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Preface | |

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Overview | |

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Introduction | |

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Signals | |

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Digital Filters | |

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The Z-transform | |

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The Frequency Domain | |

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Filter Concepts | |

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Signal Processing | |

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Digital Processing of Analog Signals | |

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Filter Design | |

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The Design of IIR Filters | |

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The Design of FIR Filters | |

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The DFT and FFT | |

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Advantages of DSP | |

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Applications of DSP | |

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Discrete Signals | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Discrete Signals | |

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Signal Measures | |

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Operations on Discrete Signals | |

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Symmetry | |

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Even and Odd Parts of Signals | |

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Decimation and Interpolation | |

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Fractional Delays | |

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Some Standard Discrete Signals | |

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Properties of the Discrete Impulse | |

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Signal Representation by Impulses | |

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Discrete Pulse Signals | |

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The Discrete Sinc Function | |

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Discrete Exponentials | |

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Discrete-Time Harmonics and Sinusoids | |

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Discrete-Time Harmonics are not Always Periodic in Time | |

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Discrete-Time Harmonics are Always Periodic in Frequency | |

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The Sampling Theorem | |

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Signal Reconstruction and Aliasing | |

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Reconstruction at Different Sampling Rates | |

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An Introduction to Random Signals | |

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Probability | |

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Measures for Random Variables | |

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The Chebyshev Inequality | |

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Probability Distributions | |

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The Uniform Distribution | |

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The Gaussian or Normal Distribution | |

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Discrete Probability Distributions | |

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Distributions for Deterministic Signals | |

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Stationary, Ergodic, and Pseudorandom Signals | |

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Statistical Estimates | |

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Random Signal Analysis | |

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Problems | |

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Time-Domain Analysis | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Discrete-Time Systems | |

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Linearity and Superposition | |

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Time Invariance | |

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LTI Systems | |

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Causality and Memory | |

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Digital Filters | |

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Digital Filter Terminology | |

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Digital Filter Realization | |

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Response of Digital Filters | |

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Response of Nonrecursive Filters | |

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Response of Recursive Filters | |

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Solving Difference Equations | |

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Zero-Input Response and Zero-State Response | |

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The Impulse Response | |

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Impulse Response of Nonrecursive Filters | |

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Impulse Response of Recursive Filters | |

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General Method for Finding the Impulse Response | |

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Impulse Response of Anti-Causal Systems | |

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System Representation in Various Forms | |

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Recursive Forms for Nonrecursive Digital Filters | |

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Difference Equations from the Impulse Response | |

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Difference Equations from Input-Output Data | |

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Application-Oriented Examples | |

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Moving Average Filters | |

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Inverse Systems | |

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Echo and Reverb | |

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Periodic Sequences and Wave-Table Synthesis | |

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How Difference Equations Arise | |

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Discrete Convolution | |

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Analytical Evaluation of Discrete Convolution | |

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Convolution Properties | |

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Convolution of Finite Sequences | |

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The Sum-by-Column Method | |

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The Flip, Shift, Multiply, and Sum Concept | |

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Discrete Convolution, Multiplication, and Zero Insertion | |

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Impulse Response of LTI Systems in Cascade and Parallel | |

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Stability and Causality of LTI Systems | |

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Stability of FIR Filters | |

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Stability of LTI Systems Described by Difference Equations | |

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Stability of LTI Systems Described by the Impulse Response | |

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Causality | |

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System Response to Periodic Inputs | |

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Periodic or Circular Convolution | |

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Periodic Convolution by the Cyclic Method | |

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Periodic Convolution by the Circulant Matrix | |

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Regular Convolution from Periodic Convolution | |

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Deconvolution | |

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Deconvolution by Recursion | |

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Discrete Correlation | |

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Autocorrelation | |

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Periodic Discrete Correlation | |

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Matched Filtering and Target Ranging | |

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Discrete Convolution and Transform Methods | |

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The z-Transform | |

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The Discrete-Time Fourier Transform | |

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Problems | |

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z-Transform Analysis | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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The Two-Sided z-Transform | |

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What the z-Transform Reveals | |

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Some z-Transform Pairs using the Defining Relation | |

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More on the ROC | |

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Properties of the Two-Sided z-Transform | |

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Poles, Zeros, and the z-Plane | |

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The Transfer Function | |

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Interconnected Systems | |

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Transfer Function Realization | |

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Transposed Realization | |

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Cascaded and Parallel Realization | |

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Causality and Stability of LTI Systems | |

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Stability and the ROC | |

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Inverse Systems | |

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The Inverse z-Transform | |

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Inverse z-Transform of Finite Sequences | |

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Inverse z-Transform by Long Division | |

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Inverse z-Transform from Partial Fractions | |

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The ROC and Inversion | |

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The One-Sided z-Transform | |

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The Right-Shift Property of the One-Sided z-Transform | |

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The Left-Shift Property of the One-Sided z-Transform | |

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The Initial Value Theorem and Final Value Theorem | |

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The z-Transform of Switched Periodic Signals | |

