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Tables of Contents for Circuits, Signals and Systems
Chapter/Section Title
Page #
Page Count
Preface
xiii
Dynamic Equations and Their Solutions for Simple Circuits
Introduction
1
1
Constitutive Relations for Elements
1
5
Interconnection Constraints: Kirchhoff's Laws
6
1
Dynamic Equations in Node and State Form
7
6
Block Diagrams
13
3
Solutions of the Dynamic Equations
16
1
Solutions of the Dynamic Equations When the Inputs Are Zero
16
3
Solutions of the Dynamic Equations for Exponential Inputs
19
6
Summary
25
18
Exercises
26
5
Problems
31
12
The Unilateral Laplace Transform
Introduction
43
1
The Unilateral Laplace Transform
44
1
Examples of L-Transforms and Theorems
45
4
The Inverse Laplace Transform
49
3
Multiple-Order Poles
52
2
Circuit Analysis with the Laplace Transform
54
7
Summary
61
11
Appendix: Short Table of Unilateral Laplace Transforms
62
1
Exercises
63
2
Problems
65
7
System Functions
Introduction
72
1
A Superposition Formula for LTI Circuits
72
2
System Functions
74
3
System Functions as the Response Amplitudes to Exponential Drives
77
2
System Functions and the Input-Output Differential Equation
79
3
Summary
82
23
Appendix: System Function Characterization of LTI 2-ports
84
3
Exercises
87
2
Problems
89
16
Poles and Zeros
Introduction
105
1
Pole-Zero Diagrams
105
4
Vectorial Interpretation of H(jw)
109
5
Potential Analogies
114
2
Bode Diagrams
116
4
Summary
120
19
Exercises
121
5
Problems
126
13
Interconnected Systems and Feedback
Introduction
139
2
Elementary System Interconnections; Effects of Loading
141
3
Simple Feedback Loops
144
2
Examples of the Effects of Negative Feedback
146
12
Summary
158
5
Exercises
159
1
Problems
160
3
The Dynamics of Feedback Systems
Introduction
163
1
Inverse Systems
163
3
Feedback Effects on Bandwidth and Response Time
166
6
Stability
172
5
Feedback Stabilization of Unstable Systems
177
6
Summary
183
24
Appendix: The Nyquist Stability Criterion
184
8
Exercises
192
3
Problems
195
12
Discrete-time Signals and Linear Difference Equations
Introduction
207
2
Linear Difference Equations
209
3
Block Diagrams and State Formulations for DT Systems
212
7
Direct Solution of Linear Difference Equations
219
3
Zero Input Response
222
2
Summary
224
7
Exercises
225
1
Problems
226
5
The Unilateral Z-Transform and Its Applications
Introduction
231
1
The Z-Transform
231
8
The Z-Transform Applied to LTI Discrete-Time Systems
239
2
Frequency-Domain Representations of Discrete-Time Systems
241
8
Summary
249
11
Appendix: Short Table of Unilateral Z-Transforms
250
1
Exercises
251
1
Problems
252
8
The Unit Sample Response and Discrete-Time Convolution
Introduction
260
1
The Convolution Theorem for Z-Transforms
261
6
Convolution and General Linear Time-Invariant Systems
267
5
Algebraic Properties of the General Convolution Operation
272
2
An Example of Deconvolution
274
4
Summary
278
8
Exercises
280
1
Problems
281
5
Convolutional Representations of Continous-Time Systems
Introduction
286
1
The L-Transform Convolution Theorem
287
4
Convolution and General LTI Systems
291
7
Causality and Stability
298
5
Summary
303
11
Exercises
304
1
Problems
305
9
Impulses and the Superposition Integral
Introduction
314
1
The Smoothing Effect of Physical Systems
314
4
Impulses and Their Fundamental Properties
318
5
General LTI Systems; The Superposition Integral
323
12
Impulses and Sudden Changes in Initial State
335
3
Doublets and Other Generalized Functions; Impulse Matching
338
6
Summary
344
20
Exercises
345
4
Problems
349
15
Frequency-Domain Methods for General LTI Systems
Introduction
364
2
Strips of Convergence for H(s)
366
1
The Fourier Integral
367
2
A Special Case-Fourier Series
369
3
Other Forms of Fourier Series; Spectra
372
8
Averages of Periodic Functions; Parseval's Theorem
380
3
Summary
383
10
Exercises
385
1
Problems
386
7
Fourier Transforms and Fourier's Theorem
Introduction
393
1
Extension of the Fourier Series to the Fourier Integral
394
8
More Careful Statements of Fourier's Theorem
402
2
Further Examples of Fourier's Theorem; Singularity Functions
404
5
The Convolution Property of Fourier Transforms
409
4
Summary
413
16
Appendix A: Tables of Fourier Transforms and Their Properties
414
3
Appendix B: The Bilateral Laplace Transform
417
2
Exercises
419
1
Problems
420
9
Sampling in Time and Frequency
Introduction
429
1
The Periodic Impulse Train
429
2
Fourier Transforms of Periodic Functions; Fourier Series Revisited
431
392
The Sampling Theorem
435
4
Pulse Modulation Systems
439
3
The Discrete-Time Fourier Transform
442
3
Summary
445
26
Appendix: Vector-Space Representations of Signals
446
9
Exercises
455
2
Problems
457
14
Filters, Real and Ideal
Introduction
471
1
Ideal Filters
472
3
Causality Conditions and Hilbert Transforms
475
5
The Ideal Filter Step Response and Gibbs' Phenomenon
480
3
Summary
483
5
Exercises
484
1
Problems
485
3
Duration-Bandwith Relationships and the Uncertainty Principle
Introduction
488
1
Definitions of Delay, Rise Time, Duration, and Bandwidth
488
9
The Significance of the Uncertainty Principle; Pulse Resolution
497
5
Summary
502
5
Exercises
503
1
Problems
504
3
Bandpass Operations and Analog Communication Systems
Introduction
507
1
Amplitude Modulation
508
12
Mixers and Superheterodyne Receivers
520
3
Single-Side-Band Modulation; General Narrowband Representations
523
7
Phase and Frequency Modulation
530
8
Summary
538
20
Exercises
539
2
Problems
541
17
Fourier Transforms in Discrete-Time Systems
Introduction
558
2
Properties of the Discrete-Time Fourier Transform
560
6
Discrete-Time Filters
566
7
The DT Fourier Series and the Discrete Fourier Transform
573
4
Properties of the DT Fourier Series and the DFT
577
2
Summary
579
16
Appendix-Short Table of Discrete-Time Fourier Transforms
581
1
Exercises
582
2
Problems
584
11
Averages and Random Signals
Introduction
595
2
Averages of Periodic Functions
597
7
Properties of Infinite-Time Averages
604
4
Probabilistic Models of Simple Random Processes
608
10
Summary
618
9
Problems
620
7
Modern Communication Systems
Introduction
627
1
Sampling and Quantizing
628
4
Error-Correcting Codes
632
2
Modulation and Detection
634
7
Pulse-Amplitude Modulation (PAM)
634
3
Pulse-Code Modulation (PCM)
637
2
Pulse-Position Modulation (PPM)
639
2
Summary
641
1
Epilogue
642
1
Index
643