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E-raamat: Discrete Signals and Systems with MATLAB(R)

(Benedict College, USA.)
  • Formaat: 360 pages
  • Ilmumisaeg: 07-Oct-2020
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781000180053
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Discrete Signals and Systems with MATLAB(R)Suurem pilt
  • Formaat: 360 pages
  • Ilmumisaeg: 07-Oct-2020
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781000180053
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The subject of Discrete Signals and Systems is broad and deserves a single book devoted to it. The objective of this textbook is to present all the required material that an undergraduate student will need to master this subject matter and the use of MATLAB.

This book is primarily intended for electrical and computer engineering students, and especially for use by juniors or seniors in these undergraduate engineering disciplines. It can also be very useful to practicing engineers. It is detailed, broad, based on mathematical basic principles, focused, and it also contains many solved problems using analytical tools as well as MATLAB.

The book is ideal for a one-semester course in the area of discrete linear systems or digital signal processing, where the instructor can cover all chapters with ease. Numerous examples are presented within each chapter to illustrate each concept when and where it is presented. Most of the worked-out examples are first solved analytically and then solved using MATLAB in a clear and understandable fashion.
Preface xiii
About the Author xv
Acknowledgment xvii
Chapter 1 Signal Representation
1(50)
1.1 Introduction
1(2)
1.2 Why Do We Discretize Continuous Systems?
3(1)
1.3 Periodic and Nonperiodic Discrete Signals
3(1)
1.4 Unit Step Discrete Signal
4(1)
1.5 Impulse Discrete Signal
4(1)
1.6 Ramp Discrete Signal
5(1)
1.7 Real Exponential Discrete Signal
6(1)
1.8 Sinusoidal Discrete Signal
7(3)
1.9 Exponentially Modulated Sinusoidal Signal
10(2)
1.10 Complex Periodic Discrete Signal
12(1)
1.11 Shifting Operation
13(2)
1.12 Representing a Discrete Signal Using Impulses
15(1)
1.13 Reflection Operation
16(1)
1.14 Time Scaling
17(1)
1.15 Amplitude Scaling
18(1)
1.16 Even and Odd Discrete Signal
19(2)
1.17 Does a Discrete Signal Have a Time Constant?
21(1)
1.18 Basic Operations on Discrete Signals
22(3)
1.18.1 Modulation
22(1)
1.18.2 Addition and Subtraction
22(1)
1.18.3 Scalar Multiplication
22(1)
1.18.4 Combined Operations
23(2)
1.19 Energy and Power Discrete Signals
25(2)
1.20 Bounded and Unbounded Discrete Signals
27(1)
1.21 Some Insights: Signals in the Real World
27(2)
1.21.1 Step Signal
28(1)
1.21.2 Impulse Signal
28(1)
1.21.3 Sinusoidal Signal
28(1)
1.21.4 Ramp Signal
28(1)
1.21.5 Other Signals
28(1)
1.22 End-of-Chapter Examples
29(17)
1.23 End-of-Chapter Problems
46(5)
Chapter 2 Discrete System
51(74)
2.1 Definition of a System
51(1)
2.2 Input and Output
51(1)
2.3 Linear Discrete Systems
52(2)
2.4 Time Invariance and Discrete Signals
54(2)
2.5 Systems with Memory
56(1)
2.6 Causal Systems
56(1)
2.7 Inverse of a System
57(1)
2.8 Stable System
58(1)
2.9 Convolution
59(4)
2.10 Difference Equations of Physical Systems
63(1)
2.11 Homogeneous Difference Equation and Its Solution
63(4)
2.11.1 Case When Roots Are All Distinct
66(1)
2.11.2 Case When Two Roots Are Real and Equal
66(1)
2.11.3 Case When Two Roots Are Complex
66(1)
2.12 Nonhomogeneous Difference Equations and Their Solutions
67(3)
