - Page 113 - 1.6 SYSTEMS - Page 115 - 1.7 CLASSIFICATION OF SYSTEMS - Page 117 - 1.7-1 Linear and Nonlinear Systems - Page 117 - 1.7-2 Time-Invariant and Time-Varying Systems - Page 122 - 1.7-3 Instantaneous and Dynamic Systems - Page 123 - 1.7-4 Causal and Noncausal Systems - Page 124 - 1.7-5 Continuous-Time and Discrete-Time Systems - Page 127 - 1.7-6 Analog and Digital Systems - Page 129 - 1.7-7 Invertible and Noninvertible Systems - Page 129 - 1.7-8 Stable and Unstable Systems - Page 130 - 1.8 SYSTEM MODEL: INPUT–OUTPUT DESCRIPTION - Page 131 - 1.8-1 Electrical Systems - Page 131 - 1.8-2 Mechanical Systems - Page 134 - 1.8-3 Electromechanical Systems - Page 138 - 1.9 INTERNAL AND EXTERNAL DESCRIPTIONS OF A SYSTEM - Page 139 - 1.10 INTERNAL DESCRIPTION: THE STATE-SPACE DESCRIPTION - Page 141 - 1.11 MATLAB: WORKING WITH FUNCTIONS - Page 146 - 1.11-1 Anonymous Functions - Page 146 - 1.11-2 Relational Operators and the Unit Step Function - Page 148 - 1.11-3 Visualizing Operations on the Independent Variable - Page 150 - 1.11-4 Numerical Integration and Estimating Signal Energy - Page 151 - 1.12 SUMMARY - Page 153 - REFERENCES - Page 155 - PROBLEMS - Page 156 - 2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS - Page 170 - 2.1 INTRODUCTION - Page 170 - 2.2 SYSTEM RESPONSE TO INTERNAL CONDITIONS: THE ZERO-INPUT RESPONSE - Page 171 - 2.2-1 Some Insights into the Zero-Input Behavior of a System - Page 181 - 2.3 THE UNIT IMPULSE RESPONSE h(t) - Page 183 - 2.4 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE - Page 188 - 2.4-1 The Convolution Integral - Page 190 - 2.4-2 Graphical Understanding of Convolution Operation - Page 198 - 2.4-3 Interconnected Systems - Page 210 - 2.4-4 A Very Special Function for LTIC Systems: The Everlasting Exponential e^{st} - Page 213 - 2.4-5 Total Response - Page 215 - 2.5 SYSTEM STABILITY - Page 216 - 2.5-1 External (BIBO) Stability - Page 216 - 2.5-2 Internal (Asymptotic) Stability - Page 218 - 2.5-3 Relationship Between BIBO and Asymptotic Stability - Page 219 - 2.6 INTUITIVE INSIGHTS INTO SYSTEM BEHAVIOR - Page 223 - 2.6-1 Dependence of System Behavior on Characteristic Modes - Page 223 - 2.6-2 Response Time of a System: The System Time Constant - Page 225 - 2.6-3 Time Constant and Rise Time of a System - Page 226 - 2.6-4 Time Constant and Filtering - Page 227 - 2.6-5 Time Constant and Pulse Dispersion (Spreading) - Page 229 - 2.6-6 Time Constant and Rate of Information Transmission - Page 229 - 2.6-7 The Resonance Phenomenon - Page 230 - 2.7 MATLAB: M-FILES - Page 232 - 2.7-1 Script M-Files - Page 233 - 2.7-2 Function M-Files - Page 234 - 2.7-3 For-Loops - Page 235 - 2.7-4 Graphical Understanding of Convolution - Page 237 - 2.8 APPENDIX: DETERMINING THE IMPULSE RESPONSE - Page 240 - 2.9 SUMMARY - Page 241 - REFERENCES - Page 243 - PROBLEMS - Page 243 - 3 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS - Page 257 - 3.1 INTRODUCTION - Page 257 - 3.1-1 Size of a Discrete-Time Signal - Page 258 - 3.2 USEFUL SIGNAL OPERATIONS - Page 260 - 3.3 SOME USEFUL DISCRETE-TIME SIGNAL MODELS - Page 265 - 3.3-1 Discrete-Time Impulse Function δ[n] - Page 265 - 3.3-2 Discrete-Time Unit Step Function u[n] - Page 266 - 3.3-3 Discrete-Time Exponential γ^n - Page 267 - 3.3-4 Discrete-Time Sinusoid cos(Omega n+θ) - Page 271 - 3.3-5 Discrete-Time Complex Exponential e^{jOmega n} - Page 272 - 3.4 EXAMPLES OF DISCRETE-TIME SYSTEMS - Page 273 - 3.4-1 