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Preface | |

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Introduction | |

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Signals, Systems, and Signal Processing | |

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Basic Elements of a Digital Signal Processing System | |

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Advantages of Digital over Analog Signal Processing | |

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Classification of Signals | |

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Multichannel and Multidimensional Signals | |

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Continuous-Time Versus Discrete-Time Signals | |

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Continuous-Valued Versus Discrete-Valued Signals | |

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Deterministic Versus Random Signals | |

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The Concept of Frequency in Continuous-Time and Discrete-Time Signals | |

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Continuous-Time Sinusoidal Signals | |

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Discrete-Time Sinusoidal Signals | |

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Harmonically Related Complex Exponentials | |

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Analog-to-Digital and Digital-to-Analog Conversion | |

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Sampling of Analog Signals | |

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The Sampling Theorem | |

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Quantization of Continuous-Amplitude Signals | |

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Quantization of Sinusoidal Signals | |

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Coding of Quantized Samples | |

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Digital-to-Analog Conversion | |

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Analysis of Digital Signals and Systems Versus Discrete-Time Signals and Systems | |

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Summary and References | |

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Problems | |

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Discrete-Time Signals and Systems | |

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Discrete-Time Signals | |

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Some Elementary Discrete-Time Signals | |

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Classification of Discrete-Time Signals | |

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Simple Manipulations of Discrete-Time Signals | |

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Discrete-Time Systems | |

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Input-Output Description of Systems | |

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Block Diagram Representation of Discrete-Time Systems | |

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Classification of Discrete-Time Systems | |

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Interconnection of Discrete-Time Systems | |

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Analysis of Discrete-Time Linear Time-Invariant Systems | |

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Techniques for the Analysis of Linear Systems | |

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Resolution of a Discrete-Time Signal into Impulses | |

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Response of LTI Systems to Arbitrary Inputs: The Convolution Sum | |

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Properties of Convolution and the Interconnection of LTI Systems | |

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Causal Linear Time-Invariant Systems | |

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Stability of Linear Time-Invariant Systems | |

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Systems with Finite-Duration and Infinite-Duration Impulse Response | |

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Discrete-Time Systems Described by Difference Equations | |

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Recursive and Nonrecursive Discrete-Time Systems | |

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Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations | |

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Solution of Linear Constant-Coefficient Difference Equations | |

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The Impulse Response of a Linear Time-Invariant Recursive System | |

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Implementation of Discrete-Time Systems | |

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Structures for the Realization of Linear Time-Invariant Systems | |

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Recursive and Nonrecursive Realizations of FIR Systems | |

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Correlation of Discrete-Time Signals | |

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Crosscorrelation and Autocorrelation Sequences | |

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Properties of the Autocorrelation and Crosscorrelation Sequences | |

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Correlation of Periodic Sequences | |

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Input-Output Correlation Sequences | |

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Summary and References | |

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Problems | |

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The z-Transform and Its Application to the Analysis of LTI Systems | |

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The z-Transform | |

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The Direct z-Transform | |

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The Inverse z-Transform | |

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Properties of the z-Transform | |

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Rational z-Transforms | |

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Poles and Zeros | |

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Pole Location and Time-Domain Behavior for Causal Signals | |

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The System Function of a Linear Time-Invariant System | |

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Inversion of the z-Transform | |

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The Inverse z-Transform by Contour Integration | |

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The Inverse z-Transform by Power Series Expansion | |

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The Inverse z-Transform by Partial-Fraction Expansion | |

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Decomposition of Rational z-Transforms | |

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Analysis of Linear Time-Invariant Systems in the z-Domain | |

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Response of Systems with Rational System Functions | |

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Transient and Steady-State Responses | |

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Causality and Stability | |

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Pole-Zero Cancellations | |

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Multiple-Order Poles and Stability | |

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Stability of Second-Order Systems | |

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The One-sided z-Transform | |

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Definition and Properties | |

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Solution of Difference Equations | |

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Response of Pole-Zero Systems with Nonzero Initial Conditions | |

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Summary and References | |

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Problems | |

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Frequency Analysis of Signals | |

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Frequency Analysis of Continuous-Time Signals | |

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The Fourier Series for Continuous-Time Periodic Signals | |

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Power Density Spectrum of Periodic Signals | |

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The Fourier Transform for Continuous-Time Aperiodic Signals | |

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Energy Density Spectrum of Aperiodic Signals | |

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Frequency Analysis of Discrete-Time Signals | |

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The Fourier Series for Discrete-Time Periodic Signals | |

