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Signals, systems, and transforms
CONTENTS
1 INTRODUCTION
1.1 Modeling
1.2 Continuous-Time Physical Systems
1.3 Samplers and Discrete-Time Physical Systems
1.4 MATLAB and SIMULINK
1.5 Signals and Systems References
2 CONTINUOUS-TIME SIGNALS AND SYSTEMS
2.1 Transformations of Continuous-Time Signals
2.2 Signal Characteristics
2.3 Common Signals in Engineering
2.4 Singularity Functions
2.5 Mathematical Functions for Signals
2.6 Continuous-Time Systems
2.7 Properties of Continuous-Time Systems
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
3.5 Differential-Equation Models
3.6 Terms in the Natural Response
3.7 System Response for Complex-Exponential Inputs
3.8 Block Diagrams
4 FOURIER SERIES
4.1 Approximating Periodic Functions
4.2 Fourier Series
4.3 Fourier Series and Frequency Spectra
4.4 Properties of Fourier Series
4.5 System Analysis
4.6 Fourier Series Transformations
5 THE FOURIER TRANSFORM
5.1 Definition of the Fourier Transform
5.2 Properties of the Fourier Transform
5.3 Fourier Transforms of Time Functions
5.4 Sampling Continuous-Time Signals
5.5 Application of the Fourier Transform
5.6 Energy and Power Density Spectra
6 APPLICATIONS OF THE FOURIER TRANSFORM
6.1 Ideal Filters
6.2 Real Filters
6.3 Bandwidth Relationships
6.4 Reconstruction of Signals from Sample Data
6.5 Sinusoidal Amplitude Modulation
6.6 Pulse-Amplitude Modulation
7 THE LAPLACE TRANSFORM
7.1 Definitions of Laplace Transforms
7.2 Examples
7.3 Laplace Transforms of Functions
7.4 Laplace Transform Properties
7.5 Additional Properties
7.6 Response of LTI Systems
7.7 LTI Systems Characteristics
7.8 Bilateral Laplace Transform
7.9 Relationship of the Laplace Transform to the Fourier Transform
8 STATE VARIABLES FOR CONTINUOUS-TIME SYSTEMS
8.1 State-Variable Modeling
8.2 Simulation Diagrams
8.3 Solution of State Equations
8.4 Properties of the State Transition Matrix
8.5 Transfer Functions
8.6 Similarity Transformations
9 DISCRETE-TIME SIGNALS AND SYSTEMS
9.1 Discrete-Time Signals and Systems
9.2 Transformations of Discrete-Time Signals
9.3 Characteristics of Discrete-Time Signals
9.4 Common Discrete-Time Signals
9.5 Discrete-Time Systems
9.6 Properties of Discrete-Time Systems
10 DISCRETE-TIME LINEAR TIME-INVARIANT SYSTEMS
10.1 Impulse Representation of Discrete-Time Signals
10.2 Convolution for Discrete-Time Systems
10.3 Properties of Discrete-Time LTI Systems
10.4 Difference-Equation Models
10.5 Terms in the Natural Response
10.6 Block Diagrams
10.7 System Response for Complex-Exponential Inputs
11 THE z-TRANSFORM
11.1 Definitions of z-Transforms
11.2 Examples
11.3 z-Transforms of Functions
11.4 z-Transform Properties
11.5 Additional Properties
11.6 LTI System Applications
11.7 Bilateral z-Transform
12 FOURIER TRANSFORMS OF DISCRETE-TIME SIGNALS
12.1 Discrete-Time Fourier Transform
12.2 Properties of the Discrete-Time Fourier Transform
12.3 Discrete-Time Fourier Transform of Periodic Sequences
12.4 Discrete Fourier Transform
12.5 Fast Fourier Transform
12.6 Applications of the Discrete Fourier Transform
12.7 The Discrete Cosine Transform
13 STATE VARIABLES FOR DISCRETE-TIME SYSTEMS
13.1 State-Variable Modeling
13.2 Simulation Diagrams
13.3 Solution of State Equations
13.4 Properties of the State Transition Matrix
13.5 Transfer Functions
13.6 Similarity Transformations
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