Continuous Signals and Systems with MATLAB® (Hardcover, 3 ed)

Chapter 1 Signal Representation1.1Examples of Continuous Signals1.2The Continuous Signal1.3Periodic and Nonperiodic Signals1.4General Form of Sinusoidal Signals1.5Energy and Power Signals1.6The Shifting Operation1.7The Reflection Operation1.8Even and Odd Functions 1.9Time Scaling1.10The Unit Step Signal 1.11The Signum Signal1.12The Ramp Signal1.13The Sampling Signal 1.14The Impulse Signal1.15Some Insights: Signals in the Real World1.16End-of-Chapter Examples 1.17End-of-Chapter ProblemsReferences Chapter 2 Continuous Systems2.1Definition of a System2.2Input and Output2.3Linear Continuous System2.4Time-Invariant System2.5Systems without Memory2.6Causal Systems2.7The Inverse of a System2.8Stable Systems2.9Convolution2.10Simple Block Diagrams2.11Graphical Convolution2.12Differential Equations and Physical Systems 2.13Homogeneous Differential Equations and Their Solutions2.14Nonhomogeneous Differential Equations and Their Solutions2.15The Stability of Linear Continuous Systems: The Characteristic Equation2.16Block Diagram Representation of Linear Systems2.17From Block Diagrams to Differential Equations 2.18From Differential Equations to Block Diagrams 2.19The Impulse Response2.20Some Insights: Calculating y(t)2.21End-of-Chapter Examples2.22End-of-Chapter ProblemsReferences Chapter 3 Fourier Series3.1Review of Complex Numbers3.2Orthogonal Functions 3.3Periodic Signals3.4Conditions for Writing a Signal as a Fourier Series Sum3.5Basis Functions3.6The Magnitude and the Phase Spectra3.7Fourier Series and the Sin-Cos Notation3.8Fourier Series Approximation and the Resulting Error3.9The Theorem of Parseval3.10Systems with Periodic Inputs3.11A Formula for Finding y(t) When x(t) Is Periodic: The Steady-State Response3.12Some Insight: Why the Fourier Series?3.13End-of-Chapter Examples3.14End-of-Chapter ProblemsReferences Chapter 4 The Fourier Transform and Linear Systems4.1Definition4.2Introduction4.3The Fourier Transform Pairs4.4Energy of Non-Periodic Signals4.5The Energy Spectral Density of a Linear System4.6Some Insights: Notes and a Useful Formula4.7End-of-Chapter Examples4.8End-of-Chapter ProblemsReferences Chapter 5 The Laplace Transform and Linear Systems5.1Definition 5.2The Bilateral Laplace Transform5.3The Unilateral Laplace Transform5.4The Inverse Laplace Transform5.5Block Diagrams Using the Laplace Transform5.6Representation of Transfer Functions as Block Diagrams5.7Procedure for Drawing the Block Diagram from the Transfer Function5.8Solving LTI Systems Using the Laplace Transform5.9Solving Differential Equations Using the Laplace Transform5.10The Final Value Theorem5.11The Initial Value Theorem5.12Some Insights: Poles and Zeros 5.13End-of-Chapter Examples 5.14End-of-Chapter ProblemsReferences Chapter 6 State-Space and Linear Systems6.1Introduction6.2A Review of Matrix Algebra6.3General Representation of Systems in State-Space6.4General Solution of State-Space Equations Using the Laplace Transform6.5General Solution of the State-Space Equations in Real Time6.6Ways of Evaluating eAt6.7Some Insights: Poles and Stability6.8End-of-Chapter Examples6.9End-of-Chapter ProblemsReferences