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Preface | |

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Introduction to Digital Signal Processing | |

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Introduction | |

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Signals | |

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Frequency-Domain Representation | |

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Notation | |

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Signal Processing | |

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Analog Filters | |

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Applications of Analog Filters | |

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Digital Filters | |

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Two DSP Applications | |

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Processing of EKG signals | |

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Processing of Stock-Exchange Data | |

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References | |

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The Fourier Series and Fourier Transform | |

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Introduction | |

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Fourier Series | |

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Definition | |

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Particular Forms | |

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Theorems and Properties | |

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Fourier Transform | |

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Derivation | |

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Particular Forms | |

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Theorems and Properties | |

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References | |

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Problems | |

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The z Transform | |

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Introduction | |

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Definition of z Transform | |

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Convergence Properties | |

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The z Transform as a Laurent Series | |

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Inverse z Transform | |

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Theorems and Properties | |

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Elementary Discrete-Time Signals | |

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z-Transform Inversion Techniques | |

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Use of Binomial Series | |

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Use of Convolution Theorem | |

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Use of Long Division | |

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Use of Initial-Value Theorem | |

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Use of Partial Fractions | |

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Spectral Representation of Discrete-Time Signals | |

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Frequency Spectrum | |

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Periodicity of Frequency Spectrum | |

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Interrelations | |

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References | |

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Problems | |

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Discrete-Time Systems | |

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Introduction | |

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Basic System Properties | |

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Linearity | |

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Time Invariance | |

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Causality | |

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Characterization of Discrete-Time Systems | |

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Nonrecursive Systems | |

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Recursive Systems | |

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Discrete-Time System Networks | |

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Network Analysis | |

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Implementation of Discrete-Time Systems | |

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Signal Flow-Graph Analysis | |

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Introduction to Time-Domain Analysis | |

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Convolution Summation | |

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Graphical Interpretation | |

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Alternative Classification | |

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Stability | |

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State-Space Representation | |

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Computability | |

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Characterization | |

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Time-Domain Analysis | |

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Applications of State-Space Method | |

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References | |

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Problems | |

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The Application of the z Transform | |

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Introduction | |

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The Discrete-Time Transfer Function | |

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Derivation of H(z) from Difference Equation | |

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Derivation of H(z) from System Network | |

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Derivation of H(z) from State-Space Characterization | |

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Stability | |

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Constraint on Poles | |

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Constraint on Eigenvalues | |

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Stability Criteria | |

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Test for Common Factors | |

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Schur-Cohn Stability Criterion | |

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Schur-Cohn-Fujiwara Stability Criterion | |

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Jury-Marden Stability Criterion | |

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Lyapunov Stability Criterion | |

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Time-Domain Analysis | |

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Frequency-Domain Analysis | |

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Steady-State Sinusoidal Response | |

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Evaluation of Frequency Response | |

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Periodicity of Frequency Response | |

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Aliasing | |

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Frequency Response of Digital Filters | |

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Transfer Functions for Digital Filters | |

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First-Order Transfer Functions | |

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Second-Order Transfer Functions | |

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Higher-Order Transfer Functions | |

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Amplitude and Delay Distortion | |

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References | |

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Problems | |

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The Sampling Process | |

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Introduction | |

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Fourier Transform Revisited | |

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Impulse Functions | |

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Periodic Signals | |

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Unit-Step Function | |

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Generalized Functions | |

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Interrelation Between the Fourier Series and the Fourier Transform | |

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Poisson's Summation Formula | |

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Impulse-Modulated Signals | |

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Interrelation Between the Fourier and z Transforms | |

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Spectral Relationship Between Discrete- and Continuous-Time Signals | |

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The Sampling Theorem | |

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Aliasing | |

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Graphical Representation of Interrelations | |

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Processing of Continuous-Time Signals Using Digital Filters | |

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Practical A/D and D/A Converters | |

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References | |

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Problems | |

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The Discrete Fourier Transform | |

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Introduction | |

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Definition | |

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Inverse DFT | |

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Properties | |

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Linearity | |

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Periodicity | |

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Symmetry | |

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Interrelation Between the DFT and the z Transform | |

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Frequency-Domain Sampling Theorem | |

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Time-Domain Aliasing | |

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Interrelation Between the DFT and the CFT | |

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Time-Domain Aliasing | |

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Interrelation Between the DFT and the Fourier Series | |

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Window Technique | |

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Continuous-Time Windows | |

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Discrete-Time Windows | |

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Periodic Discrete-Time Windows | |

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Application of Window Technique | |

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Simplified Notation | |

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Periodic Convolutions | |

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Time-Domain Periodic Convolution | |

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Frequency-Domain Periodic Convolution | |

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Fast Fourier-Transform Algorithms | |

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Decimation-in-Time Algorithm | |

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Decimation-in-Frequency Algorithm | |

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Inverse DFT | |

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Application of the FFT Approach to Signal Processing | |

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Overlap-and-Add Method | |

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Overlap-and-Save Method | |

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References | |

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Problems | |

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Realization of Digital Filters | |

