Signals, Systems, and Transforms,9780130953223

Signals, Systems, and Transforms

by ;
Edition: 2nd
ISBN13: 9780130953223
ISBN10: 0130953229
Format: Hardcover
Pub. Date: 1999-01-01
Publisher(s): Prentice Hall
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List Price: $102.00

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Summary

For sophomore/junior level signals and systems courses in Electrical and Computer Engineering departments. This text provides a clear, comprehensive presentation of both the theory and applications in signals, systems, and transforms. The text presents the mathematical background of signals and systems, including the Fourier transform, the Fourier series, the Laplace transform, the discrete-time and the discrete Fourier transforms, and the z-transform. The contents of each chapter are organized into well-defined units that allow instructors great flexibility in course emphasis.

Table of Contents

PREFACE xix
1 INTRODUCTION
1(22)
1.1 Modeling
1(3)
1.2 Continuous-Time Physical Systems
4(9)
Electric Circuits
4(1)
Operational Amplifier Circuits
5(3)
Simple Pendulum
8(1)
DC Power Supplies
9(2)
Analogous Systems
11(2)
1.3 Samplers and Discrete-Time Physical Systems
13(7)
Analog-to-Digital Converter
13(2)
Numerical Integration
15(1)
Picture in a Picture
16(1)
Compact Disks
17(1)
Sampling in Telephone Systems
18(1)
Data-Acquisition System
19(1)
1.4 MATLAB and SIMULINK
20(1)
1.5 Signals and Systems References
21(1)
References
21(2)
2 CONTINUOUS-TIME SIGNALS AND SYSTEMS
23(57)
2.1 Transformations of Continuous-Time Signals
24(7)
Time Transformations
24(6)
Amplitude Transformations
30(1)
2.2 Signal Characteristics
31(6)
Even and Odd Signals
32(2)
Periodic Signals
34(3)
2.3 Common Signals in Engineering
37(5)
2.4 Singularity Functions
42(8)
Unit Step Functions
42(4)
Unit Impulse Function
46(4)
2.5 Mathematical Functions for Signals
50(5)
2.6 Continuous-Time Systems
55(6)
Interconnecting Systems
57(2)
Feedback Systems
59(2)
2.7 Properties of Continuous-Time Systems
61(8)
Systems with Memory
61(1)
Invertibility
62(1)
Inverse of a System
62(1)
Causality
63(1)
Stability
64(1)
Time Invariance
65(2)
Linearity
67(2)
Summary
69(1)
References
70(1)
Problems
70(10)
3 CONTINUOUS-TIME LINEAR TIME-INVARIANT SYSTEMS
80(53)
3.1 Impulse Representation of Continuous-Time Signals
81(3)
3.2 Convolution for Continuous-Time LTI Systems
84(8)
3.3 Properties of Convolution
92(3)
3.4 Properties of Continuous-Time LTI Systems
95(5)
Systems with Memory
96(1)
Invertibility
96(1)
Causality
97(1)
Stability
97(2)
Unit Step Response
99(1)
3.5 Differential-Equation Models
100(6)
Solution of Differential Equations
102(1)
General Case
103(1)
Relation to Physical Systems
104(2)
3.6 Terms in the Natural Response
106(3)
Stability
107(2)
3.7 System Response for Complex-Exponential Inputs
109(6)
Linearity
109(1)
Complex Inputs for LTI Systems
110(4)
Impulse Response
114(1)
3.8 Block Diagrams
115(8)
Direct Form I
118(2)
Direct Form II
120(1)
nth-Order Realizations
121(1)
Practical Considerations
122(1)
Summary
123(1)
References
124(1)
Problems
124(9)
4 FOURIER SERIES
133(41)
4.1 Approximating Periodic Functions
134(4)
Periodic Functions
134(1)
Approximating Periodic Functions
135(3)
4.2 Fourier Series
138(5)
Fourier Series
139(1)
Fourier Coefficients
141(2)
4.3 Fourier Series and Frequency Spectra
143(9)
Frequency Spectra
144(8)
4.4 Properties of Fourier Series
152(3)
4.5 System Analysis
155(7)
4.6 Fourier Series Transformations
162(4)
Amplitude Transformations
162(2)
Time Transformations
164(2)
Summary
166(1)
References
166(1)
Problems
167(7)
5 THE FOURIER TRANSFORM
174(66)
5.1 Definition of the Fourier Transform
174(8)
5.2 Properties of the Fourier Transform
182(19)
