Schaum's Outline of Theory and Problems of Signals and Systems

Confusing Textbooks? Missed Lectures? Tough Test Questions? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved. Cover......Page 2 Preface......Page 5 To the Student......Page 7 Contents......Page 9 A. Continuous-Time & Discrete-Time Signals......Page 13 C. Real & Complex Signals......Page 14 E. Even & Odd Signals......Page 15 F. Periodic & Nonperiodic Signals......Page 16 G. Energy & Power Signals......Page 17 B. Unit Impulse Function......Page 18 Generalized Derivatives......Page 20 C. Complex Exponential Signals......Page 21 Real Exponential Signals......Page 22 D. Sinusoidal Signals......Page 23 B. Unit Impulse Sequence......Page 24 Periodicity of e(j.omega0.n)......Page 25 General Complex Exponential Sequences......Page 27 A. System Representation......Page 28 D. Causal & Noncausal Systems......Page 29 G. Linear Time-Invariant Systems......Page 30 1.2 Signals & Classification of Signals......Page 31 1.3 & 1.4 Basic Signals......Page 46 1.5 Systems & Classification of Systems......Page 55 Supplementary Problems......Page 63 B. Response to Arbitrary Input......Page 68 E. Convolution Integral Operation......Page 69 B. Causality......Page 70 2.4 Eigenfunctions of Continuous-Time LTI Systems......Page 71 B. Linearity......Page 72 A. Impulse Response......Page 73 D. Properties of Convolution Sum......Page 74 A. Systems with or without Memory......Page 75 2.8 Eigenfunctions of Discrete-Time LTI Systems......Page 76 B. Recursive Formulation......Page 77 2.2 Response of Continuous-Time LTI System & Convolution Integral......Page 78 2.3 Properties of Continuous-Time LTI Systems......Page 89 2.4 Eigenfunctions of Continuous-Time LTI Systems......Page 93 2.5 Systems Described by Differential Equations......Page 95 2.6 Response of Discrete-Time LTI System & Convolution Sum......Page 101 2.7 Properties of Discrete-Time LTI Systems......Page 109 2.9 Systems Described by Difference Equations......Page 112 Supplementary Problems......Page 117 A. Definition......Page 122 B. Region of Convergence......Page 123 D. Properties of ROC......Page 124 3.4 Properties of Laplace Transform......Page 126 A. Linearity......Page 127 D. Time Scaling......Page 128 E. Time Reversal......Page 129 I. Convolution......Page 130 A. Inversion Formula......Page 131 2. Multiple Pole Case......Page 132 B. Characterization of LTI Systems......Page 133 C. System Function for LTI Systems Described by Linear Constant-Coefficient Differential Equations......Page 134 D. Systems Interconnection......Page 135 B. Basic Properties......Page 136 2. Resistance R......Page 137 3.2 Laplace Transform......Page 139 3.4 Properties of Laplace Transform......Page 144 3.5 Inverse Laplace Transform......Page 149 3.6 System Function......Page 155 3.7 Unilateral Laplace Transform......Page 160 Application of Unilateral Laplace Transform......Page 164 Supplementary Problems......Page 171 A. Definition......Page 177 B. Region of Convergence......Page 178 A. Unit Impulse Sequence delta[n]......Page 181 C. z-Transform Pairs......Page 182 C. Multiplication by z n,0......Page 183 G. Convolution......Page 184 B. Use of Tables of z-Transform Pairs......Page 185 D. Partial-Fraction Expansion......Page 186 A. System Function......Page 187 C. System Function for LTI Systems Described by Linear Constant-Coefficient Difference Equations......Page 188 A. Definition......Page 189 4.2 z-Transform......Page 190 4.4 Properties of z-Transform......Page 196 4.5 Inverse z-Transform......Page 200 4.6 System Function......Page 206 4.7 Unilateral z-Transform......Page 214 Supplementary Problems......Page 218 B. Complex Exponential Fourier Series Representation......Page 223 Even & Odd Signals......Page 224 F. Amplitude & Phase Spectra of Periodic Signal......Page 225 A. From Fourier Series to Fourier Transform......Page 226 C. Fourier Spectra......Page 228 E. Connection between Fourier Transform & Laplace Transform......Page 229 D. Time Scaling......Page 231 J. Convolution......Page 232 M. Parseval's Relations......Page 233 A. Frequency Response......Page 235 B. Distortionless Transmission......Page 237 C. LTI Systems Characterized by Differential Equations......Page 238 2. Ideal High-Pass Filter......Page 239 4. Ideal Bandstop Filter......Page 240 B. Nonideal Frequency-Selective Filters......Page 241 2. 