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Preface | |

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Each chapter ends with a Summary and References. | |

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Each Matlab section ends with Problems. | |

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Background | |

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Complex Numbers | |

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Sinusoids | |

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Sketching Signals | |

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Cramer's Rule | |

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Partial Fraction Expansion | |

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Vectors and Matrices | |

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Miscellaneous | |

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Elementary Operations | |

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Matlab Overview | |

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Calculator Operations | |

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Vector Operations | |

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Simple Plotting | |

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Element-by-Element Operations | |

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Matrix Operations | |

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Partial Fraction Expansions | |

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Signals and Systems | |

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Size of a Signal | |

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Some Useful Signal Operations | |

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Classification of Signals | |

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Some Useful Signal Models | |

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Even and Odd Functions | |

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Systems | |

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Classification of Systems | |

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System Model: Input-Output Description | |

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Internal and External Descriptions of a System | |

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Internal Description: The State-Space Description | |

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Working with Functions | |

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Inline Functions | |

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Relational Operators and the Unit Step Function | |

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Visualizing Operations on the Independent Variable | |

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Numerical Integration and Estimating Signal Energy | |

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Time-Domain Analysis of Continuous-Time Systems | |

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Introduction | |

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System Response to Internal Conditions: The Zero-Input Response | |

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The Unit Impulse Response h(t) | |

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System Response to External Input: Zero-State Response | |

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Classical Solution of Differential Equations | |

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System Stability | |

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Intuitive Insights into System Behavior | |

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Appendix 2.1: Determining the Impulse Response | |

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M-Files | |

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Script M-Files | |

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Function M-Files | |

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For Loops | |

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Graphical Understanding of Convolution | |

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Time-Domain Analysis of Discrete-Time Systems | |

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Introduction | |

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Useful Signal Operations | |

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Some Useful Discrete-Time Signal Models | |

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Examples of Discrete-Time Systems | |

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Discrete-Time System Equations | |

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System Response to Internal Conditions: The Zero-Input Response | |

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The Unit Impulse Response h[n] | |

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System Response to External Input: The Zero-State Response | |

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Classical Solution of Linear Difference Equations | |

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System Stability: The External (BIBO) Stability Criterion | |

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Intuitive Insights into System Behavior | |

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Appendix 3.1: Impulse Response for a Special Case When aN = 0 | |

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Discrete-Time Signals and Systems | |

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Discrete-Time Functions and Stem Plots | |

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System Responses Through Filtering | |

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A Custom Filter Function | |

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Discrete-Time Convolution | |

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Continuous-Time System Analysis Using the Laplace Transform | |

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The Laplace Transform | |

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Some Properties of the Laplace Transform | |

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Solution of Differential and Integro-Differential Equations | |

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Analysis of Electrical Networks: The Transformed Network | |

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Block Diagrams | |

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System Realization | |

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Application to Feedback and Controls | |

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Frequency-Response of an LTIC System | |

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Bode Plots | |

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Filter Design by Placement of Poles and Zeros of H(s) | |

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The Bilateral Laplace Transform | |

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Continuous-Time Filters | |

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Frequency Response and Polynomial Evaluation | |

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Design and Evaluation of a Simple RC Filter | |

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A Cascaded RC Filter and Polynomial Expansion | |

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Butterworth Filters and the FIND Command | |

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Butterworth Filter Realization Using Cascaded Second.Order Sections | |

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Chebyshev Filters | |

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Discrete-Time System Analysis Using the z-Transform | |

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The z-Transform | |

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Some Properties of the z-Transform | |

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z-Transform Solution of Linear Difference equations | |

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System Realization | |

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Frequency Response of Discrete-Time Systems | |

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Frequency Response from Pole-Zero Location | |

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Digital Processing of Analog Signals | |

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Connection Between the Laplace and the z-Transform | |

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The Bilateral z-Transform | |

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Discrete-Time IIR Filters | |

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Frequency Response and Pole-Zero Plots | |

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Transformation Basics | |

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Transformation by First-Order Backward Difference | |

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Bilinear Transformation | |

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Bilinear Transformation with Prewarping | |

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Example: Butterworth Filter Transformation | |

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Problems Finding Polynomial Roots | |

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Improved Design Using Cascaded Second-Order Sections | |

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Continuous-Time Signal Analysis: The Fourier Series | |

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Periodic Signal Representation by Trigonometric Fourier Series | |

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Existence and Convergence of the Fourier Series | |

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Exponential Fourier Series | |

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LTIC System Response to Periodic Inputs | |

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Generalized Fourier Series: Signals as Vectors | |

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Numerical Computation of Dn | |

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Fourier Series Applications | |

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Periodic Functions and the Gibbs Phenomenon | |

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Optimization and Phase Spectra | |

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Continuous-Time Signal Analysis: The Fourier Transform | |

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Aperiodic Signal Representation by Fourier Integral | |

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Transforms of Some Useful Functions | |

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Some Properties of the Fourier Transform | |

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Signal Transmission Through LTIC Systems | |

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Ideal and Practical Filters | |

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Signal Energy | |

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Application to Communications: Amplitude Modulation | |

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Data Truncation: Window Functions | |

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Fourier Transform Topics | |

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The Sinc Function and the Scaling Property | |

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Parseval's Theorem and Essential Bandwidth | |

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Spectral Sampling | |

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Kaiser Window Functions | |

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Sampling: The Bridge from Continuous to Discrete | |

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The Sampling Theorem | |

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Signal Reconstruction | |

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Analog-to-Digital (A/D) Conversion | |

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Dual of Time-Sampling: The Spectral Sampling | |

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Numerical Computation of the Fourier Transform: The Discrete Fourier Transform (DFT) | |

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The Fast Fourier Transform (FFT) | |

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The Discrete Fourier Transform | |

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Computing the Discrete Fourier Transform | |

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Improving the Picture with Zero-Padding | |

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Quantization | |

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Fourier Analysis of Discrete-Time Signals | |

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Discrete-Time Fourier Series (DTFS) | |

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Aperiodic Signal Representation by Fourier Integral | |

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Properties of DTFT | |

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LTI Discrete-Time System Analysis by DTFT | |

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DTFT Connection with the CTFT | |

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Generalization of the DTFT and the z-Transform | |

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Working with the DTFS and the DTFT | |

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Computing the Discrete-Time Fourier Series | |

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Measuring Code Performance | |

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FIR Filter Design by Frequency Sampling | |

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State-Space Analysis | |

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Introduction | |

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A Systematic Procedure for Determining State Equations | |

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Solution of State Equations | |

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Linear Transformation of State Vectors | |

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Controllability and Observability | |

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State-Space Analysis of Discrete-Time Systems | |

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Toolboxes and State-Space Analysis | |

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z-Transform Solutions to Discrete-Time State-Space Systems | |

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Transfer Functions from State-Space Representations | |

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Controllability and Observability of Discrete-Time Systems | |

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Matrix Exponentiation and the Matrix Exponential | |

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Index | |