Linearity
183(1)
Time Scaling
183(3)
Time Shifting
186(1)
Time Transformation
187(2)
Duality
189(2)
Convolution
191(1)
Frequency Shifting
192(2)
Time Differentiation
194(4)
Time Integration
198(2)
Frequency Differentiation
200(1)
Summary
201(1)
5.3 Fourier Transforms of Time Functions
201(11)
DC Level
202(1)
Unit Step Function
202(1)
Switched Cosine
203(1)
Pulsed Cosine
203(2)
Exponential Pulse
205(1)
Fourier Transforms of Periodic Functions
206(4)
Fourier Transforms of Sampled Signals
210(2)
Summary
212(1)
5.4 Application of the Fourier Transform
212(11)
Frequency Response of Linear Systems
212(8)
Frequency Spectra of Signals
220(3)
Summary
223(1)
5.5 Energy and Power Density Spectra
223(8)
Energy Density Spectrum
223(2)
Power Density Spectrum
225(4)
Power and Energy Transmission
229(2)
Summary
231(1)
References
232(1)
Problems
233(7)
6 APPLICATIONS OF THE FOURIER TRANSFORM
240(49)
6.1 Ideal Filters
240(9)
6.2 Real Filters
249(13)
RC Low-Pass Filter
249(2)
Butterworth Filter
251(6)
Chebyschev and Elliptic Filters
257(3)
Bandpass Filters
260(1)
Summary
261(1)
6.3 Bandwidth Relationships
262(3)
6.4 Sinusoidal Amplitude Modulation
265(10)
Frequency-Division Multiplexing
272(3)
6.5 Pulse-Amplitude Modulation
275(4)
Time-Division Multiplexing
277(2)
6.6 Sampling Continuous-Time Signals
279(5)
Summary
284(1)
References
284(1)
Problems
284(5)
7 THE LAPLACE TRANSFORM
289(54)
7.1 Definitions of Laplace Transforms
290(2)
7.2 Examples
292(5)
7.3 Laplace Transforms of Functions
297(3)
7.4 Laplace Transform Properties
300(8)
Real Shifting
300(5)
Differentiation
305(2)
Integration
307(1)
7.5 Additional Properties
308(4)
Multiplication by t
308(1)
Initial Value
309(1)
Final Value
310(1)
Independent-Variable Transformation
311(1)
7.6 Response of LTI Systems
312(11)
Initial Conditions
313(2)
Transfer Functions
315(2)
Convolution
317(3)
Transforms with Complex Poles
320(2)
Functions with Repeated Poles
322(1)
7.7 LTI Systems Characteristics
323(5)
Causality
324(1)
Stability
324(1)
Invertibility
325(1)
Frequency Response
326(2)
7.8 Bilateral Laplace Transform
328(8)
Region of Convergence
329(2)
Bilateral Transform from Unilateral Tables
331(3)
Inverse Bilateral Laplace Transform
334(2)
7.9 Relationship of the Laplace Transform to the Fourier Transform
336(1)
Summary
337(1)
References
337(1)
Problems
337(6)
8 STATE VARIABLES FOR CONTINUOUS-TIME SYSTEMS
343(40)
8.1 State-Variable Modeling
344(4)
8.2 Simulation Diagrams
348(5)
8.3 Solution of State Equations
353(9)
Laplace-Transform Solution
353(4)
Convolution Solution
357(2)
Infinite Series Solution
359(3)
8.4 Properties of the State Transition Matrix
362(2)
8.5 Transfer Functions
364(3)
Stability
366(1)
8.6 Similarity Transformations
367(8)
Transformations
368(4)
Properties
372(3)
References
375(1)
Problems
375(8)
9 DISCRETE-TIME SIGNALS AND SYSTEMS
383(44)
9.1 Discrete-Time Signals and Systems
385(5)
Unit Step and Unit Impulse Functions
387(1)
Equivalent Operations
388(2)
9.2 Transformations of Discrete-Time Signals
390(7)
Time Transformations
390(6)
Amplitude Transformations
396(1)
9.3 Characteristics of Discrete-Time Signals
397(7)
Even and Odd Signals
398(2)
Signals Periodic in n
400(3)
Signals Periodic in Omega
403(1)
9.4 Common Discrete-Time Signals
404(6)
9.5 Discrete-Time Systems
410(1)
Interconnecting Systems
411(1)
9.6 Properties of Discrete-Time Systems
412(7)
Systems with Memory
413(1)
Invertibility
414(1)
Inverse of a System
414(1)
Causality
415(1)
Stability
415(1)
Time Invariance
416(1)
Linearity
417(2)
Summary
419(1)
References
419(1)
Problems
419(8)
10 DISCRETE-TIME LINEAR TIME-INVARIANT SYSTEMS
427(50)
10.1 Impulse Representation of Discrete-Time Signals
428(1)
10.2 Convolution for Discrete-Time Systems
429(11)
