Continuous and Discrete Signals and Systems,9780135184738

Continuous and Discrete Signals and Systems

by ;
Edition: 2nd
ISBN13: 9780135184738
ISBN10: 0135184738
Format: Paperback
Pub. Date: 1997-12-22
Publisher(s): Pearson
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $229.79

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

Buy from our Marketplace starting at $5.35

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

This complete introductory book assists readers in developing the ability to understand and analyze both continuous and discrete-time systems.The author presents the most widely used techniques of signal and system analysis in a highly readable and understandable fashion.For anyone interested in Signals & Systems, and Transform Theory.

Table of Contents

PREFACE xiii
1 REPRESENTING SIGNALS
1(40)
1.1 Introduction
1(1)
1.2 Continuous-Time vs. Discrete-Time Signals
2(2)
1.3 Periodic vs. Aperiodic Signals
4(3)
1.4 Energy and Power Signals
7(3)
1.5 Transformations of the Independent Variable
10(9)
1.5.1 The Shifting Operation
10(3)
1.5.2 The Reflection Operation
13(4)
1.5.3 The Time-Scaling Operation
17(2)
1.6 Elementary Signals
19(13)
1.6.1 The Unit Step Function
19(2)
1.6.2 The Ramp Function
21(1)
1.6.3 The Sampling Function
22(1)
1.6.4 The Unit Impulse Function
22(8)
1.6.5 Derivatives of the Impulse Function
30(2)
1.7 Other Types of Signals
32(1)
1.8 Summary
33(2)
1.9 Checklist of Important Terms
35(1)
1.10 Problems
35(6)
2 CONTINUOUS-TIME SYSTEMS
41(65)
2.1 Introduction
41(1)
2.2 Classification of Continuous-Time Systems
42(10)
2.2.1 Linear and Nonlinear Systems
42(4)
2.2.2 Time-Varying and Time-Invariant Systems
46(1)
2.2.3 Systems with and without Memory
47(1)
2.2.4 Causal Systems
48(2)
2.2.5 Invertibility and Inverse Systems
50(1)
2.2.6 Stable Systems
51(1)
2.3 Linear Time-Invariant Systems
52(12)
2.3.1 The Convolution Integral
52(6)
2.3.2 Graphical Interpretation of Convolution
58(6)
2.4 Properties of Linear, Time-Invariant Systems
64(3)
2.4.1 Memoryless LTI Systems
64(1)
2.4.2 Causal LTI Systems
64(1)
2.4.3 Invertible LTI Systems
65(1)
2.4.4 Stable LTI Systems
65(2)
2.5 Systems Described by Differential Equations
67(9)
2.5.1 Linear, Constant-Coefficient Differential Equations
67(1)
2.5.2 Basic System Components
68(2)
2.5.3 Simulation Diagrams for Continuous-Time Systems
70(3)
2.5.4 Finding the Impulse Response
73(3)
2.6 State-Variable Representation
76(18)
2.6.1 State Equations
77(1)
2.6.2 Time-Domain Solution of the State Equations
78(8)
2.6.3 State Equations in First Canonical Form
86(1)
2.6.4 State Equations in Second Canonical Form
87(4)
2.6.5 Stability Considerations
91(3)
2.7 Summary
94(2)
2.8 Checklist of Important Terms
96(1)
2.9 Problems
96(10)
3 FOURIER SERIES
106(56)
3.1 Introduction
106(1)
3.2 Orthogonal Representations of Signals
107(5)
3.3 The Exponential Fourier Series
112(10)
3.4 Dirichlet Conditions
122(3)
3.5 Properties of Fourier Series
125(10)
3.5.1 Least Squares Approximation Property
125(2)
3.5.2 Effects of Symmetry
127(2)
3.5.3 Linearity
129(1)
3.5.4 Product of Two Signals
130(1)
3.5.5 Convolution of Two Signals
131(1)
3.5.6 Parseval's Theorem
132(1)
3.5.7 Shift in Time
133(1)
3.5.8 Integration of Periodic Signals
134(1)
3.6 Systems with Periodic Inputs
135(7)
3.7 The Gibbs Phenomenon
142(3)
3.8 Summary
145(3)
3.9 Checklist of Important Terms
148(1)
3.10 Problems
148(12)
3.11 Computer Problems
160(2)
4 THE FOURIER TRANSFORM
162(62)
4.1 Introduction
162(1)
4.2 The Continuous-Time Fourier Transform
163(8)
