Schaum’s outline of theory and problems of signal and systems

Hwei Hsu9780070306417, 9780071368094, 0070306419

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!

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Table of contents :
Schaum’s Outlines of Signals & Systems……Page 1
Copyright……Page 3
Preface……Page 4
To the Student……Page 6
Contents……Page 8
A. Continuous-Time & Discrete-Time Signals……Page 12
C. Real & Complex Signals……Page 13
E. Even & Odd Signals……Page 14
F. Periodic & Nonperiodic Signals……Page 15
G. Energy & Power Signals……Page 16
B. Unit Impulse Function……Page 17
Generalized Derivatives……Page 19
C. Complex Exponential Signals……Page 20
Real Exponential Signals……Page 21
D. Sinusoidal Signals……Page 22
B. Unit Impulse Sequence……Page 23
Periodicity of e(j.omega0.n)……Page 24
General Complex Exponential Sequences……Page 26
A. System Representation……Page 27
D. Causal & Noncausal Systems……Page 28
G. Linear Time-Invariant Systems……Page 29
1.2 Signals & Classification of Signals……Page 30
1.3 & 1.4 Basic Signals……Page 45
1.5 Systems & Classification of Systems……Page 54
Supplementary Problems……Page 62
B. Response to Arbitrary Input……Page 67
E. Convolution Integral Operation……Page 68
B. Causality……Page 69
2.4 Eigenfunctions of Continuous-Time LTI Systems……Page 70
B. Linearity……Page 71
A. Impulse Response……Page 72
D. Properties of Convolution Sum……Page 73
A. Systems with or without Memory……Page 74
2.8 Eigenfunctions of Discrete-Time LTI Systems……Page 75
B. Recursive Formulation……Page 76
2.2 Response of Continuous-Time LTI System & Convolution Integral……Page 77
2.3 Properties of Continuous-Time LTI Systems……Page 88
2.4 Eigenfunctions of Continuous-Time LTI Systems……Page 92
2.5 Systems Described by Differential Equations……Page 94
2.6 Response of Discrete-Time LTI System & Convolution Sum……Page 100
2.7 Properties of Discrete-Time LTI Systems……Page 108
2.9 Systems Described by Difference Equations……Page 111
Supplementary Problems……Page 116
A. Definition……Page 121
B. Region of Convergence……Page 122
D. Properties of ROC……Page 123
3.4 Properties of Laplace Transform……Page 125
A. Linearity……Page 126
D. Time Scaling……Page 127
E. Time Reversal……Page 128
I. Convolution……Page 129
A. Inversion Formula……Page 130
2. Multiple Pole Case……Page 131
B. Characterization of LTI Systems……Page 132
C. System Function for LTI Systems Described by Linear Constant-Coefficient Differential Equations……Page 133
D. Systems Interconnection……Page 134
B. Basic Properties……Page 135
2. Resistance R……Page 136
3.2 Laplace Transform……Page 138
3.4 Properties of Laplace Transform……Page 143
3.5 Inverse Laplace Transform……Page 148
3.6 System Function……Page 154
3.7 Unilateral Laplace Transform……Page 159
Application of Unilateral Laplace Transform……Page 163
Supplementary Problems……Page 170
A. Definition……Page 176
B. Region of Convergence……Page 177
A. Unit Impulse Sequence delta[n]……Page 180
C. z-Transform Pairs……Page 181
C. Multiplication by z n,0……Page 182
G. Convolution……Page 183
B. Use of Tables of z-Transform Pairs……Page 184
D. Partial-Fraction Expansion……Page 185
A. System Function……Page 186
C. System Function for LTI Systems Described by Linear Constant-Coefficient Difference Equations……Page 187
A. Definition……Page 188
4.2 z-Transform……Page 189
4.4 Properties of z-Transform……Page 195
4.5 Inverse z-Transform……Page 199
4.6 System Function……Page 205
4.7 Unilateral z-Transform……Page 213
Supplementary Problems……Page 217
B. Complex Exponential Fourier Series Representation……Page 222