Properties of Convolution
437(3)
10.3 Properties of Discrete-Time LTI Systems
440(4)
Systems with Memory
440(1)
Invertibility
440(1)
Causality
441(1)
Stability
442(1)
Unit Step Response
443(1)
10.4 Difference-Equation Models
444(8)
Difference-Equation Models
445(1)
Classical Method
446(5)
Solution by Iteration
451(1)
10.5 Terms in the Natural Response
452(2)
Stability
453(1)
10.6 Block Diagrams
454(7)
Two Standard Forms
456(5)
10.7 System Response for Complex-Exponential Inputs
461(7)
Linearity
461(1)
Complex Inputs for LTI Systems
461(5)
Stability
466(1)
Sampled Signals
466(1)
Impulse Response
466(2)
Summary
468(1)
Reference
469(1)
Problems
469(8)
11 THE z-TRANSFORM
477(47)
11.1 Definitions of z-Transforms
477(3)
11.2 Examples
480(5)
Two z-Transforms
480(3)
Digital-Filter Example
483(2)
11.3 z-Transforms of Functions
485(4)
Sinusoids
486(3)
11.4 z-Transform Properties
489(5)
Real Shifting
490(2)
Initial and Final Values
492(2)
11.5 Additional Properties
494(3)
Time Scaling
494(2)
Convolution in Time
496(1)
11.6 LTI System Applications
497(11)
Transfer Functions
498(1)
Inverse z-Transform
499(3)
Complex Poles
502(2)
Causality
504(1)
Stability
505(2)
Invertibility
507(1)
11.7 Bilateral z-Transform
508(10)
Bilateral Transforms
512(2)
Regions of Convergence
514(1)
Inverse Bilateral Transforms
515(3)
Summary
518(1)
References
518(1)
Problems
518(6)
12 FOURIER TRANSFORMS OF DISCRETE-TIME SIGNALS
524(77)
12.1 Review of Sampling Continuous-Time Signals
524(7)
Impulse Sampling
526(3)
Data Reconstruction
529(2)
12.2 Discrete-Time Fourier Transform
531(4)
z-Transform
533(2)
12.3 Properties of the Discrete-Time Fourier Transform
535(6)
Periodicity
536(1)
Linearity
537(1)
Time Shift
537(1)
Frequency Shift
538(1)
Symmetry
539(1)
Time Reversal
539(1)
Convolution in Time
539(1)
Convolution in Frequency
540(1)
Multiplication by n
540(1)
Parseval's Theorem
541(1)
12.4 Transform of Periodic Sequences
541(6)
12.5 Discrete Fourier Transform
547(10)
Practical Look at Development of the DFT
551(2)
Shorthand Notation for the DFT
553(4)
Summary
557(1)
12.6 Fast Fourier Transform
557(8)
Decomposition-in-Time Fast Fourier Transform Algorithm
558(4)
Decomposition-in-Frequency Fast Frequency Fourier Transform
562(2)
Summary
564(1)
12.7 Applications of the Discrete Fourier Transform
565(30)
Calculation of Fourier Transforms
565(9)
Convolution
574(7)
Filtering
581(6)
Correlation
587(7)
Energy Spectrum Density Estimation
594(1)
Summary
595(1)
Summary
595(1)
References
595(1)
Problems
596(5)
13 STATE VARIABLES FOR DISCRETE-TIME SYSTEMS
601(33)
13.1 State-Variable Modeling
602(4)
13.2 Simulation Diagrams
606(4)
13.3 Solution of State Equations
610(8)
Recursive Solution
611(2)
z-Transform Solution
613(5)
13.4 Properties of the State Transition Matrix
618(1)
13.5 Transfer Functions
619(3)
Stability
621(1)
13.6 Similarity Transformations
622(4)
Properties
625(1)
Summary
626(1)
References
627(1)
Problems
627(7)
APPENDICES
634(23)
A. Integrals and Trigonometric Identities
634(1)
Integrals
634(1)
Trigonometric Identities
634(1)
B. Leibnitz's and L'Hospital's Rules
635(1)
Leibnitz's Rule
635(1)
L'Hospital's Rule
635(1)
C. Summation Formulas for Geometric Series
636(1)
D. Complex Numbers and Euler's Relation
637(7)
Complex-Number Arithmetic
638(2)
Euler's Relation
640(2)
Conversion Between Forms
642(1)
References
643(1)
E. Solution of Differential Equations
644(4)
Complementary Function
644(1)
Particular Solution
645(1)
General Solution
646(1)
Repeated Roots
646(1)
References
647(1)
F. Partial-Fraction Expansions
648(3)
References
650(1)
G. Review of Matrices
651(6)
Algebra of Matrices
655(1)
Other Relationships
655(1)
References
656(1)
INDEX 657

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