4.2.1 Development of the Fourier Transform
163(2)
4.2.2 Existence of the Fourier Transform
165(1)
4.2.3 Examples of the Continuous-Time Fourier Transform
166(5)
4.3 Properties of the Fourier Transform
171(19)
4.3.1 Linearity
171(2)
4.3.2 Symmetry
173(2)
4.3.3 Time Shifting
175(1)
4.3.4 Time Scaling
175(2)
4.3.5 Differentiation
177(2)
4.3.6 Energy of Aperiodic Signals
179(2)
4.3.7 Convolution
181(3)
4.3.8 Duality
184(1)
4.3.9 Modulation
185(5)
4.4 Applications of the Fourier Transform
190(14)
4.4.1 Amplitude Modulation
190(2)
4.4.2 Multiplexing
192(2)
4.4.3 The Sampling Theorem
194(6)
4.4.4 Signal Filtering
200(4)
4.5 Duration-Bandwidth Relationships
204(7)
4.5.1 Definitions of Duration and Bandwidth
204(4)
4.5.2 The Uncertainty Principle
208(3)
4.6 Summary
211(1)
4.7 Checklist of Important Terms
212(1)
4.8 Problems
212(12)
5 THE LAPLACE TRANSFORM
224(54)
5.1 Introduction
224(1)
5.2 The Bilateral Laplace Transform
225(3)
5.3 The Unilateral Laplace Transform
228(1)
5.4 Bilateral Transforms Using Unilateral Transforms
229(2)
5.5 Properties of the Unilateral Laplace Transform
231(15)
5.5.1 Linearity
232(1)
5.5.2 Time Shifting
232(1)
5.5.3 Shifting in the s Domain
233(1)
5.5.4 Time Scaling
234(1)
5.5.5 Differentiation in the Time Domain
234(3)
5.5.6 Integration in the Time Domain
237(1)
5.5.7 Differentiation in the s Domain
238(1)
5.5.8 Modulation
239(1)
5.5.9 Convolution
240(3)
5.5.10 Initial-Value Theorem
243(1)
5.5.11 Final-Value Theorem
244(2)
5.6 The Inverse Laplace Transform
246(4)
5.7 Simulation Diagrams for Continuous-Time Systems
250(7)
5.8 Applications of the Laplace Transform
257(6)
5.8.1 Solution of Differential Equations
257(1)
5.8.2 Application to RLC Circuit Analysis
258(2)
5.8.3 Application to Control
260(3)
5.9 State Equations and the Laplace Transform
263(3)
5.10 Stability in the s Domain
266(2)
5.11 Summary
268(2)
5.12 Checklist of Important Terms
270(1)
5.13 Problems
270(8)
6 DISCRETE-TIME SYSTEMS
278(51)
6.1 Introduction
278(4)
6.1.1 Classification of Discrete-Time Signals
279(2)
6.1.2 Transformations of the Independent Variable
281(1)
6.2 Elementary Discrete-Time Signals
282(5)
6.2.1 Discrete Impulse and Step Functions
283(1)
6.2.2 Exponential Sequences
284(3)
6.3 Discrete-Time Systems
287(7)
6.4 Periodic Convolution
294(4)
6.5 Difference-Equation Representation of Discrete-Time Systems
298(8)
6.5.1 Homogeneous Solution of the Difference Equation
299(3)
6.5.2 The Particular Solution
302(3)
6.5.3 Determination of the Impulse Response
305(1)
6.6 Simulation Diagrams for Discrete-Time Systems
306(4)
6.7 State-Variable Representation of Discrete-Time Systems
310(6)
6.7.1 Solution of State-Space Equations
313(3)
6.7.2 Impulse Response of Systems Described by State Equation
316(1)
6.8 Stability of Discrete-Time Systems
316(2)
6.9 Summary
318(2)
6.10 Checklist of Important Terms
320(1)
6.11 Problems
320(9)
7 FOURIER ANALYSIS OF DISCRETE-TIME SYSTEMS
329(46)
7.1 Introduction
329(2)
7.2 Fourier-Series Representation of Discrete-Time Periodic Signals
331(9)
7.3 The Discrete-Time Fourier Transform
340(5)
7.4 Properties of the Discrete-Time Fourier Transform
345(6)
7.4.1 Periodicity
345(1)
7.4.2 Linearity
345(1)
7.4.3 Time and Frequency Shifting
345(1)
7.4.4 Differentiation in Frequency
346(1)
7.4.5 Convolution
346(4)
7.4.6 Modulation
350(1)
7.4.7 Fourier Transform of Discrete-Time Periodic Sequences
350(1)
7.5 Fourier Transform of Sampled Continuous-Time Signals
351(16)
7.5.1 Reconstruction of Sampled Signals
356(3)
7.5.2 Sampling-Rate Conversion
359(5)
7.5.3 A/D and D/A Conversion