Classification of Discrete-Time Systems - Page 282 - 3.5 DISCRETE-TIME SYSTEM EQUATIONS - Page 285 - 3.5-1 Recursive (Iterative) Solution of Difference Equation - Page 286 - 3.6 SYSTEM RESPONSE TO INTERNAL CONDITIONS: THE ZERO-INPUT RESPONSE - Page 290 - 3.7 THE UNIT IMPULSE RESPONSE h[n] - Page 297 - 3.7-1 The Closed-Form Solution of h[n] - Page 298 - 3.8 SYSTEM RESPONSE TO EXTERNAL INPUT: THE ZERO-STATE RESPONSE - Page 300 - 3.8-1 Graphical Procedure for the Convolution Sum - Page 308 - 3.8-2 Interconnected Systems - Page 314 - 3.8-3 Total Response - Page 317 - 3.9 SYSTEM STABILITY - Page 318 - 3.9-1 External (BIBO) Stability - Page 318 ## Available Raw Markdown Chunks (Direct Raw .md URLs) - [Raw 001_Cover.md](/engineering/linear-systems-and-signals-3rd-edition-bp-lathi/001_Cover.md) - [Raw 002_Half title.md](/engineering/linear-systems-and-signals-3rd-edition-bp-lathi/002_Half title.md) - [Raw 003_B.2 SINUSOIDS.md](/engineering/linear-systems-and-signals-3rd-edition-bp-lathi/003_B.2 SINUSOIDS.md) - [Raw 004_B.3 SKETCHING SIGNALS.md](/engineering/linear-systems-and-signals-3rd-edition-bp-lathi/004_B.3 SKETCHING SIGNALS.md) - 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[Web 056_4.4 ANALYSIS OF ELECTRICAL NETWORKS - THE TRANSFORMED NETWORK.md](/engineering/linear-systems-and-signals/056_4-4-analysis-of-electrical-networks-the-transformed-network/) - [Web 057_4.5 BLOCK DIAGRAMS.md](/engineering/linear-systems-and-signals/057_4-5-block-diagrams/) - [Web 058_4.6 SYSTEM REALIZATION.md](/engineering/linear-systems-and-signals/058_4-6-system-realization/) - [Web 059_4.7 APPLICATION TO FEEDBACK AND CONTROLS.md](/engineering/linear-systems-and-signals/059_4-7-application-to-feedback-and-controls/) - [Web 060_4.8 FREQUENCY RESPONSE OF AN LTIC SYSTEM.md](/engineering/linear-systems-and-signals/060_4-8-frequency-response-of-an-ltic-system/) - [Web 061_4.9 BODE PLOTS.md](/engineering/linear-systems-and-signals/061_4-9-bode-plots/) - [Web 062_4.10 FILTER DESIGN BY PLACEMENT OF POLES AND ZEROS OF H(s).md](/engineering/linear-systems-and-signals/062_4-10-filter-design-by-placement-of-poles-and-zeros-of-h-s/) - [Web 063_4.11 THE BILATERAL LAPLACE TRANSFORM.md](/engineering/linear-systems-and-signals/063_4-11-the-bilateral-laplace-transform/) - 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[Web 072_5.7 DIGITAL PROCESSING OF ANALOG SIGNALS.md](/engineering/linear-systems-and-signals/072_5-7-digital-processing-of-analog-signals/) - [Web 073_5.8 THE BILATERAL z-TRANSFORM.md](/engineering/linear-systems-and-signals/073_5-8-the-bilateral-z-transform/) - [Web 074_5.9 CONNECTING THE LAPLACE AND z-TRANSFORMS.md](/engineering/linear-systems-and-signals/074_5-9-connecting-the-laplace-and-z-transforms/) - [Web 075_5.10 MATLAB - DISCRETE-TIME IIR FILTERS.md](/engineering/linear-systems-and-signals/075_5-10-matlab-discrete-time-iir-filters/) - [Web 076_5.11 SUMMARY.md](/engineering/linear-systems-and-signals/076_5-11-summary/) - [Web 077_REFERENCES.md](/engineering/linear-systems-and-signals/077_references/) - [Web 078_6 CONTINUOUS-TIME SIGNAL ANALYSIS - THE FOURIER SERIES.md](/engineering/linear-systems-and-signals/078_6-continuous-time-signal-analysis-the-fourier-series/) - [Web 079_6.1 PERIODIC SIGNAL REPRESENTATION BY TRIGONOMETRIC FOURIER SERIES.md](/engineering/linear-systems-and-signals/079_6-1-periodic-signal-representation-by-trigonometric-fourier-series/) - [Web 080_6.2 