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elali t discrete systems dsp matlab 2003

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Textbook in PDF format Books on linear systems typically cover both discrete and continuous systems together in one book. However, with coverage of this magnitude, not enough information is presented on either of the two subjects. Discrete linear systems warrant a book of their own, and Discrete Systems and Digital Signal Processing with MATLAB provides just that. It offers comprehensive coverage of both discrete linear systems and signal processing in one volume. This detailed book is firmly rooted in basic mathematical principles, and it includes many problems solved first by using analytical tools, then by using MATLAB. Examples that illustrate the theoretical concepts are provided at the end of each chapter. Preface Acknowledgments Author Signal Representation Introduction Why Do We Discretize Continuous Systems? Periodic and Nonperiodic Discrete Signals Unit Step Discrete Signal Impulse Discrete Signal Ramp Discrete Signal Real Exponential Discrete Signal Sinusoidal Discrete Signal Exponentially Modulated Sinusoidal Signal Complex Periodic Discrete Signal Shifting Operation Representing a Discrete Signal Using Impulses Reflection Operation Time Scaling Amplitude Scaling Even and Odd Discrete Signal Does a Discrete Signal Have a Time Constant? Basic Operations on Discrete Signals Modulation Addition and Subtraction Scalar Multiplication Combined Operations Energy and Power Discrete Signals Bounded and Unbounded Discrete Signals Some Insights: Signals in the Real World Step Signal Impulse Signal Sinusoidal Signal Ramp Signal Other Signals End of Chapter Examples End of Chapter Problems Discrete System Definition of a System Input and Output Linear Discrete Systems Time Invariance and Discrete Signals Systems with Memory Causal Systems Inverse of a System Stable System Convolution Difference Equations of Physical Systems Homogeneous Difference Equation and Its Solution Case When Roots Are All Distinct Case When Two Roots Are Real and Equal Case When Two Roots Are Complex Nonhomogeneous Difference Equations and Their Solutions How Do We Find the Particular Solution? Stability of Linear Discrete Systems: The Characteristic Equation Stability Depending on the Values of the Poles Stability from the Jury Test Block Diagram Representation of Linear Discrete Systems Delay Element Summing/Subtracting Junction Multiplier From the Block Diagram to the Difference Equation From the Difference Equation to the Block Diagram: A Formal Procedure Impulse Response Correlation Cross-Correlation Auto-Correlation Some Insights How Can We Find These Eigenvalues? Stability and Eigenvalues End of Chapter Examples End of Chapter Problems Fourier Series and the Fourier Transform of Discrete Signals Introduction Review of Complex Numbers Definition Addition Subtraction Multiplication Division From Rectangular to Polar From Polar to Rectangular Fourier Series of Discrete Periodic Signals Discrete System with Periodic Inputs: The Steady-State Response General Form for Yss(n) Frequency Response of Discrete Systems Properties of the Frequency Response Periodicity Property Symmetry Property Fourier Transform of Discrete Signals Convergence Conditions Properties of the Fourier Transform of Discrete Signals Periodicity Property Linearity Property Discrete-Time Shifting Property Frequency Shifting Property Reflection Property Convolution Property Parseval’s Relation and Energy Calculations Numerical Evaluation of the Fourier Transform of Discrete Signals Some Insights: Why Is This Fourier Transform? Ease in Analysis and Design Sinusoidal Analysis End of Chapter Examples End of Chapter Problems z-Transform and Discrete Systems Introduction Bilateral z-Transform Unilateral z-Transform Convergence Considerations Inverse z-Transform Partial Fraction Expansion Long Division Properties of the z-Transform Linearity Property Shifting Property Multiplication by e−an Convolution Representation of Transfer Functions as Block Diagrams x(n), h(n), y(n), and the z-Transform Solving Difference Equation Using the z-Transform Convergence Revisited Final-Value Theorem Initial-Value Theorem Some Insights: Poles and Zeroes Poles of the System Zeros of the System Stability of the System End of Chapter Exercises End of Chapter Problems State-Space and Discrete Systems Introduction Review on Matrix Algebra Definition, General Terms, and Notations Identity Matrix Adding Two Matrices Subtracting Two Matrices Multiplying a Matrix by a Constant Determinant of a Two-by-Two Matrix Transpose of a Matrix Inverse of a Matrix Matrix Multiplication Eigenvalues of a Matrix Diagonal Form of a Matrix Eigenvectors of a Matrix General Representation of Systems in State Space Recursive Systems Nonrecursive Systems