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Introduction | |

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Realization | |

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Direct Realization | |

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Direct Canonic Realization | |

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State-Space Realization | |

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Lattice Realization | |

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Cascade Realization | |

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Parallel Realization | |

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Transposition | |

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Implementation | |

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Design Considerations | |

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Systolic Implementations | |

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References | |

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Problems | |

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Design of Nonrecursive (FIR) Filters | |

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Introduction | |

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Properties of Constant-Delay Nonrecursive Filters | |

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Impulse Response Symmetries | |

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Frequency Response | |

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Location of Zeros | |

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Design Using the Fourier Series | |

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Use of Window Functions | |

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Rectangular Window | |

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Von Hann and Hamming Windows | |

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Blackman Window | |

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Dolph-Chebyshev Window | |

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Kaiser Window | |

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Prescribed Filter Specifications | |

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Other Windows | |

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Design Based on Numerical-Analysis Formulas | |

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References | |

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Problems | |

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Approximations for Analog Filters | |

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Introduction | |

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Basic Concepts | |

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Characterization | |

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Laplace Transform | |

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The Transfer Function | |

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Time-Domain Response | |

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Frequency-Domain Analysis | |

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Ideal and Practical Filters | |

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Realizability Constraints | |

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Butterworth Approximation | |

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Derivation | |

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Normalized Transfer Function | |

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Minimum Filter Order | |

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Chebyshev Approximation | |

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Derivation | |

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Zeros of Loss Function | |

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Normalized Transfer Function | |

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Minimum Filter Order | |

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Inverse-Chebyshev Approximation | |

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Normalized Transfer Function | |

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Minimum Filter Order | |

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Elliptic Approximation | |

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Fifth-Order Approximation | |

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Nth-Order Approximation (n Odd) | |

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Zeros and Poles of L(-s[superscript 2]) | |

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Nth-Order Approximation (n Even) | |

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Specification Constraint | |

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Normalized Transfer Function | |

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Bessel-Thomson Approximation | |

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Transformations | |

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Lowpass-to-Lowpass Transformation | |

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Lowpass-to-Bandpass Transformation | |

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References | |

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Problems | |

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Design of Recursive (IIR) Filters | |

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Introduction | |

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Realizability Constraints | |

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Invariant Impulse-Response Method | |

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Modified Invariant Impulse-Response Method | |

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Matched-z Transformation Method | |

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Bilinear-Transformation Method | |

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Derivation | |

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Mapping Properties of Bilinear Transformation | |

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The Warping Effect | |

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Digital-Filter Transformations | |

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General Transformation | |

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Lowpass-to-Lowpass Transformation | |

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Lowpass-to-Bandstop Transformation | |

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Application | |

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Comparison Between Recursive and Nonrecursive Designs | |

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References | |

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Problems | |

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Recursive (IIR) Filters Satisfying Prescribed Specifications | |

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Introduction | |

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Design Procedure | |

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Design Formulas | |

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Lowpass and Highpass Filters | |

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Bandpass and Bandstop Filters | |

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Butterworth Filters | |

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Chebyshev Filters | |

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Inverse-Chebyshev Filters | |

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Elliptic Filters | |

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Design Using the Formulas and Tables | |

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Constant Group Delay | |

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Delay Equalization | |

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Zero-Phase Filters | |

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Amplitude Equalization | |

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References | |

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Problems | |

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Random Signals | |

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Introduction | |

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Random Variables | |

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Probability-Distribution Function | |

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Probability-Density Function | |

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Uniform Probability Density | |

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Gaussian Probability Density | |

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Joint Distributions | |

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Mean Values and Moments | |

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Random Processes | |

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Notation | |

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First- and Second-Order Statistics | |

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Moments and Autocorrelation | |

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Stationary Processes | |

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Frequency-Domain Representation | |

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Discrete-Time Random Processes | |

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Filtering of Discrete-Time Random Signals | |

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References | |

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Problems | |

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Effects of Finite Word Length in Digital Filters | |

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Introduction | |

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Number Representation | |

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Binary System | |

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Fixed-Point Arithmetic | |

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Floating-Point Arithmetic | |

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Number Quantization | |

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Coefficient Quantization | |

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Low-Sensitivity Structures | |

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Case I | |

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Case II | |

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Product Quantization | |

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Signal Scaling | |

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Method A | |

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Method B | |

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Types of Scaling | |

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Application of Scaling | |

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Minimization of Output Roundoff Noise | |

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Application of Error-Spectrum Shaping | |

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Limit-Cycle Oscillations | |

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Quantization Limit Cycles | |

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Overflow Limit Cycles | |

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Elimination of Quantization Limit Cycles | |

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Elimination of Overflow Limit Cycles | |

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References | |

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Problems | |

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Design of Nonrecursive Filters Using Optimization Methods | |

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Introduction | |

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Problem Formulation | |

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Lowpass and Highpass Filters | |

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Bandpass and Bandstop Filters | |

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Alternation Theorem | |

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Remez Exchange Algorithm | |

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Initialization of Extremals | |

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Location of Maxima of the Error Function | |

