Contents
Preface
1 Introduction
1.1 Modeling
1.2 Continuous-Time Physical Systems
Electric Circuits,
Operational Amplifier Circuits,
Simple Pendulum,
DC Power Supplies,
Analogous Systems,
1.3 Samplers and Discrete-Time Physical Systems
Analog-to-Digital Converter,
Numerical Integration,
Picture in a Picture,
Compact Disks,
Sampling in Telephone Systems,
Data-Acquisition System,
1.4 Matlab and Simulink
2 Continuous-Time Signals and Systems
2.1 Transformations of Continuous-Time Signals
Time Transformations,
Amplitude Transformations,
2.2 Signal Characteristics
Even and Odd Signals,
Periodic Signals,
2.3 Common Signals in Engineering
2.4 Singularity Functions
Unit Step Function,
Unit Impulse Function,
2.5 Mathematical Functions for Signals
2.6 Continuous-Time Systems
Interconnecting Systems,
Feedback System,
2.7 Properties of Continuous-Time Systems
Stability
Linearity
Summary
Problems
3 Continuous-Time Linear Time-Invariant Systems
3.1 Impulse Representation of Continuous-Time Signals
3.2 Convolution for Continuous-Time LTI Systems
3.3 Properties of Convolution
3.4 Properties of Continuous-Time LTI Systems
Memoryless Systems,
Invertibility,
Causality,
Stability,
Unit Step Response,
3.5 Differential-Equation Models
Solution of Differential Equations,
General Case,
Relation to Physical Systems,
3.6 Terms in the Natural Response
Stability,
3.7 System Response for Complex-Exponential Inputs
Linearity,
Complex Inputs for LTI Systems,
Impulse Response,
3.8 Block Diagrams
Direct Form I,
Direct Form II,
nth-Order Realizations,
Practical Considerations,
Summary
Problems
4 Fourier Series
4.1 Approximating Periodic Functions
Periodic Functions,
Approximating Periodic Functions,
4.2 Fourier Series
Fourier Series,
Fourier Coefficients,
4.3 Fourier Series and Frequency Spectra
Frequency Spectra,
4.4 Properties of Fourier Series
4.5 System Analysis
4.6 Fourier Series Transformations
Amplitude Transformations,
Time Transformations,
Summary
Problems
5 The Fourier Transform
5.1 Definition of the Fourier Transform
5.2 Properties of the Fourier Transform
Linearity,
Time Scaling,
Time Shifting,
Time Transformation,
Duality,
Convolution,
Frequency Shifting,
Time Differentiation,
Time Integration,
Frequency Differentiation,
Summary,
5.3 Fourier Transforms of Time Functions
DC Level,
Unit Step Function,
Switched Cosine,
Pulsed Cosine,
Exponential Pulse,
Fourier Transforms of Periodic Functions,
Summary,
5.4 Sampling Continuous-Time Signals
Impulse Sampling,
Shannon’s Sampling Theorem,
Practical Sampling,
5.5 Application of the Fourier Transform
Frequency Response of Linear Systems,
Frequency Spectra of Signals,
Summary,
5.6 Energy and Power Density Spectra
Energy Density Spectrum,
Power Density Spectrum,
Power and Energy Transmission,
Summary,
Summary
Problems
6 Applications of the Fourier Transform
6.1 Ideal Filters
6.2 Real Filters
RC Low-Pass Filter,
Butterworth Filter,
Chebyschev and Elliptic Filters,
Bandpass Filters,
Summary,
6.3 Bandwidth Relationships
6.4 Reconstruction of signals from sample data
Interpolating Function,
Digital-to-analog Conversion,
6.5 Sinusoidal Amplitude Modulation
Frequency-Division Multiplexing,
6.6 Pulse-Amplitude Modulation
Time-Division Multiplexing,
Flat-Top PAM,
Summary
Problems
7 The Laplace Transform
7.1 Definitions of Laplace Transforms
7.2 Examples
7.3 Laplace Transforms of Functions
7.4 Laplace Transform Properties
Real Shifting,
Differentiation,
Integration,
7.5 Additional Properties
Multiplication by t,
Initial Value,
Final Value,
Time Transformation,
7.6 Response of LTI Systems
Initial Conditions,
Transfer Functions,
Convolution,
Transforms with Complex Poles,
Functions with Repeated Poles,
7.7 LTI Systems Characteristics
Causality,
Stability,
Invertibility,
Frequency Response,
7.8 Bilateral Laplace Transform
Region of Convergence,
Bilateral Transform from Unilateral Tables,
Inverse Bilateral Laplace Transform,
7.9 Relationship of the Laplace Transform to the Fourier Transform