Even & Odd Signals……Page 223
F. Amplitude & Phase Spectra of Periodic Signal……Page 224
A. From Fourier Series to Fourier Transform……Page 225
C. Fourier Spectra……Page 227
E. Connection between Fourier Transform & Laplace Transform……Page 228
D. Time Scaling……Page 230
J. Convolution……Page 231
M. Parseval’s Relations……Page 232
A. Frequency Response……Page 234
B. Distortionless Transmission……Page 236
C. LTI Systems Characterized by Differential Equations……Page 237
2. Ideal High-Pass Filter……Page 238
4. Ideal Bandstop Filter……Page 239
B. Nonideal Frequency-Selective Filters……Page 240
2. 3-dB (or Half-Power) Bandwidth……Page 241
5.2 Fourier Series……Page 242
5.3 Fourier Transform……Page 257
5.5 Frequency Response……Page 273
5.6 Filtering……Page 284
Supplementary Problems……Page 294
A. Periodic Sequences……Page 299
2. Duality……Page 300
E. Parseval’s Theorem……Page 301
A. From Discrete Fourier Series to Fourier Transform……Page 302
E. Connection between Fourier Transform & z-Transform……Page 304
F. Time Reversal……Page 306
H. Duality……Page 307
M. Multiplication……Page 308
O. Parseval’s Relations……Page 309
A. Frequency Response……Page 311
A. System Responses……Page 313
6.7 Simulation……Page 314
B. Relationship between DFT & Discrete Fourier Series……Page 316
4. Conjugation……Page 317
10. Parseval’s Relation……Page 318
6.2 Discrete Fourier Series……Page 319
6 3 Fourier Transform……Page 327
6.5 Frequency Response……Page 337
6.7 Simulation……Page 348
6.8 Discrete Fourier Transform……Page 356
Supplementary Problems……Page 371
B. Selection of State Variables……Page 376
A. Systems described by Difference Equations……Page 377
B. Similarity Transformation……Page 378
A. Systems described by Differential Equations……Page 379
B. Multiple-Input Multiple-Output Systems……Page 381
B. Determination of An……Page 382
C. z-Transform Solution……Page 383
E. Stability……Page 384
B. System Function H(s)……Page 385
C. Solution in Time Domain……Page 386
D. Evaluation of e(At)……Page 387
7.3 & 7.4 State Space Representation……Page 388
State Equations of Discrete-Time LTI Systems described by Difference Equations……Page 393
State Equations of Discrete-Time LTI Systems described by Differential Equations……Page 399
7.5 Solutions of State Equations for Discrete-Time LTI Systems……Page 405
7.6 Solutions of State Equations for Continuous-Time LTI Systems……Page 420
Supplementary Problems……Page 432
A. Definitions……Page 439
B. Operations……Page 440
B. Inverses……Page 442
A. Linear independence……Page 443
A. Definitions……Page 444
C. Inverse of Matrix……Page 445
B. Characteristic Equation……Page 446
A. Diagonalization……Page 447
A. Powers of Matrix……Page 448
B. Function of Matrix……Page 449
C. Cayley-Hamilton Theorem……Page 450
D. Minimal Polynomial of A……Page 451
E. Spectral Decomposition……Page 453
B. Differentiation of Product of 2 Matrices……Page 455
Properties of Bilateral Laplace Transform……Page 456
Differentiation in Time Domain……Page 457
Properties of Fourier Transform……Page 458
Common Fourier Transforms Pairs……Page 459
Some Common z-Transforms Pairs……Page 460
Time-Shifting Property……Page 461
Parseval’s Relations……Page 462
Properties of DFT……Page 463
Harmonic Form Fourier Series……Page 464
Parseval’s Theorem for Discrete Fourier Series……Page 465
C.1 Representation of Complex Numbers……Page 466
C.4 Powers & Roots of Complex Numbers……Page 467
D.3 Trigonometric Identities……Page 469
D.5 Exponential & Logarithmic Functions……Page 470
D.6 Some Definite Integrals……Page 471
Index……Page 472
Backcover……Page 483