364(3)
7.6 Summary
367(2)
7.7 Checklist of Important Terms
369(1)
7.8 Problems
369(6)
8 THE Z-TRANSFORM
375(44)
8.1 Introduction
375(1)
8.2 The Z-Transform
376(2)
8.3 Convergence of the Z-Transform
378(5)
8.4 Properties of the Z-Transform
383(9)
8.4.1 Linearity
385(1)
8.4.2 Time Shifting
386(1)
8.4.3 Frequency Scaling
387(1)
8.4.4 Differentiation with Respect to z
388(1)
8.4.5 Initial Value
389(1)
8.4.6 Final Value
389(1)
8.4.7 Convolution
390(2)
8.5 The Inverse Z-Transform
392(6)
8.5.1 Inversion by a Power-Series Expansion
394(1)
8.5.2 Inversion by Partial-Fraction Expansion
395(3)
8.6 Z-Transfer Functions of Causal Discrete-Time Systems
398(4)
8.7 Z-Transform Analysis of State-Variable Systems
402(8)
8.8 Relation Between the Z-Transform and the Laplace Transform
410(1)
8.9 Summary
411(3)
8.10 Checklist of Important Terms
414(1)
8.11 Problems
414(5)
9 THE DISCRETE FOURIER TRANSFORM
419(33)
9.1 Introduction
419(2)
9.2 The Discrete Fourier Transform and Its Inverse
421(1)
9.3 Properties of the DFT
422(4)
9.3.1 Linearity
422(1)
9.3.2 Time Shifting
422(1)
9.3.3 Alternative Inversion Formula
423(1)
9.3.4 Time Convolution
423(1)
9.3.5 Relation to the Discrete-Time Fourier and Z-Transforms
424(1)
9.3.6 Matrix Interpretation of the DFT
425(1)
9.4 Linear Convolution Using the DFT
426(2)
9.5 Fast Fourier Transforms
428(8)
9.5.1 The Decimation-in-Time Algorithm
429(4)
9.5.2 The Decimation-in-Frequency Algorithm
433(3)
9.6 Spectral Estimation of Analog Signals Using the DFT
436(9)
9.7 Summary
445(3)
9.8 Checklist of Important Terms
448(1)
9.9 Problems
448(4)
10 DESIGN OF ANALOG AND DIGITAL FILTERS
452(33)
10.1 Introduction
452(3)
10.2 Frequency Transformations
455(2)
10.3 Design of Analog Filters
457(11)
10.3.1 The Butterworth Filter
458(4)
10.3.2 The Chebyshev Filter
462(6)
10.4 Digital Filters
468(14)
10.4.1 Design of IIR Digital Filters Using Impulse Invariance
469(4)
10.4.2 IIR Design Using the Bilinear Transformation
473(2)
10.4.3 FIR Filter Design
475(6)
10.4.4 Computer-Aided Design of Digital Filters
481(1)
10.5 Summary
482(1)
10.6 Checklist of Important Terms
483(1)
10.7 Problems
483(2)
APPENDIX A COMPLEX NUMBERS
485(6)
A.1 Definition
485(2)
A.2 Arithmetic Operations
487(2)
A.2.1 Addition and Subtraction
487(1)
A.2.2 Multiplication
487(1)
A.2.3 Division
488(1)
A.3 Powers and Roots of Complex Numbers
489(1)
A.4 Inequalities
490(1)
APPENDIX B MATHEMATICAL RELATIONS
491(11)
B.1 Trigonometric Identities
491(1)
B.2 Exponential and Logarithmic Functions
492(1)
B.3 Special Functions
493(1)
B.3.1 Gamma Functions
493(1)
B.3.2 Incomplete Gamma Functions
494(1)
B.3.3 Beta Functions
494(1)
B.4 Power-Series Expansion
494(1)
B.5 Sums of Powers of Natural Numbers
495(1)
B.5.1 Sums of Binomial Coefficients
496(1)
B.5.2 Series of Exponentials
496(1)
B.6 Definite Integrals
496(2)
B.7 Indefinite Integrals
498(4)
APPENDIX C ELEMENTARY MATRIX THEORY
502(10)
C.1 Basic Definition
502(1)
C.2 Basic Operations
503(1)
C.2.1 Matrix Addition
503(1)
C.2.2 Differentiation and Integration
503(1)
C.2.3 Matrix Multiplication
503(1)
C.3 Special Matrices
504(2)
C.4 The Inverse of a Matrix
506(1)
C.5 Eigenvalues and Eigenvectors
507(1)
C.6 Functions of a Matrix
508(4)
APPENDIX D PARTIAL FRACTIONS
512(7)
D.1 Case I: Nonrepeated Linear Factors
513(1)
D.2 Case II: Repeated Linear Factors
514(2)
D.3 Case III: Nonrepeated Irreducible Second-Degree Factors
516(1)
D.4 Case IV: Repeated Irreducible Second-Degree Factors
517(2)
BIBLIOGRAPHY 519(2)
INDEX 521

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.