Signals and Systems Laboratory with MATLAB
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1 Signals and Systems Laboratory with MATLAB Alex Palamides Anastasia CRC Press Taylor &. Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa business
2 Contents Preface Authors xiii xvii 1. Introduction to MATLAB What Is MATLAB? Working Environment Getting Started Simple Arithmetic Operations Comments The Variable ans Priority of Operations Constants Built-in Functions Variables Format Help in MATLAB Memory Management Commands save-load-exit-quit The Command clear Commands diary and clc Vectors Row Vectors Commands length/size Addition/Subtraction Multiplication, Division, and Power Column Vectors Dot Product of Two Vectors Useful Commands Matrices Matrix Concatenation Working with Matrices Addition/Subtraction Multiplication of Matrices The Dot Product as a Special Case of Matrix Multiplication Power of a Matrix Inverse of a Matrix Determinant of a Matrix Division of Matrices Transpose of a Matrix Special Forms of Matrices Useful Commands Plotting with MATLAB Plotting in Two Dimensions 27 V
3 vi Contents The Fig File The Command linspace Plotting Several Functions in One Figure Formatting a Figure Plotting in Different Figures Commands for Plotting Plotting Discrete-Time Functions Graph in Polar Coordinates Piecewise Functions Plotting in Three Dimensions Plotting Curves in Three Dimensions Plotting Surfaces in Three Dimensions Complex Numbers Useful Commands Forms of Complex Numbers Operations with Complex Numbers Graph of Complex Numbers M-Files Scripts Functions Input/Output Commands File Management Logical/Relational Operators Control Flow Symbolic Variables Differentiation of a Function Integration of a Function Summation of a Function Rational Form Solving Algebraic Equations Solving Differential Equations The Command subs Polynomials (Pseudo)Random Numbers Solved Problems Homework Problems Signals Categorization by the Variable Type Continuous-Time Signals Discrete-Time Signals Digital Signals Basic Continuous-Time Signals Sinusoidal Signals Exponential Signals Complex Exponential Signals Unit Step Function Unit Impulse or Dirac Delta Function 89
4 Contents vii Ramp Function Rectangular Pulse Function Discrete-Time Signals Unit Impulse Sequence Unit Step Sequence Real Exponential Sequence Complex Exponential Sequence Sinusoidal Sequence Properties of Signals Ill Periodic Signals Ill Sum of Periodic Continuous-Time Signals Construction of Periodic Signals Causal Signals Even and Odd Signals Energy and Power Signals Deterministic and Stochastic Signals Transformations of the Time Variable for Continuous-Time Signals Time Reversal or Reflection Time Scaling Time Shifting Transformations of the Time Variable for Discrete-Time Signals Solved Problems Homework Problems Systems Systems Classification Classification according to the Number of Inputs and Outputs Continuous-Time and Discrete-Time Signals Deterministic and Stochastic Systems Properties of Systems Causal and Noncausal Systems Static (Memoryless) and Dynamic (with Memory) Systems Linear and Nonlinear Systems Time-Invariant and Time-Variant Systems Invertible and Non-Invertible Systems Construction of the Inverse System Stable and Unstable Systems Solved Problems Homework Problems Time Domain System Analysis Impulse Response Continuous-Time Convolution Computation of Convolution The Command conv Deconvolution Continuous-Time Convolution Examples Convolution Properties 199
5 viii Contents 4.4 Interconnections of Systems Stability Discrete-Time Convolution The Unit Impulse Sequence as Input to a System Computation of Discrete-Time Convolution Discrete-Time Convolution Examples Systems Described by Difference Equations Filters The Command filter Infinite Impulse Response Filters Finite Impulse Response Filters Stability Criterion for Discrete-Time Systems Systems Described by Differential Equations Step Response of a System Solved Problems Homework Problems Fourier Series Orthogonality of Complex Exponential Signals Complex Exponential Fourier Series Trigonometric Fourier Series Fourier Series in the Cosine with Phase Form Plotting the Fourier Series Coefficients Fourier Series of Complex Signals Fourier Series of Periodic Signals Line Spectra Properties of Fourier Series Linearity Time Shifting Time Reversal Time Scaling Signal Multiplication Symmetry Even Symmetry Odd Symmetry Parseval's Identity Criterion for the Approximation of a Signal by a Fourier Series Expansion Relationship between Complex Exponential and Trigonometric Fourier Series Coefficients Solved Problems Homework Problems Fourier Transform Mathematical Definition The Commands f ourier and if ourier Fourier Transform Pairs Properties of Fourier Transform Convolution in Time and Frequency 311
6 6.6 Symmetry of the Real and Imaginary Parts of Fourier Transform Parseval's Theorem Autocorrelation and Cross-Correlation Solved Problems Homework Problems Fourier Analysis of Discrete-Time Signals Discrete-Time Fourier Transform Properties of Discrete-Time Fourier Transform Parseval's Theorem for Discrete-Time Fourier Transform Discrete Fourier Transform Properties of Discrete Fourier Transform Inverse Discrete Fourier Transform Circular Shift of a Sequence Discrete Fourier Transform of a Circularly Shifted Sequence Circular Convolution Discrete Fourier Transform of Circular Convolution Relationship between Linear and Circular Convolution Fast Fourier Transform Relationship between DFT and DTFT Relationship between Fourier Transform and Discrete Fourier Transform Linear Convolution Computation via Fast Fourier Transform Solved Problems Homework Problems Frequency Response Continuous-Time Frequency Response The Command freqs The Command invf reqs The Command lsim System Response to Sinusoidal Input Ideal Filters Frequency Response of Discrete-Time Systems The Command freqz The Command invf reqz System Response to Discrete-Time Sinusoidal Input Moving Average Filter Solved Problems Homework Problems Laplace Transform Mathematical Definition Commands laplace and ilaplace Region of Convergence Laplace Transform Pairs Laplace Transform Properties and Theorems Partial Fraction Expansion of a Rational Function The Command residue 429
7 x Contents 9.7 Convolution in Time and in Complex Frequency Convolution in the Time Domain Convolution in the Complex Frequency Domain Using the Laplace Transform to Solve Differential Equations Solved Problems Homework Problems z-transform Mathematical Definition Commands ztrans and iztrans Region of Convergence z-transform Pairs Properties of z-transform Partial Fraction Expansion of a Rational Function Commands residue and residuez Using the z-transform to Solve Difference Equations Solved Problems Homework Problems Transfer Function Continuous-Time Systems The tf Command Stability of Continuous-Time Systems Transfer Function in Zero/Pole/Gain Form Interconnections of Systems Continuous-Time System Response Discrete-Time Systems The Command tf for Discrete-Time Systems Stability of Discrete-Time Systems Discrete-Time System Response Step Response Impulse Response The Command dlsim Conversion between Continuous-Time and Discrete-Time Systems Transfer Function and Frequency Response Bode Plot State-Space Representation Construction of a State-Space Model Discrete-Time State-Space Models Solved Problems Homework Problems Suggested Laboratory Exercises Laboratory 1: Introduction to MATLAB Laboratory 2: Signals Laboratory 3: Systems Laboratory 4: Time Domain System Analysis Laboratory 5: Fourier Series Laboratory 6: Fourier Transform 527
8 Contents xi 12.7 Laboratory 7: Fourier Analysis of Discrete-Time Systems Laboratory 8: Frequency Response Laboratory 9: Laplace Transform Laboratory 10: z-transform Laboratory 11: Transfer Function 531 Appendix A: Signal Crossword 533 Appendix B: Notation 535 Bibliography 537 Index 539
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