Systems and Signal Processing with MATLAB® : Two Volume Set (Multiple-component retail product, 3 ed)

Volume 1Chapter 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 ProblemsReferencesChapter 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 ProblemsReferencesChapter 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 ProblemsReferencesChapter 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 ProblemsReferencesChapter 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 eAt 6.7Some Insights: Poles and Stability6.8End-of-Chapter Examples6.9End-of-Chapter ProblemsReferences Volume 21. Signal Representation1.1 Introduction1.2 Why Do We Discretize Continuous Signals?1.3 Periodic And Nonperiodic Discrete Signals1.4 The Unit Step Discrete Signal1.5 The Impulse Discrete Signal1.6 The Ramp Discrete Signal1.7 The Real Exponential Discrete Signal1.8 The Sinusoidal Discrete Signal1.9 The Exponentially Modulated Sinusoidal Signal1.10 The Complex Periodic Discrete Signal1.11 The Shifting Operation1.12 Representing A Discrete Signal Using Impulses1.13 The Reflection Operation1.14 Time Scaling1.15 Amplitude Scaling1.16 Even And Odd Discrete Signal1.17 Does A Discrete Signal Have A Time Constant?1.18 Basic Operations On Discrete Signals1.19 Energy And Power Discrete Signals1.20 Bounded And Unbounded Discrete Signals1.21 Some Insights: Signals In The Real World1.22 End Of Chapter Examples1.23 End Of Chapter Problems 2. The Discrete System2.1 Definition of A System2.2 Input and Output 2.3 Linear Discrete Systems2.4 Time Invariance and Discrete Systems2.5 Systems with Memory2.6 Casual Systems2.7 The Inverse of A System2.8 Stable System2.9 Convolution2.10 Difference Equations of Physical Systems2.11 The Homogenous Difference Equation and Its Solution2.12 Nonhomogenous Difference Equations And Their Solutions2.13 The Stability Of Linear Discrete Systems: The Characteristic Equation2.14 Block Diagram Representation Of Linear Discrete Systems2.15 From The Block Diagram To The Difference Equation2.16 From The Difference Equation To The Block Diagram: A Formal Procedure2.17 The Impulse Response2.18 Correlation2.19 Some Insights2.20 End Of Chapter Examples2.21 End Of Chapter Problems 3. The Fourier Series And The Fourier Transform Of Discrete Signals3.1 Introduction3.2 Review Of Complex Numbers3.3 The Fourier Series Of Discrete Periodic Signals3.4 The Discrete System With Periodic Inputs: The Steady-State Response3.5 THE FREQUANCY RESPONSE OF DISCRETE SYSTEMS3.6 THE FOURIER TRANSFORM OF DISCRETE SIGNALS3.7 CONVERGENCE CONDITIONS3.8 PROPERTIES OF THE FOURIER TRANSFORM OF DISCRETE SIGNALS3.9 Parseval’s Relation And Energy Calculations3.10 Numerical Evaluation Of The Fourier Transform Of Discrete Signals3.11 Some Insights: Why Is This Fourier Transform?3.12 End Of Chapter Examples3.13 End Of Chapter Problems 4. The Z-Transform And Discrete Systems4.1 Introduction4.2 The Bilateral Z-Transform4.3 The Unilateral Z-Transform4.4 Convergence Considerations4.5 The Inverse Z-Transform4.6 Properties Of The Z-Transform4.7 Representation Of Transfer Functions As Block Diagrams4.8 X(N), H(N), Y(N), And The Z-Transform4.9 Solving Difference Equation Using The Z-Transform4.10 Convergence Revisisted4.11 The Final Value Theorem4.12 The Initial Value Theorem4.13 Some Insights : Poles And Zeros4.14 End Of Chapter Examples4.15 End Of Chapter Problems 5. The Discrete Fourier Transform And Discrete Systems5.1 Introduction5.2 The Discrete Fourier Transform And The Finite-Duration Discrete Signals5.3 Properties Of The Discrete Fourier Transform5.4 The Relation The Dft Has With The Fourier Transform Of Discrete Signals, The Z-Transform, And The Continuous Fourier Transform5.5 Numerical Computation Of The Dft5.6 The Fast Fourier Transform: A Faster Way Of Computing The Dft5.7 Applications Of The Dft5.8 Some Insights5.9 End Of Chapter Examples5.10 End Of Chapter Problems 6. State-Space And Discrete Systems6.1 Introduction6.2 A Review On Matrix Algebra6.3 General Representation Of Systems In State-Space6.4 Solution Of The State-Space Equations Is The Z-Domain6.5 General Solution Of The State Equation In Real Time6.6 Properties Of And Its Evaluation6.7 Transformations For In State-Space Representations6.8 Some Insights: Poles And Stability6.9 End Of Chapter Examples6.10 End Of Chapter Problems