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Power Density Spectrum of Periodic Signals | |

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The Fourier Transform of Discrete-Time Aperiodic Signals | |

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Convergence of the Fourier Transform | |

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Energy Density Spectrum of Aperiodic Signals | |

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Relationship of the Fourier Transform to the z-Transform | |

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The Cepstrum | |

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The Fourier Transform of Signals with Poles on the Unit Circle | |

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Frequency-Domain Classification of Signals: The Concept of Bandwidth | |

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The Frequency Ranges of Some Natural Signals | |

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Frequency-Domain and Time-Domain Signal Properties | |

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Properties of the Fourier Transform for Discrete-Time Signals | |

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Symmetry Properties of the Fourier Transform | |

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Fourier Transform Theorems and Properties | |

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Summary and References | |

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Problems | |

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Frequency-Domain Analysis of LTI Systems | |

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Frequency-Domain Characteristics of Linear Time-Invariant Systems | |

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Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function | |

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Steady-State and Transient Response to Sinusoidal Input Signals | |

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Steady-State Response to Periodic Input Signals | |

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Response to Aperiodic Input Signals | |

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Frequency Response of LTI Systems | |

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Frequency Response of a System with a Rational System Function | |

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Computation of the Frequency Response Function | |

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Correlation Functions and Spectra at the Output of LTI Systems | |

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Input-Output Correlation Functions and Spectra | |

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Correlation Functions and Power Spectra for Random Input Signals | |

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Linear Time-Invariant Systems as Frequency-Selective Filters | |

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Ideal Filter Characteristics | |

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Lowpass, Highpass, and Bandpass Filters | |

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Digital Resonators | |

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Notch Filters | |

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Comb Filters | |

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All-Pass Filters | |

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Digital Sinusoidal Oscillators | |

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Inverse Systems and Deconvolution | |

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Invertibility of Linear Time-Invariant Systems | |

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Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems | |

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System Identification and Deconvolution | |

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Homomorphic Deconvolution | |

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Summary and References | |

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Problems | |

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Sampling and Reconstruction of Signals | |

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Ideal Sampling and Reconstruction of Continuous-Time Signals | |

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Discrete-Time Processing of Continuous-Time Signals | |

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Analog-to-Digital and Digital-to-Analog Converters | |

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Analog-to-Digital Converters | |

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Quantization and Coding | |

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Analysis of Quantization Errors | |

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Digital-to-Analog Converters | |

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Sampling and Reconstruction of Continuous-Time Bandpass Signals | |

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Uniform or First-Order Sampling | |

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Interleaved or Nonuniform Second-Order Sampling | |

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Bandpass Signal Representations | |

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Sampling Using Bandpass Signal Representations | |

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Sampling of Discrete-Time Signals | |

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Sampling and Interpolation of Discrete-Time Signals | |

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Representation and Sampling of Bandpass Discrete-Time Signals | |

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Oversampling A/D and D/A Converters | |

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Oversampling A/D Converters | |

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Oversampling D/A Converters | |

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Summary and References | |

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Problems | |

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The Discrete Fourier Transform: Its Properties and Applications | |

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Frequency-Domain Sampling: The Discrete Fourier Transform | |

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Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals | |

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The Discrete Fourier Transform (DFT) | |

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The DFT as a Linear Transformation | |

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Relationship of the DFT to Other Transforms | |

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Properties of the DFT | |

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Periodicity, Linearity, and Symmetry Properties | |

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Multiplication of Two DFTs and Circular Convolution | |

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Additional DFT Properties | |

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Linear Filtering Methods Based on the DFT | |

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Use of the DFT in Linear Filtering | |

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Filtering of Long Data Sequences | |

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Frequency Analysis of Signals Using the DFT | |

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The Discrete Cosine Transform | |

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Forward DCT | |

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Inverse DCT | |

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DCT as an Orthogonal Transform | |

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Summary and References | |

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Problems | |

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Efficient Computation of the DFT: Fast Fourier Transform Algorithms | |

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Efficient Computation of the DFT: FFT Algorithms | |

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Direct Computation of the DFT | |

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Divide-and-Conquer Approach to Computation of the DFT | |

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Radix-2 FFT Algorithms | |

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Radix-4 FFT Algorithms | |

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Split-Radix FFT Algorithms | |

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Implementation of FFT Algorithms | |

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Applications of FFT Algorithms | |

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Efficient Computation of the DFT of Two Real Sequences | |

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Efficient Computation of the DFT of a 2N-Point Real Sequence | |

