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ОбложкаOppenheim A.V. Signals, systems & inference / A.V.Oppenheim, G.C.Verghese. - Boston: Pearson, 2016. - xxx, 573 p.: ill. – (Prentice-Hall signal processing series). - Bibliogr.: p.555-560. - Ind.: p.561-573. - ISBN 978-0-13-394328-3; ISBN 0-13-394328-3
Шифр: (И/З.81-O.65) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ........................................................ xi
The Cover ...................................................... xv
Acknowledgments .............................................. xvii
Prologue .................................................... xxiii

1    Signals and Systems ........................................ 1
1.1  Signals, Systems, Models, and Properties ................... 1
     1.1.1   System Properties .................................. 3
1.2  Linear, Time-Invariant Systems ............................. 5
     1.2.1  Impulse-Response Representation of LTI Systems ...... 5
     1.2.2  Eigenfunction and Transform Representation of
            LTI Systems ......................................... 6
     1.2.3  Fourier Transforms ................................. 10
1.3  Deterministic Signals and Their Fourier Transforms ........ 11
     1.3.1  Signal Classes and Their Fourier Transforms ........ 11
     1.3.2  Parseval's Identity, Energy Spectral Density,
            and Deterministic Autocorrelation .................. 14
1.4  Bilateral Laplace and Z-Transforms ........................ 16
     1.4.1  The Bilateral z-Transform .......................... 16
     1.4.2  The Bilateral Laplace Transform .................... 20
1.5  Discrete-Time Processing of Continuous-Time Signals ....... 21
     1.5.1  Basic Structure for DT Processing of CT Signals .... 22
     1.5.2  DT Filtering and Overall CT Response ............... 24
     1.5.3  Nonideal D/C Converters ............................ 26
1.6  Further Reading ........................................... 28
     Problems .................................................. 29
     Basic Problems ............................................ 29
     Advanced Problems ......................................... 40
     Extension Problems ........................................ 51

2    Amplitude, Phase, and Group Delay ......................... 62
2.1  Fourier Transform Magnitude and Phase ..................... 62
2.2  Group Delay and the Effect of Nonlinear Phase ............. 66
     2.2.1  Narrowband Input Signals ........................... 66
     2.2.2  Broadband Input Signals ............................ 68
2.3  All-Pass and Minimum-Phase Systems ........................ 73
     2.3.1  All-Pass Systems ................................... 73
     2.3.2  Minimum-Phase Systems .............................. 75
2.4  Spectral Factorization .................................... 78
2.5  Further Reading ........................................... 80
     Problems .................................................. 80
     Basic Problems ............................................ 80
     Advanced Problems ......................................... 88
     Extension Problems ....................................... 100

3    Pulse-Amplitude Modulation ............................... 102
3.1  Baseband Pulse-Amplitude Modulation ...................... 103
     3.1.1  The Transmitted Signal ............................ 103
     3.1.2  The Received Signal ............................... 105
     3.1.3  Frequency-Domain Characterizations ................ 105
     3.1.4  Intersymbol Interference at the Receiver .......... 108
3.2  Nyquist Pulses ........................................... 110
3.3  Passband Pulse-Amplitude Modulation ...................... 113
     3.3.1  Frequency-Shift Keying (FSK) ...................... 114
     3.3.2  Phase-Shift Keying (PSK) .......................... 114
     3.3.3  Quadrature-Amplitude Modulation (QAM) ............. 116
3.4  Further Reading .......................................... 118
     Problems ................................................. 119
     Basic Problems ........................................... 119
     Advanced Problems ........................................ 123
     Extension Problems ....................................... 126

4    State-Space Models ....................................... 133
4.1  System Memory ............................................ 133
4.2  Illustrative Examples .................................... 134
4.3  State-Space Models ....................................... 146
     4.3.1  DT State-Space Models ............................. 146
     4.3.2  CT State-Space Models ............................. 149
     4.3.3  Defining Properties of State-Space Models ......... 151
4.4  State-Space Models from LTI Input-Output
     Models ................................................... 153
4.5  Equilibria and Linearization of Nonlinear State-Space
     Models ................................................... 158
     4.5.1  Equilibrium ....................................... 158
     4.5.2  Linearization ..................................... 161
4.6  Further Reading .......................................... 164
     Problems ................................................. 165
     Basic Problems ........................................... 165
     Advanced Problems ........................................ 169
     Extension Problems ....................................... 172

