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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 | |