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The z-Transform and System Analysis | |

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Systems Described by Difference Equations | |

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Systems Described by the Transfer Function | |

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Forced and Steady-State Response from the Transfer Function | |

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Problems | |

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Frequency Domain Analysis | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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The DTFT from the z-Transform | |

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Symmetry of the Spectrum for a Real Signal | |

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Some DTFT Pairs | |

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Relating the z-Transform and DTFT | |

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Properties of the DTFT | |

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Time Reversal | |

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Time Shift of x[n] | |

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Frequency Shift of X(F) | |

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Modulation | |

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Convolution | |

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The Times-n Property | |

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Parseval's Relation | |

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Central Ordinate Theorems | |

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The DTFT of Discrete-Time Periodic Signals | |

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The DFS and DFT | |

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The Inverse DTFT | |

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The Frequency Response | |

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System Analysis using the DTFT | |

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The Steady-State Response to Discrete-Time Harmonics | |

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Connections | |

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Problems | |

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Filter Concepts | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Frequency Response and Filter Characteristics | |

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Gain | |

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Phase Delay and Group Delay | |

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Minimum-Phase | |

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Minimum-Phase Filters from the Magnitude Spectrum | |

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The Frequency Response: A Graphical View | |

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The Rubber Sheet Analogy | |

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FIR Filters and Linear Phase | |

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Pole-Zero Patterns of Linear-Phase Filters | |

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Types of Linear-Phase Sequences | |

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Averaging Filters | |

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Zeros of Averaging Filters | |

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FIR Comb Filters | |

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IIR Filters | |

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First-Order Highpass Filters | |

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Pole-Zero Placement and Filter Design | |

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Second-Order IIR Filters | |

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Digital Resonators | |

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Periodic Notch Filters | |

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Allpass Filters | |

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Transfer Function of Allpass Filters | |

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Minimum-Phase Filters using Allpass Filters | |

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Concluding Remarks | |

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Problems | |

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Digital Processing of Analog Signals | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Ideal Sampling | |

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Sampling of Sinusoids and Periodic Signals | |

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Application Example: The Sampling Oscilloscope | |

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Sampling of Bandpass Signals | |

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Natural Sampling or Pulse-Amplitude Modulation | |

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Zero-Order-Hold Sampling | |

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Sampling, Interpolation, and Signal Recovery | |

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Ideal Recovery and the Sinc Interpolating Function | |

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Interpolating Functions | |

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Interpolation in Practice | |

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Sampling Rate Conversion | |

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Zero Interpolation and Spectrum Compression | |

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Sampling Rate Increase | |

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Sampling Rate Reduction | |

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Quantization | |

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Uniform Quantizers | |

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Quantization Error and Quantization Noise | |

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Digital Processing of Analog Signals | |

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Practical ADC Considerations | |

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Anti-Aliasing Filter Considerations | |

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Anti-Imaging Filter Considerations | |

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Compact Disc Digital Audio | |

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Recording | |

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Playback | |

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Dynamic-Range Processors | |

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Companders | |

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Audio Equalizers | |

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Shelving Filters | |

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Graphic Equalizers | |

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Parametric Equalizers | |

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Digital Audio Effects | |

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Gated Reverb and Reverse Reverb | |

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Chorusing, Flanging, and Phasing | |

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Plucked-String Filters | |

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Digital Oscillators and DTMF Receivers | |

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DTMF Receivers | |

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Multirate Signal Processing | |

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Quantization and Oversampling | |

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Single-Bit Oversampling Sigma-Delta ADC | |

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Problems | |

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The Discrete Fourier Transform and Its Applications | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Introduction | |

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Connections between Frequency-Domain Transforms | |

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The DFT | |

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Properties of the DFT | |

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Symmetry | |

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Central Ordinates and Parseval's Theorem | |

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Circular Shift and Circular Symmetry | |

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Shifting, Reversal, and Modulation Properties of the DFT | |

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Product and Convolution Properties of the DFT | |

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The FFT | |

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Signal Replication and Spectrum Zero Interpolation | |

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Some Useful DFT Pairs | |

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The Inverse DFT | |

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Some Practical Guidelines | |

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The DTFT and the DFT | |

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Approximating the DTFT by the DFT | |

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The DFT of Periodic Signals and the DFS | |

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Understanding the DFS Results | |

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The DFT and DFS of Sinusoids | |

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The DFT and DFS of Sampled Periodic Signals | |

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The Effects of Leakage | |

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The DFT of Nonperiodic Signals | |

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Spectral Spacing and Zero Padding | |

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Spectral Smoothing by Time Windows | |

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Performance Characteristics of Windows | |

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The Spectrum of Windowed Sinusoids | |

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Resolution | |

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Detecting Hidden Periodicity using the DFT | |

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Applications in Signal Processing | |

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Convolution of Long Sequences | |

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Deconvolution | |

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Band-Limited Signal Interpolation | |

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The Discrete Hilbert Transform | |

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Spectrum Estimation | |

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The Periodogram Estimate | |

