Continuous Signals and Systems with MATLAB

Preface
Signal Representation
Examples of Continuous Signals
The Continuous Signal
Periodic and Nonperiodic Signals
General Form of Sinusoidal Signals
Energy and Power Signals
The Shifting Operation
The Reflection Operation
Even and Odd Functions
Time Scaling
The Unit Step Signal
The Signum Signal
The Ramp Signal
The Sampling Signal
The Impulse Signal
Some Insights: Signals in the Real World
Continuous Systems
Definition of a System
Input and Output
Linear Continuous System
Time-Invariant System
Systems without Memory
Causal Systems
The Inverse of a System
Stable Systems
Convolution
Simple Block Diagrams
Graphical Convolution
Differential Equations and Physical Systems
Homogeneous Differential Equations and Their Solutions
Nonhomogeneous Differential Equations and Their Solutions
The Stability of Linear Continuous Systems:
The Characteristic Equation
Block Diagram Representation of Linear Systems
From Block Diagrams to Differential Equations
From Differential Equations to Block Diagrams
The Impulse Response
Some Insights: Calculating y(t)
Fourier Series
Review of Complex Numbers
Orthogonal Functions
Periodic Signals
Conditions for Writing a Signal as a Fourier Series Sum
Basis Functions
The Magnitude and the Phase Spectra
Fourier Series and the Sin-Cos Notation
Fourier Series Approximation and the Resulting Error
The Theorem of Parseval
Systems with Periodic Inputs
A Formula for Finding y(t) When x(t) Is Periodic: The Steady-State Response
Some Insight: Why the Fourier Series?
The Fourier Transform and Linear Systems
Definition
Introduction
The Fourier Transform Pairs
Energy of Nonperiodic Signals
The Energy Spectral Density of a Linear System
Some Insights: Notes and a Useful Formula
The Laplace Transform and Linear Systems
Definition
The Bilateral Laplace Transform
The Unilateral Laplace Transform
The Inverse Laplace Transform
Block Diagrams Using the Laplace Transform
Representation of Transfer Functions as Block Diagrams
Procedure for Drawing the Block Diagram from the Transfer Function
Solving LTI Systems Using the Laplace Transform
Solving Differential Equations Using the Laplace Transform
The Final Value Theorem
The Initial Value Theorem
Some Insights: Poles and Zeros
State-Space and Linear Systems
Introduction
A Review of Matrix Algebra
General Representation of Systems in State Space
General Solution of State-Space Equations Using the Laplace Transform
General Solution of the State-Space Equations in Real Time
Ways of Evaluating eAt
Some Insights: Poles and Stability
Block Diagrams
Introduction
Basic Block Diagram Components
Block Diagrams as Interconnected Subsystems
The Controllable Canonical Form Block Diagrams with Basic Blocks
The Observable Canonical Form Block Diagrams with Basic Blocks
The Diagonal Form Block Diagrams with Basic Blocks
The Parallel Block Diagrams with Subsystems
The Series Block Diagrams with Subsystems
Block Diagram Reduction Rules
Analog Filter Design
Introduction
Analogue Filter Specifications
Butterworth Filter Approximation
Chebyshev Filters
Elliptic Filter Approximation
Bessel Filters
Analog Frequency Transformation
Analog Filter Design Using MATLAB
How Do We Find the Cutoff Frequency Analytically?
Limitations
Comparison between Analog Filter Types
Implementation of Analog Filters
Some Insights: Filters with High Gain versus Filters with Low Gain and the Relation between the Time Constant and the Cutoff Frequency for First-Order Circuits and the Series RLC Circuit
Introduction to Nonlinear Systems
Introduction
Linear and Nonlinear Differential Equations
The Process of Linearization
Some Insights: The Meaning of Linear and Nonlinear
Index
Each chapter contains Examples, Problems, and References at the end.