3-dB (or Half-Power) Bandwidth......Page 242 5.2 Fourier Series......Page 243 5.3 Fourier Transform......Page 258 5.5 Frequency Response......Page 274 5.6 Filtering......Page 285 Supplementary Problems......Page 295 A. Periodic Sequences......Page 300 2. Duality......Page 301 E. Parseval's Theorem......Page 302 A. From Discrete Fourier Series to Fourier Transform......Page 303 E. Connection between Fourier Transform & z-Transform......Page 305 F. Time Reversal......Page 307 H. Duality......Page 308 M. Multiplication......Page 309 O. Parseval's Relations......Page 310 A. Frequency Response......Page 312 A. System Responses......Page 314 6.7 Simulation......Page 315 B. Relationship between DFT & Discrete Fourier Series......Page 317 4. Conjugation......Page 318 10. Parseval's Relation......Page 319 6.2 Discrete Fourier Series......Page 320 6 3 Fourier Transform......Page 328 6.5 Frequency Response......Page 338 6.7 Simulation......Page 349 6.8 Discrete Fourier Transform......Page 357 Supplementary Problems......Page 372 B. Selection of State Variables......Page 377 A. Systems described by Difference Equations......Page 378 B. Similarity Transformation......Page 379 A. Systems described by Differential Equations......Page 380 B. Multiple-Input Multiple-Output Systems......Page 382 B. Determination of An......Page 383 C. z-Transform Solution......Page 384 E. Stability......Page 385 B. System Function H(s)......Page 386 C. Solution in Time Domain......Page 387 D. Evaluation of e(At)......Page 388 7.3 & 7.4 State Space Representation......Page 389 State Equations of Discrete-Time LTI Systems described by Difference Equations......Page 394 State Equations of Discrete-Time LTI Systems described by Differential Equations......Page 400 7.5 Solutions of State Equations for Discrete-Time LTI Systems......Page 406 7.6 Solutions of State Equations for Continuous-Time LTI Systems......Page 421 Supplementary Problems......Page 433 A. Definitions......Page 440 B. Operations......Page 441 B. Inverses......Page 443 A. Linear independence......Page 444 A. Definitions......Page 445 C. Inverse of Matrix......Page 446 B. Characteristic Equation......Page 447 A. Diagonalization......Page 448 A. Powers of Matrix......Page 449 B. Function of Matrix......Page 450 C. Cayley-Hamilton Theorem......Page 451 D. Minimal Polynomial of A......Page 452 E. Spectral Decomposition......Page 454 B. Differentiation of Product of 2 Matrices......Page 456 Properties of Bilateral Laplace Transform......Page 457 Differentiation in Time Domain......Page 458 Properties of Fourier Transform......Page 459 Common Fourier Transforms Pairs......Page 460 Some Common z-Transforms Pairs......Page 461 Time-Shifting Property......Page 462 Parseval's Relations......Page 463 Properties of DFT......Page 464 Harmonic Form Fourier Series......Page 465 Parseval's Theorem for Discrete Fourier Series......Page 466 C.1 Representation of Complex Numbers......Page 467 C.4 Powers & Roots of Complex Numbers......Page 468 D.3 Trigonometric Identities......Page 470 D.5 Exponential & Logarithmic Functions......Page 471 D.6 Some Definite Integrals......Page 472 Index......Page 473 Backcover......Page 484 Local Disk......Page 0 articlopedia.gigcities.com......Page 1 This powerful study guide gives you 571 problems in signals and systems, fully solved step-by-step! From SchaumOs, the original study guide, and studentsO favorite with over 30 million guides soldNthis solution-packed timesaver helps you master every type of problem you will face on your tests, from simple questions on linear time-invariant systems to complex Fourier analysis of discrete-time systems and state space analysis. Go directly to the answers you need with a complete index. Compatible with any classroom text, SchaumOs Outline of Signals and Systems is so complete itOs the perfect tool for graduate or professional exam prep! Signals And Systems -- Linear Time-invariant Systems -- Laplace Transform And Continuous-time Lti Systems -- The Z-transform And Discrete-time Lti Systems -- Fourier Analysis Of Continuous-time Signals And Systems -- Fourier Analysis Of Discrete-time Signals And Systems -- State Space Analysis -- Appendices: -- Review Of Matrix Theory -- Properties Of Linear Time-invariant Systems And Various Transforms -- Review Of Complex Numbers. Hwei P. Hsu. Includes Index.