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PSD Estimation by the Welch Method | |

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PSD Estimation by the Blackman-Tukey Method | |

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Non-Parametric System Identification | |

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Time-Frequency Plots | |

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The Cepstrum and Homomorphic Filtering | |

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Homomorphic Filters and Deconvolution | |

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Echo Detection and Cancellation | |

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Optimal Filtering | |

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Matrix Formulation of the DFT and IDFT | |

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The IDFT from the Matrix Form | |

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Using the DFT to Find the IDFT | |

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The FFT | |

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Some Fundamental Results | |

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The Decimation-in-Frequency FFT Algorithm | |

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The Decimation-in-Time FFT Algorithm | |

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Computational Cost | |

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Why Equal Lengths for the DFT and IDFT? | |

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The Inverse DFT | |

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How Unequal Lengths Affect the DFT Results | |

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Problems | |

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Design of IIR Filters | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Introduction | |

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Filter Specifications | |

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Techniques of Digital Filter Design | |

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IIR Filter Design | |

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Equivalence of Analog and Digital Systems | |

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The Effects of Aliasing | |

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Practical Mappings | |

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Response Matching | |

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The Impulse-Invariant Transformation | |

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Modifications to Impulse-Invariant Design | |

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The Matched z-Transform for Factored Forms | |

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Modifications to Matched z-Transform Design | |

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Mappings from Discrete Algorithms | |

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Mappings from Difference Algorithms | |

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Stability Properties of the Backward-Difference Algorithm | |

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The Forward-Difference Algorithm | |

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Mappings from Integration Algorithms | |

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Stability Properties of Integration-Algorithm Mappings | |

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Frequency Response of Discrete Algorithms | |

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Mappings from Rational Approximations | |

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The Bilinear Transformation | |

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Using the Bilinear Transformation | |

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Spectral Transformations for IIR Filters | |

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Digital-to-Digital Transformations | |

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Direct (A2D) Transformations for Bilinear Design | |

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Bilinear Transformation for Peaking and Notch Filters | |

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Design Recipe for IIR Filters | |

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Finite-Word-Length Effects | |

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Effects of Coefficient Quantization | |

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Concluding Remarks | |

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Problems | |

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Design of FIR Filters | |

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Scope and Overview | |

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Goals and Learning Objectives | |

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Ideal Filters | |

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Frequency Transformations | |

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Truncation and Windowing | |

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The Rectangular Window and its Spectrum | |

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The Triangular Window and its Spectrum | |

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The Consequences of Windowing | |

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Design Specifications for FIR Filters | |

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FIR Filters and Linear Phase | |

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Symmetric Sequences and Linear Phase | |

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Types of Linear-Phase Sequences for FIR Filter Design | |

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Applications of Linear-Phase Sequences | |

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FIR Filter Design | |

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Window-Based Design | |

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Characteristics of Window Functions | |

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Some Other Windows | |

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What Windowing Means | |

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Some Design Issues | |

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Characteristics of the Windowed Spectrum | |

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Selection of Window and Design Parameters | |

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Spectral Transformations | |

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Half-Band FIR Filters | |

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FIR Filter Design by Frequency Sampling | |

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Frequency Sampling and Windowing | |

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Implementing Frequency-Sampling FIR Filters | |

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Design of Optimal Linear-Phase FIR Filters | |

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The Alternation Theorem | |

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Optimal Half-Band Filters | |

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Application: Multistage Interpolation and Decimation | |

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Multistage Decimation | |

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Maximally Flat FIR Filters | |

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FIR Differentiators and Hilbert Transformers | |

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Hilbert Transformers | |

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Design of FIR Differentiators and Hilbert Transformers | |

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Least Squares and Adaptive Signal Processing | |

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Adaptive Filtering | |

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Applications of Adaptive Filtering | |

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Problems | |

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MATLAB Examples | |

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Introduction | |

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MATLAB Tips and Pointers | |

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Array Operations | |

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A List of Useful Commands | |

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Examples of MATLAB Code | |

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Useful Concepts from Analog Theory | |

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Scope and Objectives | |

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Signals | |

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System Analysis | |

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The Zero-State Response and Zero-Input Response | |

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Step Response and Impulse Response | |

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Convolution | |

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Useful Convolution Results | |

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The Laplace Transform | |

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The Inverse Laplace Transform | |

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Interconnected Systems | |

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Stability | |

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The Laplace Transform and System Analysis | |

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The Steady-State Response to Harmonic Inputs | |

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The Fourier Transform | |

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Connections between Laplace and Fourier Transforms | |

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Amplitude Modulation | |

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Fourier Series | |

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Fourier Series Coefficients from the Fourier Transform | |

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Some Useful Results | |

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Fourier Transform of Periodic Signals | |

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Spectral Density | |

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Ideal Filters | |

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Measures for Real Filters | |

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A First-Order Lowpass Filter | |

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A Second-Order Lowpass Filter | |

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Bode Plots | |

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Classical Analog Filter Design | |

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References | |

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Index | |