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.