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| Introduction | |
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| Mathematical Representation of Signals | |
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| Mathematical Representation of Systems | |
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| Thinking about Systems | |
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| Sinusoids | |
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| Tuning Fork Experiment | |
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| Review of Sine and Cosine Functions | |
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| Sinusoidal Signals | |
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| Sampling and Plotting Sinusoids | |
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| Complex Exponentials and Phasors | |
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| Phasor Addition | |
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| Physics of the Tuning Fork | |
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| Time Signals: More Than Formulas | |
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| Spectrum Representation | |
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| The Spectrum of a Sum of Sinusoids | |
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| Beat Notes | |
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| Periodic Waveforms | |
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| More Periodic Signals | |
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| Fourier Series Analysis and Synthesis | |
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| Time-Frequency Spectrum | |
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| Frequency Modulation: Chirp Signals | |
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| Sampling and Aliasing | |
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| Sampling | |
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| Spectrum View of Sampling and Reconstruction | |
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| Strobe Demonstration | |
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| Discrete-to-Continuous Conversion | |
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| The Sampling Theorem | |
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| FIR Filters | |
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| Discrete-Time Systems | |
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| The Running Average Filter | |
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| The General FIR Filter | |
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| Implementation of FIR Filters | |
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| Linear Time-Invariant (LTI) Systems | |
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| Convolution and LTI Systems | |
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| Cascaded LTI Systems | |
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| Example of FIR Filtering | |
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| Frequency Response of FIR Filters | |
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| Sinusoidal Response of FIR Systems | |
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| Superposition and the Frequency Response | |
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| Steady State and Transient Response | |
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| Properties of the Frequency Response | |
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| Graphical Representation of the Frequency Response | |
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| Cascaded LTI Systems | |
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| Running-Average Filtering | |
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| Filtering Sampled Continuous-Time Signals | |
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| z-Transforms | |
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| Definition of the z-Transform | |
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| The z-Transform and Linear Systems | |
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| Properties of the z-Transform | |
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| The z-Transform as an Operator | |
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| Convolution and the z-Transform | |
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| Relationship between the z -Domain and the <F128>w-Domain | |
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| Useful Filters | |
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| Practical Bandpass Filter Design | |
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| Properties of Linear Phase Filters | |
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| IIR Filters | |
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| The General IIR Difference Equation | |
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| Time-Domain Response | |
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| System Function of an IIR Filter | |
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| Poles and Zeros | |
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| Frequency Response of an IIR Filter | |
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| Three Domains | |
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| The Inverse z-Transform and Some Applications | |
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| Steady-State Response and Stability | |
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| Second-Order Filters | |
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| Frequency Response of Second-Order IIR Filter | |
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| Example of an IIR Lowpass Filter | |
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| Continuous-Time Signals and LTI Systems | |
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| Continuous-Time Signals | |
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| The Unit Impulse | |
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| Continuous-Time Systems | |
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| Linear Time-Invariant Systems | |
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| Impulse Responses of Basic LTI Systems | |
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| Convolution of Impulses | |
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| Evaluating Convolution Integrals | |
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| Properties of LTI Systems | |
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| Using Convolution to Remove Multipath Distortion | |
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| The Frequency Response | |
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| The Frequency Response Function for LTI Systems | |
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| Response to Real Sinusoidal Signals | |
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| Ideal Filters | |
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| Application of Ideal Filters | |
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| Time-Domain or Frequency-Domain? | |
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| Continuous-Time Fourier Transform | |
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| Definition of the Fourier Transform | |
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| The Fourier Transform and the Spectrum | |
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| Existence and Convergence of the Fourier Transform | |
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| Examples of Fourier Transform Pairs | |
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| Properties of Fourier Transform Pairs | |
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| The Convolution Property | |
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| Basic LTI Systems | |
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| The Multiplication Property | |
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| Table of Fourier Transform Properties and Pairs | |
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| Using the Fourier Transform for Multipath Analysis | |
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| Filtering, Modulation, and Sampling | |
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| Linear Time-Invariant Systems | |
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| Sinewave Amplitude Modulation | |
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| Sampling and Reconstruction | |
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| Computing the Spectrum | |
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| Finite Fourier Sum | |
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| Too Many Fourier Transforms? Time-windowing | |
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| Analysis of a Sum of | |