Summary
Problems
8 State Variables for Continuous-Time Systems
8.1 State-Variable Modeling
8.2 Simulation Diagrams
8.3 Solution of State Equations
Laplace-Transform Solution,
Convolution Solution,
Infinite Series Solution,
8.4 Properties of the State Transition Matrix
8.5 Transfer Functions
Stability,
8.6 Similarity Transformations
Transformations,
Properties,
Summary
Problems
9 Discrete-Time Signals and Systems
9.1 Discrete-Time Signals and Systems
Unit Step and Unit Impulse Functions,
Equivalent Operations,
9.2 Transformations of Discrete-Time Signals
Time Transformations,
Amplitude Transformations,
9.3 Characteristics of Discrete-Time Signals
Even and Odd Signals,
Signals Periodic in n,
Signals Periodic in W
9.4 Common Discrete-Time Signals
9.5 Discrete-Time Systems
Interconnecting Systems,
9.6 Properties of Discrete-Time Systems
Systems with Memory,
Invertibility,
Inverse of a System,
Causality,
Stability,
Time Invariance,
Linearity,
Summary
Problems
10 Discrete-Time Linear Time-Invariant Systems
10.1 Impulse Representation of Discrete-Time Signals
10.2 Convolution for Discrete-Time Systems
Properties of Convolution,
10.3 Properties of Discrete-Time LTI Systems
Memory,
Invertibility,
Causality,
Stability,
Unit Step Response,
10.4 Difference-Equation Models
Difference-Equation Models,
Classical Method,
Solution by Iteration,
10.5 Terms in the Natural Response
Stability,
10.6 Block Diagrams
Two Standard Forms,
10.7 System Response for Complex-Exponential Inputs
Linearity,
Complex Inputs for LTI Systems,
Stability,
Sampled Signals,
Impulse Response,
Summary
Problems
11 The z-Transform
11.1 Definitions of z-Transforms
11.2 Examples
Two z-Transforms,
Digital-Filter Example,
11.3 z-Transforms of Functions
Sinusoids,
11.4 z-Transform Properties
Real Shifting,
Initial and Final Values,
11.5 Additional Properties
Time Scaling,
Convolution in Time,
11.6 LTI System Applications
Transfer Functions,
Inverse z-Transform,
Complex Poles,
Causality,
Stability,
Invertibility,
11.7 Bilateral z-Transform
Bilateral Transforms,
Regions of Convergence,
Inverse Bilateral Transforms,
Summary
Problems
12 Fourier Transforms of Discrete-Time Signals
12.1 Discrete-Time Fourier Transform
z-Transform,
12.2 Properties of the Discrete-Time Fourier Transform
Periodicity,
Linearity,
Time Shift,
Frequency Shift,
Symmetry,
Time Reversal,
Convolution in Time,
Convolution in Frequency,
Multiplication by n,
Parseval’s Theorem,
12.3 Discrete-Time Fourier Transform of Periodic Sequences
12.4 Discrete Fourier Transform
Shorthand Notation for the DFT,
Frequency Resolution of the DFT,
Validity of the DFT,
Summary,
12.5 Fast Fourier Transform
Decomposition-in-Time Fast Fourier Transform Algorithm,
Decomposition-in-Frequency Fast Fourier Transform,
Summary,
12.6 Applications of the Discrete Fourier Transform
Calculation of Fourier Transforms,
Convolution,
Filtering,
Correlation,
Energy Spectral Density Estimation,
Summary,
12.7 The Discrete Cosine Transform,
Summary
Problems
13 State Variables for Discrete-Time Systems
13.1 State-Variable Modeling
13.2 Simulation Diagrams
13.3 Solution of State Equations
Recursive Solution,
z-Transform Solution,
13.4 Properties of the State Transition Matrix
13.5 Transfer Functions
Stability,
13.6 Similarity Transformations
Properties,
Summary
Problems
Appendices
A. Integrals and Trigonometric Identities
Integrals,
Trigonometric Identities,
B. Leibnitz’s and L’Hôpital’s Rules
Leibnitz’s Rule,
L’Hôpital’s Rule,
C. Summation Formulas for Geometric Series
D. Complex Numbers and Euler’s Relation
Complex-Number Arithmetic,
Euler’s Relation,
Conversion Between Forms,
E. Solution of Differential Equations
Complementary Function,
Particular Solution,
General Solution,
Repeated Roots,
F. Partial-Fraction Expansions
G. Review of Matrices
Algebra of Matrices,
Other Relationships
H. Answers to Selected Problems
I. Signals and Systems References
Index
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