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Signals and Systems | |
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Continuous-Time and Discrete-Time Signals | |
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Transformations of the Independent Variable | |
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Exponential and Sinusoidal Signals | |
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The Unit Impulse and Unit Step Functions | |
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Continuous-Time and Discrete-Time Systems | |
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Basic System Properties | |
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Linear Time-Invariant Systems | |
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Discrete-Time LTI Systems: The Convolution Sum | |
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Continuous-Time LTI Systems: The Convolution Integral | |
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Properties of Linear Time-Invariant Systems | |
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Causal LTI Systems Described by Differential and Difference Equations | |
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Singularity Functions | |
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Fourier Series Representation of Periodic Signals | |
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A Historical Perspective | |
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The Response of LTI Systems to Complex Exponentials | |
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Fourier Series Representation of Continuous-Time Periodic Signals | |
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Convergence of the Fourier Series | |
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Properties of Continuous-Time Fourier Series | |
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Fourier Series Representation of Discrete-Time Periodic Signals | |
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Properties of Discrete-Time Fourier Series | |
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Fourier Series and LTI Systems | |
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Filtering | |
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Examples of Continuous-Time Filters Described by Differential Equations | |
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Examples of Discrete-Time Filters Described by Difference Equations | |
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The Continuous-Time Fourier Transform | |
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Representation of Aperiodic Signals: The Continuous-Time Fourier Transform | |
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The Fourier Transform for Periodic Signals | |
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Properties of the Continuous-Time Fourier Transform | |
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The Convolution Property | |
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The Multiplication Property | |
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Tables of Fourier Properties and Basic Fourier Transform Pairs | |
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Systems Characterized by Linear Constant-Coefficient Differential Equations | |
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The Discrete-Time Fourier Transform | |
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Representation of Aperiodic Signals: The Discrete-Time Fourier Transform | |
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The Fourier Transform for Periodic Signals | |
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Properties of the Discrete-Time Fourier Transform | |
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The Convolution Property | |
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The Multiplication Property | |
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Tables of Fourier Transform Properties and Basic Fourier Transform Pairs | |
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Duality | |
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Systems Characterized by Linear Constant-Coefficient Difference Equations | |
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Time- and Frequency Characterization of Signals and Systems | |
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The Magnitude-Phase Representation of the Fourier Transform | |
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The Magnitude-Phase Representation of the Frequency Response of LTI Systems | |
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Time-Domain Properties of Ideal Frequency-Selective Filters | |
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Time- Domain and Frequency-Domain Aspects of Nonideal Filters | |
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First-Order and Second-Order Continuous-Time Systems | |
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First-Order and Second-Order Discrete-Time Systems | |
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Examples of Time- and Frequency-Domain Analysis of Systems | |
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Sampling | |
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Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem | |
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Reconstruction of a Signal from Its Samples Using Interpolation | |
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The Effect of Undersampling: Aliasing | |
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Discrete-Time Processing of Continuous-Time Signals | |
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Sampling of Discrete-Time Signals | |
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Communication Systems | |
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Complex Exponential and Sinusoidal Amplitude Modulation | |
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Demodulation for Sinusoidal AM. Frequency-Division Multiplexing | |
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Single-Sideband Sinusoidal Amplitude Modulation | |
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Amplitude Modulation with a Pulse-Train Carrier | |
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Pulse-Amplitude Modulation | |
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Sinusoidal Frequency Modulation | |
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Discrete-Time Modulation | |
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The Laplace Transform | |
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The Laplace Transform | |
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The Region of Convergence for Laplace Transforms | |
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The Inverse Laplace Transform | |
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Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot | |
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Properties of the Laplace Transform | |
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Some Laplace Transform Pairs | |
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Analysis and Characterization of LTI System | |