EXISTENCE AND CONVERGENCE OF THE FOURIER SERIES.md](/engineering/linear-systems-and-signals/080_6-2-existence-and-convergence-of-the-fourier-series/) - [Web 081_6.3 EXPONENTIAL FOURIER SERIES.md](/engineering/linear-systems-and-signals/081_6-3-exponential-fourier-series/) - [Web 082_6.4 LTIC SYSTEM RESPONSE TO PERIODIC INPUTS.md](/engineering/linear-systems-and-signals/082_6-4-ltic-system-response-to-periodic-inputs/) - [Web 083_6.5 GENERALIZED FOURIER SERIES - SIGNALS AS VECTORS.md](/engineering/linear-systems-and-signals/083_6-5-generalized-fourier-series-signals-as-vectors/) - [Web 084_6.6 NUMERICAL COMPUTATION OF D_n.md](/engineering/linear-systems-and-signals/084_6-6-numerical-computation-of-d_n/) - [Web 085_6.7 MATLAB - FOURIER SERIES APPLICATIONS.md](/engineering/linear-systems-and-signals/085_6-7-matlab-fourier-series-applications/) - [Web 086_6.8 SUMMARY.md](/engineering/linear-systems-and-signals/086_6-8-summary/) - [Web 087_REFERENCES.md](/engineering/linear-systems-and-signals/087_references/) - [Web 088_PROBLEMS.md](/engineering/linear-systems-and-signals/088_problems/) - [Web 089_7 CONTINUOUS-TIME SIGNAL ANALYSIS - THE FOURIER TRANSFORM.md](/engineering/linear-systems-and-signals/089_7-continuous-time-signal-analysis-the-fourier-transform/) - [Web 090_7.2 TRANSFORMS OF SOME USEFUL FUNCTIONS.md](/engineering/linear-systems-and-signals/090_7-2-transforms-of-some-useful-functions/) - [Web 091_7.3 SOME PROPERTIES OF THE FOURIER TRANSFORM.md](/engineering/linear-systems-and-signals/091_7-3-some-properties-of-the-fourier-transform/) - [Web 092_7.4 SIGNAL TRANSMISSION THROUGH LTIC SYSTEMS.md](/engineering/linear-systems-and-signals/092_7-4-signal-transmission-through-ltic-systems/) - [Web 093_7.5 IDEAL AND PRACTICAL FILTERS.md](/engineering/linear-systems-and-signals/093_7-5-ideal-and-practical-filters/) - [Web 094_7.6 SIGNAL ENERGY.md](/engineering/linear-systems-and-signals/094_7-6-signal-energy/) - [Web 095_7.7 APPLICATION TO COMMUNICATIONS - AMPLITUDE MODULATION.md](/engineering/linear-systems-and-signals/095_7-7-application-to-communications-amplitude-modulation/) - [Web 096_7.8 DATA TRUNCATION - WINDOW FUNCTIONS.md](/engineering/linear-systems-and-signals/096_7-8-data-truncation-window-functions/) - [Web 097_7.9 MATLAB - FOURIER TRANSFORM TOPICS.md](/engineering/linear-systems-and-signals/097_7-9-matlab-fourier-transform-topics/) - [Web 098_7.10 SUMMARY.md](/engineering/linear-systems-and-signals/098_7-10-summary/) - [Web 099_REFERENCES.md](/engineering/linear-systems-and-signals/099_references/) - [Web 100_PROBLEMS.md](/engineering/linear-systems-and-signals/100_problems/) - [Web 101_8 SAMPLING - THE BRIDGE FROM CONTINUOUS TO DISCRETE.md](/engineering/linear-systems-and-signals/101_8-sampling-the-bridge-from-continuous-to-discrete/) - [Web 102_8.1 THE SAMPLING THEOREM.md](/engineering/linear-systems-and-signals/102_8-1-the-sampling-theorem/) - [Web 103_8.2 SIGNAL RECONSTRUCTION.md](/engineering/linear-systems-and-signals/103_8-2-signal-reconstruction/) - [Web 104_8.3 ANALOG-TO-DIGITAL (A - D) CONVERSION.md](/engineering/linear-systems-and-signals/104_8-3-analog-to-digital-a-d-conversion/) - [Web 105_8.4 DUAL OF TIME SAMPLING - SPECTRAL SAMPLING.md](/engineering/linear-systems-and-signals/105_8-4-dual-of-time-sampling-spectral-sampling/) - [Web 106_8.5 NUMERICAL COMPUTATION OF THE FOURIER TRANSFORM - THE DISCRETE FOURIER