2.12.1 How Do We find the Particular Solution?
69(1)
2.13 Stability of Linear Discrete Systems: The Characteristic Equation
70(3)
2.13.1 Stability Depending on the Values of the Poles
70(1)
2.13.2 Stability from the Jury Test
70(3)
2.14 Block Diagram Representation of Linear Discrete Systems
73(2)
2.14.1 Delay Element
73(1)
2.14.2 Summing/Subtracting Junction
73(1)
2.14.3 Multiplier
74(1)
2.15 From the Block Diagram to the Difference Equation
75(1)
2.16 From the Difference Equation to the Block Diagram: A Formal Procedure
76(3)
2.17 Impulse Response
79(2)
2.18 Correlation
81(2)
2.18.1 Cross-Correlation
81(1)
2.18.2 Auto-Correlation
82(1)
2.19 Some Insights
83(1)
2.19.1 How Can We Find These Eigenvalues?
83(1)
2.19.2 Stability and Eigenvalues
84(1)
2.20 End-of-Chapter Examples
84(34)
2.21 End-of-Chapter Problems
118(7)
Chapter 3 Fourier Series and the Fourier Transform of Discrete Signals
125(46)
3.1 Introduction
125(1)
3.2 Review of Complex Numbers
125(4)
3.2.1 Definition
125(1)
3.2.2 Addition
126(1)
3.2.3 Subtraction
126(1)
3.2.4 Multiplication
127(1)
3.2.5 Division
127(1)
3.2.6 From Rectangular to Polar
128(1)
3.2.7 From Polar to Rectangular
128(1)
3.3 Fourier Series of Discrete Periodic Signals
129(2)
3.4 Discrete System with Periodic Inputs: The Steady-State Response
131(4)
3.4.1 General Form for yss (n)
134(1)
3.5 Frequency Response of Discrete Systems
135(5)
3.5.1 Properties of the Frequency Response
137(1)
3.5.1.1 Periodicity Property
137(1)
3.5.1.2 Symmetry Property
138(2)
3.6 Fourier Transform of Discrete Signals
140(1)
3.7 Convergence Conditions
141(1)
3.8 Properties of the Fourier Transform of Discrete Signals
141(5)
3.8.1 Periodicity Property
141(1)
3.8.2 Linearity Property
142(1)
3.8.3 Discrete-Time-Shifting Property
142(1)
3.8.4 Frequency-Shifting Property
142(1)
3.8.5 Reflection Property
143(1)
3.8.6 Convolution Property
143(3)
3.9 Parseval's Relation and Energy Calculations
146(1)
3.10 Numerical Evaluation of the Fourier Transform of Discrete Signals
147(3)
3.11 Some Insights: Why Is This Fourier Transform?
150(1)
3.11.1 Ease in Analysis and Design
150(1)
3.11.2 Sinusoidal Analysis
151(1)
3.12 End-of-Chapter Examples
151(12)
3.13 End-of-Chapter Problems
163(8)
Chapter 4 Z-Transform and Discrete Systems
171(60)
4.1 Introduction
171(1)
4.2 Bilateral z-Transform
171(2)
4.3 Unilateral z-Transform
173(2)
4.4 Convergence Considerations
175(3)
4.5 Inverse z-Transform
178(4)
4.5.1 Partial Fraction Expansion
178(3)
4.5.2 Long Division
181(1)
4.6 Properties of the z-Transform
182(3)
4.6.1 Linearity Property
182(1)
4.6.2 Shifting Property
182(2)
4.6.3 Multiplication by
184(1)
4.6.4 Convolution
184(1)
4.7 Representation of Transfer Functions as Block Diagrams
185(1)
4.8 X(n), h(ri), y(n), and the z-Transform
186(2)
4.9 Solving Difference Equation Using the z-Transform
188(2)
4.10 Convergence Revisited
190(2)
4.11 Final-Value Theorem
192(1)
4.12 Initial-Value Theorem
192(1)
4.13 Some Insights: Poles and Zeroes
193(1)
4.13.1 Poles of the System
193(1)
4.13.2 Zeros of the System
194(1)
4.13.3 Stability of the System
194(1)
4.14 End-of-Chapter Examples
194(28)
4.15 End-of-Chapter Problems
222(9)
Chapter 5 Discrete Fourier Transform and Discrete Systems
231(46)
5.1 Introduction
231(1)
5.2 Discrete Fourier Transform and the Finite-Duration Discrete Signals
232(1)
5.3 Properties of the DFT
233(6)