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Computation of [vertical bar]E([omega])[vertical bar] and P[subscript c]([omega]) | |

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Rejection of Superfluous Potential Extremals | |

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Computation of Impulse Response | |

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Improved Search Methods | |

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Selective Step-by-Step Search | |

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Cubic Interpolation | |

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Quadratic Interpolation | |

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Improved Formulation | |

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Efficient Remez Exchange Algorithm | |

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Gradient Information | |

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Property 1 | |

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Property 2 | |

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Property 3 | |

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Property 4 | |

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Property 5 | |

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Prescribed Specifications | |

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Generalization | |

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Antisymmetrical Impulse Response and Odd Filter Length | |

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Even Filter Length | |

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Digital Differentiators | |

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Problem Formulation | |

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First Derivative | |

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Prescribed Specifications | |

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Arbitrary Amplitude Responses | |

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Multiband Filters | |

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References | |

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Additional References | |

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Problems | |

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Design of Recursive Filters Using Optimization Methods | |

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Introduction | |

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Problem Formulation | |

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Newton's Method | |

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Quasi-Newton Algorithms | |

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Basic Quasi-Newton Algorithm | |

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Updating Formulas for Matrix S[subscript k+1] | |

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Inexact Line Searches | |

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Practical Quasi-Newton Algorithm | |

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Minimax Algorithms | |

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Improved Minimax Algorithms | |

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Design of Recursive Filters | |

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Objective Function | |

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Gradient Information | |

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Stability | |

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Minimum Filter Order | |

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Use of Weighting | |

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Design of Recursive Delay Equalizers | |

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References | |

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Additional References | |

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Problems | |

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Wave Digital Filters | |

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Introduction | |

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Sensitivity Considerations | |

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Wave Network Characterization | |

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Element Realizations | |

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Impedances | |

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Voltage Sources | |

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Series Wire Interconnection | |

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Parallel Wire Interconnection | |

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2-Port Adaptors | |

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Transformers | |

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Unit Elements | |

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Circulators | |

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Resonant Circuits | |

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Realizability Constraint | |

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Lattice Wave Digital Filters | |

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Analysis | |

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Alternative Lattice Configuration | |

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Digital Realization | |

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Ladder Wave Digital Filters | |

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Filters Satisfying Prescribed Specifications | |

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Frequency-Domain Analysis | |

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Scaling | |

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Elimination of Limit-Cycle Oscillations | |

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Related Synthesis Methods | |

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A Cascade Synthesis Based on the Wave Characterization | |

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Generalized-Immittance Converters | |

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Analog G-CGIC Configuration | |

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Digital G-CGIC Configuration | |

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Cascade Synthesis | |

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Signal Scaling | |

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Output Noise | |

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Choice of Structure | |

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References | |

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Problems | |

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Digital Signal Processing Applications | |

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Introduction | |

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Sampling-Frequency Conversion | |

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Decimators | |

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Interpolators | |

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Sampling Frequency Conversion by a Noninteger Factor | |

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Design Considerations | |

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Quadrature-Mirror-Image Filter Banks | |

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Operation | |

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Elimination of Aliasing Errors | |

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Design Considerations | |

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Perfect Reconstruction | |

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Hilbert Transformers | |

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Design of Hilbert Transformers | |

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Single-Sideband Modulation | |

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Sampling of Bandpassed Signals | |

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Adaptive Digital Filters | |

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Wiener Filters | |

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Newton Algorithm | |

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Steepest-Descent Algorithm | |

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Least-Mean-Square Algorithm | |

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Recursive Filters | |

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Applications | |

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Two-Dimensional Digital Filters | |

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Two-Dimensional Convolution | |

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Two-Dimensional z Transform | |

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Two-Dimensional Transfer Function | |

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Stability | |

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Frequency-Domain Analysis | |

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Types of 2-D Filters | |

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Approximations | |

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Applications | |

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References | |

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Additional References | |

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Problems | |

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Complex Analysis | |

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Introduction | |

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Complex Numbers | |

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Complex Arithmetic | |

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De Moivre's Theorem | |

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Euler's Formula | |

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Exponential Form | |

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Vector Representation | |

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Spherical Representation | |

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Functions of a Complex Variable | |

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Polynomials | |

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Inverse Algebraic Functions | |

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Trigonometric Functions and Their Inverses | |

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Hyperbolic Functions and Their Inverses | |

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Multi-Valued Functions | |

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Periodic Functions | |

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Rational Algebraic Functions | |

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Basic Principles of Complex Analysis | |

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Limit | |

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Differentiability | |

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Analyticity | |

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Zeros | |

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Singularities | |

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Zero-Pole Plots | |

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Series | |

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Laurent Theorem | |

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Residue Theorem | |

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Analytic Continuation | |

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Conformal Transformations | |

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References | |

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Elliptic Functions | |

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Introduction | |

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Elliptic Integral of the First Kind | |

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Elliptic Functions | |

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Imaginary Argument | |

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Formulas | |

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Periodicity | |

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Transformation | |

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Series Representation | |

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References | |