TRANSFORM.md](/engineering/linear-systems-and-signals/106_8-5-numerical-computation-of-the-fourier-transform-the-discrete-fourier-transform/) - [Web 107_8.6 THE FAST FOURIER TRANSFORM (FFT).md](/engineering/linear-systems-and-signals/107_8-6-the-fast-fourier-transform-fft/) - [Web 108_8.7 MATLAB - THE DISCRETE FOURIER TRANSFORM.md](/engineering/linear-systems-and-signals/108_8-7-matlab-the-discrete-fourier-transform/) - [Web 109_8.8 SUMMARY.md](/engineering/linear-systems-and-signals/109_8-8-summary/) - [Web 110_REFERENCES.md](/engineering/linear-systems-and-signals/110_references/) - [Web 111_PROBLEMS.md](/engineering/linear-systems-and-signals/111_problems/) - [Web 112_9 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS.md](/engineering/linear-systems-and-signals/112_9-fourier-analysis-of-discrete-time-signals/) - [Web 113_9.2 APERIODIC SIGNAL REPRESENTATION BY FOURIER INTEGRAL.md](/engineering/linear-systems-and-signals/113_9-2-aperiodic-signal-representation-by-fourier-integral/) - [Web 114_9.3 PROPERTIES OF THE DTFT.md](/engineering/linear-systems-and-signals/114_9-3-properties-of-the-dtft/) - [Web 115_9.4 LTI DISCRETE-TIME SYSTEM ANALYSIS BY DTFT.md](/engineering/linear-systems-and-signals/115_9-4-lti-discrete-time-system-analysis-by-dtft/) - [Web 116_9.5 DTFT CONNECTION WITH THE CTFT.md](/engineering/linear-systems-and-signals/116_9-5-dtft-connection-with-the-ctft/) - [Web 117_9.6 GENERALIZATION OF THE DTFT TO THE z-TRANSFORM.md](/engineering/linear-systems-and-signals/117_9-6-generalization-of-the-dtft-to-the-z-transform/) - [Web 118_9.7 MATLAB - WORKING WITH THE DTFS AND THE DTFT.md](/engineering/linear-systems-and-signals/118_9-7-matlab-working-with-the-dtfs-and-the-dtft/) - [Web 119_9.8 SUMMARY.md](/engineering/linear-systems-and-signals/119_9-8-summary/) - [Web 120_REFERENCE.md](/engineering/linear-systems-and-signals/120_reference/) - [Web 121_PROBLEMS.md](/engineering/linear-systems-and-signals/121_problems/) - [Web 122_10 STATE-SPACE ANALYSIS.md](/engineering/linear-systems-and-signals/122_10-state-space-analysis/) - [Web 123_10.1 MATHEMATICAL PRELIMINARIES.md](/engineering/linear-systems-and-signals/123_10-1-mathematical-preliminaries/) - [Web 124_10.2 INTRODUCTION TO STATE SPACE.md](/engineering/linear-systems-and-signals/124_10-2-introduction-to-state-space/) - [Web 125_10.3 A SYSTEMATIC PROCEDURE TO DETERMINE STATE EQUATIONS.md](/engineering/linear-systems-and-signals/125_10-3-a-systematic-procedure-to-determine-state-equations/) - [Web 126_10.4 SOLUTION OF STATE EQUATIONS.md](/engineering/linear-systems-and-signals/126_10-4-solution-of-state-equations/) - [Web 127_10.5 LINEAR TRANSFORMATION OF A STATE VECTOR.md](/engineering/linear-systems-and-signals/127_10-5-linear-transformation-of-a-state-vector/) - [Web 128_10.6 CONTROLLABILITY AND OBSERVABILITY.md](/engineering/linear-systems-and-signals/128_10-6-controllability-and-observability/) - [Web 129_10.7 STATE-SPACE ANALYSIS OF DISCRETE-TIME SYSTEMS.md](/engineering/linear-systems-and-signals/129_10-7-state-space-analysis-of-discrete-time-systems/) - [Web 130_10.8 MATLAB - TOOLBOXES AND STATE-SPACE ANALYSIS.md](/engineering/linear-systems-and-signals/130_10-8-matlab-toolboxes-and-state-space-analysis/) - [Web 131_10.9 SUMMARY.md](/engineering/linear-systems-and-signals/131_10-9-summary/) - [Web 132_REFERENCES.md](/engineering/linear-systems-and-signals/132_references/) - [Web 133_INDEX.md](/engineering/linear-systems-and-signals/133_index/)