From the Block Diagram to State Space From the Transfer Function H(z) to State Space Solution of the State-Space Equations in the z-Domain General Solution of the State Equation in Real Time Properties of An and Its Evaluation Transformations for State-Space Representations Some Insights: Poles and Stability End of Chapter Examples End of Chapter Problems Block Diagrams and Review of Discrete System Representations Introduction Basic Block Diagram Components Ideal Delay Adder Subtractor Multiplier Block Diagrams as Interconnected Subsystems General Transfer Function Representation Parallel Representation Series Representation Basic Feedback Representation Controllable Canonical Form Block Diagrams with Basic Blocks Observable Canonical Form Block Diagrams with Basic Blocks Diagonal Form Block Diagrams with Basic Blocks Distinct Roots Case Repeated Roots Case Parallel Block Diagrams with Subsystems Distinct Roots Case Repeated Roots Case Series Block Diagrams with Subsystems Distinct Real Roots Case Mixed Complex and Real Roots Case Block Diagram Reduction Rules Using the Reduction Rules Using Mason’s Rule End of Chapter Examples End of Chapter Problems Discrete Fourier Transform and Discrete Systems Introduction Discrete Fourier Transform and the Finite-Duration Discrete Signals Properties of the DFT How Does the Defining Equation Work? DFT Symmetry DFT Linearity Magnitude of the DFT What Does k in X(k), the DFT, Mean? Relation the DFT Has with the Fourier Transform of Discrete Signals, the z-Transform, and the Continuous Fourier Transform DFT and the Fourier Transform of x(n) DFT and the z-Transform of x(n) DFT and the Continuous Fourier Transform of x(t) Numerical Computation of the DFT Fast Fourier Transform: A Faster Way of Computing the DFT Applications of the DFT Circular Convolution Linear Convolution Approximation to the Continuous Fourier Transform Approximation to the Coefficients of the Fourier Series and the Average Power of the Periodic Signal x(t) Total Energy in the Signal x(n) and x(t) Block Filtering Correlation Some Insights DFT Is the Same as the fft DFT Points Are the Samples of the Fourier Transform of x(n) How Can We Be Certain That Most of the Frequency Contents of x(t) Are in the DFT? Is the Circular Convolution the Same as the Linear Convolution? Is |X(w)| ≅ |X(k)|? Frequency Leakage and the DFT End of Chapter Exercises End of Chapter Problems Sampling and Transformations Need for Converting a Continuous Signal to a Discrete Signal From the Continuous Signal to Its Binary Code Representation From the Binary Code to the Continuous Signal Sampling Operation Ambiguity in Real-Time Domain Ambiguity in the Frequency Domain Sampling Theorem Filtering before Sampling Sampling and Recovery of the Continuous Signal How Do We Discretize the Derivative Operation? Discretization of the State-Space Representation Bilinear Transformation and the Relationship between the Laplace-Domain and the z-Domain Representations Other Transformation Methods Impulse Invariance Method Step Invariance Method Forward Difference Method Backward Difference Method Bilinear Transformation Some Insights Choice of the Sampling Interval Ts Effect of Choosing Ts on the Dynamics of the System Does Sampling Introduce Additional Zeros to the Transfer Function H(z)? End of Chapter Examples End of Chapter Problems Infinite Impulse Response Filter Design Introduction Design Process Design Based on the Impulse Invariance Method Design Based on the Bilinear Transform Method IIR Filter Design Using MATLAB From the Analogue Prototype to the IIR Digital Filter Direct Design Some Insights Difficulty in Designing IIR Digital Filters in the z-Domain Using the Impulse Invariance Method Choice of the Sampling Interval Ts End of Chapter Examples End of Chapter Problems Finite Impulse Response Digital Filters Introduction What Is an FIR Digital Filter? Motivating Example FIR Filter Design Stability of FIR Filters Linear Phase of FIR Filters Design Based on the Fourier Series: The Windowing Method Ideal Lowpass FIR Filter Design Other Ideal Digital FIR Filters Windows Used in the Design of the Digital FIR Filter Which Window Does Give the Optimal h(n)? Design of a Digital FIR Differentiator Design of Comb FIR Filters Design of a Digital Shifter: The Hilbert Transform Filter From IIR to FIR Digital Filters: An Approximation Frequency Sampling and FIR Filter Design FIR Digital Design Using MATLAB Design Using Windows Design Using Least-Squared Error Design Using the Equiripple Linear Phase How to Obtain the Frequency Response Some Insights Comparison with IIR Filters Different Methods Used in the FIR Filter Design End of the Chapter Examples End of Chapter Problems Bibliography

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elali t discrete systems dsp matlab 2003

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