5    LTI State-Space Models ................................... 174
5.1  Continuous-Time and Discrete-Time LTI Models ............. 174
5.2  Zero-Input Response and Modal Representation ............. 177
     5.2.1  Undriven CT Systems ............................... 177
     5.2.2  Undriven DT Systems ............................... 185
     5.2.3  Asymptotic Stability of LTI Systems ............... 187
5.3  General Response in Modal Coordinates .................... 191
     5.3.1  Driven CT Systems ................................. 191
     5.3.2  Driven DT Systems ................................. 194
     5.3.3  Similarity Transformations and Diagonalization .... 196
5.4  Transfer Functions, Hidden Modes, Reachability,
     and Observability ........................................ 202
     5.4.1  Input-State-Output Structure of CT Systems ........ 202
     5.4.2  Input-State-Output Structure of DT Systems ........ 210
5.5  Further Reading .......................................... 219
     Problems ................................................. 220
     Basic Problems ........................................... 220
     Advanced Problems ........................................ 228
     Extension Problems ....................................... 233

6    State Observers and State Feedback ....................... 236
6.1  Plant and Model .......................................... 237
6.2  State Estimation and Observers ........................... 239
     6.2.1  Real-Time Simulation .............................. 239
     6.2.2  The State Observer ................................ 241
     6.2.3  Observer Design ................................... 243
6.3  State Feedback Control ................................... 252
     6.3.1  Open-Loop Control ................................. 252
     6.3.2  Closed-Loop Control via LTI State Feedback ........ 253
     6.3.3  LTI State Feedback Design ......................... 254
6.4  Observer-Based Feedback Control .......................... 262
6.5  Further Reading .......................................... 267
     Problems ................................................. 267
     Basic Problems ........................................... 267
     Advanced Problems ........................................ 274
     Extension Problems ....................................... 277

7    Probabilistic Models ..................................... 279
7.1  The Basic Probability Model .............................. 279
7.2  Conditional Probability, Bayes' Rule, and Independence ... 280
7.3  Random Variables ......................................... 283
7.4  Probability Distributions ................................ 283
7.5  Jointly Distributed Random Variables ..................... 285
7.6  Expectations, Moments, and Variance ...................... 287
7.7  Correlation and Covariance for Bivariate Random
     Variables ................................................ 290
7.8  A Vector-Space Interpretation of Correlation Properties .. 294
7.9  Further Reading .......................................... 296
Problems ...................................................... 297
Basic Problems ................................................ 297
Advanced Problems ............................................. 298
Extension Problems ............................................ 302

8    Estimation ............................................... 306
8.1  Estimation of a Continuous Random Variable ............... 307
8.2  From Estimates to the Estimator .......................... 312
     8.2.1  Orthogonality ..................................... 317
8.3  Linear Minimum Mean Square Error Estimation .............. 318
     8.3.1  Linear Estimation of One Random Variable from
            a Single Measurement of Another ................... 318
     8.3.2  Multiple Measurements ............................. 323
8.4  Further Reading .......................................... 327
     Problems ................................................. 328
     Basic Problems ........................................... 328
     Advanced Problems ........................................ 332
     Extension Problems ....................................... 338

9    Hypothesis Testing ....................................... 343
9.1  Binary Pulse-Amplitude Modulation in Noise ............... 343
9.2  Hypothesis Testing with Minimum Error Probability ........ 345
     9.2.1  Deciding with Minimum Conditional Probability
            of Error .......................................... 346
     9.2.2  MAP Decision Rule for Minimum Overall Probability
            of Error .......................................... 347
     9.2.3  Hypothesis Testing in Coded Digital
            Communication ..................................... 350
9.3  Binary Hypothesis Testing ................................ 353
     9.3.1  False Alarm, Miss, and Detection .................. 354
     9.3.2  The Likelihood Ratio Test ......................... 356
     9.3.3  Neyman-Pearson Decision Rule and Receiver
            Operating Characteristic .......................... 357
9.4  Minimum Risk Decisions ................................... 361
9.5  Further Reading .......................................... 363
     Problems ................................................. 363
     Basic Problems ........................................... 363
     Advanced Problems ........................................ 368
     Extension Problems ....................................... 373