5.3.1 How Does the Denning Equation Work?
234(1)
5.3.2 DFT Symmetry
234(2)
5.3.3 DFT Linearity
236(1)
5.3.4 Magnitude of the DFT
237(1)
5.3.5 What Does k in the DFT, Mean?
237(2)
5.4 Relation the DFT Has with the Fourier Transform of Discrete Signals, the z-Transform, and the Continuous Fourier Transform
239(3)
5.4.1 DFT and the Fourier Transform of x(n)
239(1)
5.4.2 DFT and the z-Transform of x(n)
239(1)
5.4.3 DFT and the Continuous Fourier Transform of x(t)
240(2)
5.5 Numerical Computation of the DFT
242(1)
5.6 Fast Fourier Transform: A Faster Way of Computing the DFT
243(1)
5.7 Applications of the DFT
244(13)
5.7.1 Circular Convolution
244(5)
5.7.2 Linear Convolution
249(1)
5.7.3 Approximation to the Continuous Fourier Transform
250(1)
5.7.4 Approximation to the Coefficients of the Fourier Series and the Average Power of the Periodic Signal x(t)
251(3)
5.7.5 Total Energy in the Signal x{n) and x(t)
254(2)
5.7.6 Block Filtering
256(1)
5.7.7 Correlation
256(1)
5.8 Some Insights
257(2)
5.8.1 DFT is the Same as the fft
257(1)
5.8.2 DFT Points Are the Samples of the Fourier Transform of x(n)
257(1)
5.8.3 How Can We Be Certain that Most of the Frequency Contents of x(t) Are in the DFT?
257(1)
5.8.4 Is the Circular Convolution the Same as the Linear Convolution?
258(1)
5.8.5 Is IX(w)
258(1)
5.8.6 Frequency Leakage and the DFT
258(1)
5.9 End-of-Chapter Examples
259(13)
5.10 End-of-Chapter Problems
272(5)
Chapter 6 State-Space and Discrete Systems
277(56)
6.1 Introduction
277(1)
6.2 Review on Matrix Algebra
278(4)
6.2.1 Definition, General Terms, and Notations
278(1)
6.2.2 Identity Matrix
278(1)
6.2.3 Adding Two Matrices
278(1)
6.2.4 Subtracting Two Matrices
279(1)
6.2.5 Multiplying a Matrix by a Constant
279(1)
6.2.6 Determinant of a Two-by-Two Matrix
279(1)
6.2.7 Inverse of a Matrix
280(1)
6.2.8 Matrix Multipl ication
280(1)
6.2.9 Eigenvalues of a Matrix
281(1)
6.2.10 Diagonal Form of a Matrix
281(1)
6.2.11 Eigenvectors of a Matrix
281(1)
6.3 General Representation of Systems in State Space
282(13)
6.3.1 Recursive Systems
282(1)
6.3.2 Nonrecursive Systems
283(2)
6.3.3 From the Block Diagram to State Space
285(2)
6.3.4 From the Transfer Function H(z) to State Space
287(8)
6.4 Solution of the State-Space Equations in the z-Domain
295(1)
6.5 General Solution of the State Equation in Real Time
295(2)
6.6 Properties of A and Its Evaluation
297(3)
6.7 Transformations for State-Space Representations
300(2)
6.8 Some Insights: Poles and Stability
302(1)
6.9 End-of-Chapter Examples
303(23)
6.10 End-of-Chapter Problems
326(7)
Index 333
Dr. Taan S. ElAli, PhD, is a full professor of electrical engineering. He is currently the Coordinator of the Engineering Program in the College of Aeronautics at Embry Riddle Aeronautical University.
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