10   Random Processes ......................................... 380
10.1 Definition and Examples of a Random Process .............. 380
10.2 First- and Second-Moment Characterization of Random
     Processes ................................................ 385
10.3 Stationarity ............................................. 386
     10.3.1 Strict-Sense Stationarity ......................... 386
     10.3.2 Wide-Sense Stationarity ........................... 386
     10.3.3 Some Properties of WSS Correlation and Covariance
            Functions ......................................... 388
10.4 Ergodicity ............................................... 391
10.5 Linear Estimation of Random Processes .................... 392
     10.5.1 Linear Prediction ................................. 392
     10.5.2 Linear FIR Filtering .............................. 394
10.6 LTI Filtering of WSS Processes ........................... 395
10.7 Further Reading .......................................... 401
     Problems ................................................. 401
     Basic Problems ........................................... 401
     Advanced Problems ........................................ 406
     Extension Problems ....................................... 412

11   Power Spectral Density ................................... 421
11.1 Spectral Distribution of Expected Instantaneous
     Power .................................................... 422
     11.1.1 Power Spectral Density ............................ 422
     11.1.2 Fluctuation Spectral Density ...................... 426
     11.1.3 Cross-Spectral Density ............................ 431
11.2 Expected Time-Averaged Power Spectrum and the
     Einstein-Wiener-Khinchin Theorem ......................... 432
11.3 Applications ............................................. 437
     11.3.1 Revealing Cyclic Components ....................... 437
     11.3.2 Modeling Filters .................................. 439
     11.3.3 Whitening Filters ................................. 443
     11.3.4 Sampling Bandlimited Random Processes ............. 444
11.4 Further Reading .......................................... 444
     Problems ................................................. 445
     Basic Problems ........................................... 445
     Advanced Problems ........................................ 451
     Extension Problems ....................................... 455

12   Signal Estimation ........................................ 464
12.1 LMMSE Estimation for Random Variables .................... 465
12.2 FIR Wiener Filters ....................................... 467
12.3 The Unconstrained DT Wiener Filter ....................... 472
12.4 Causal DT Wiener Filtering ............................... 480
12.5 Optimal Observers and Kalman Filtering ................... 487
     12.5.1 Causal Wiener Filtering of a Signal Corrupted
            by Additive Noise ................................. 487
     12.5.2 Observer Implementation of the Wiener Filter ...... 489
     12.5.3 Optimal State Estimates and Kalman Filtering ...... 491
12.6 Estimation of CT Signals ................................. 492
12.7 Further Reading .......................................... 493
     Problems ................................................. 493
     Basic Problems ........................................... 493
     Advanced Problems ........................................ 504
     Extension Problems ....................................... 510

13   Signal Detection ......................................... 511
13.1 Hypothesis Testing with Multiple Measurements ............ 512
13.2 Detecting a Known Signal in I.I.D. Gaussian Noise ........ 514
     13.2.1 The Optimal Solution .............................. 515
     13.2.2 Characterizing Performance ........................ 517
     13.2.3 Matched Filtering ................................. 519
13.3 Extensions of Matched-Filter Detection ................... 522
     13.3.1 Infinite-Duration, Finite-Energy Signals .......... 522
     13.3.2 Maximizing SNR for Signal Detection in White
            Noise ............................................. 522
     13.3.3 Detection in Colored Noise ........................ 525
     13.3.4 Continuous-Time Matched Filters ................... 528
     13.3.5 Matched Filtering and Nyquist Pulse Design ........ 529
     13.3.6 Unknown Arrival Time and Pulse Compression ........ 530
13.4 Signal Discrimination in I.I.D. Gaussian Noise ........... 532
13.5 Further Reading .......................................... 538
     Problems ................................................. 538

Basic Problems ................................................ 538
Advanced Problems ............................................. 543
Extension Problems ............................................ 552
Bibliography .................................................. 555
Index ......................................................... 561

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