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Use of the FFT Algorithm in Linear Filtering and Correlation | |

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A Linear Filtering Approach to Computation of the DFT | |

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The Goertzel Algorithm | |

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The Chirp-z Transform Algorithm | |

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Quantization Effects in the Computation of the DFT | |

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Quantization Errors in the Direct Computation of the DFT | |

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Quantization Errors in FFT Algorithms | |

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Summary and References | |

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Problems | |

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Implementation of Discrete-Time Systems | |

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Structures for the Realization of Discrete-Time Systems | |

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Structures for FIR Systems | |

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Direct-Form Structure | |

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Cascade-Form Structures | |

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Frequency-Sampling Structures | |

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Lattice Structure | |

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Structures for IIR Systems | |

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Direct-Form Structures | |

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Signal Flow Graphs and Transposed Structures | |

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Cascade-Form Structures | |

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Parallel-Form Structures | |

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Lattice and Lattice-Ladder Structures for IIR Systems | |

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Representation of Numbers | |

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Fixed-Point Representation of Numbers | |

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Binary Floating-Point Representation of Numbers | |

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Errors Resulting from Rounding and Truncation | |

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Quantization of Filter Coefficients | |

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Analysis of Sensitivity to Quantization of Filter Coefficients | |

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Quantization of Coefficients in FIR Filters | |

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Round-Off Effects in Digital Filters | |

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Limit-Cycle Oscillations in Recursive Systems | |

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Scaling to Prevent Overflow | |

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Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters | |

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Summary and References | |

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Problems | |

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Design of Digital Filters | |

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General Considerations | |

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Causality and Its Implications | |

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Characteristics of Practical Frequency-Selective Filters | |

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Design of FIR Filters | |

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Symmetric and Antisymmetric FIR Filters | |

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Design of Linear-Phase FIR Filters Using Windows | |

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Design of Linear-Phase FIR Filters by the Frequency-Sampling Method | |

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Design of Optimum Equiripple Linear-Phase FIR Filters | |

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Design of FIR Differentiators | |

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Design of Hilbert Transformers | |

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Comparison of Design Methods for Linear-Phase FIR Filters | |

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Design of IIR Filters From Analog Filters | |

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IIR Filter Design by Approximation of Derivatives | |

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IIR Filter Design by Impulse Invariance | |

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IIR Filter Design by the Bilinear Transformation | |

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Characteristics of Commonly Used Analog Filters | |

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Some Examples of Digital Filter Designs Based on the Bilinear Transformation | |

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Frequency Transformations | |

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Frequency Transformations in the Analog Domain | |

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Frequency Transformations in the Digital Domain | |

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Summary and References | |

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Problems | |

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Multirate Digital Signal Processing | |

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Introduction | |

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Decimation by a Factor D | |

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Interpolation by a Factor I | |

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Sampling Rate Conversion by a Rational Factor I/D | |

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Implementation of Sampling Rate Conversion | |

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Polyphase Filter Structures | |

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Interchange of Filters and Downsamplers/Upsamplers | |

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Sampling Rate Conversion with Cascaded Integrator Comb Filters | |

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Polyphase Structures for Decimation and Interpolation Filters | |

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Structures for Rational Sampling Rate Conversion | |

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Multistage Implementation of Sampling Rate Conversion | |

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Sampling Rate Conversion of Bandpass Signals | |

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Sampling Rate Conversion by an Arbitrary Factor | |

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Arbitrary Resampling with Polyphase Interpolators | |

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Arbitrary Resampling with Farrow Filter Structures | |

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Applications of Multirate Signal Processing | |

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Design of Phase Shifters | |

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Interfacing of Digital Systems with Different Sampling Rates | |

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Implementation of Narrowband Lowpass Filters | |

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Subband Coding of Speech Signals | |

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Digital Filter Banks | |

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Polyphase Structures of Uniform Filter Banks | |

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Transmultiplexers | |

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Two-Channel Quadrature Mirror Filter Bank | |

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Elimination of Aliasing | |

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Condition for Perfect Reconstruction | |

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Polyphase Form of the QMF Bank | |

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Linear Phase FIR QMF Bank | |

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IIR QMF Bank | |

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Perfect Reconstruction Two-Channel FIR QMF Bank | |

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Two-Channel QMF Banks in Subband Coding | |

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M-Channel QMF Bank | |

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Alias-Free and Perfect Reconstruction Condition | |

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Polyphase Form of the M-Channel QMF Bank | |

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Summary and References | |

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Problems | |

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Linear Prediction and Optimum Linear Filters | |

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Random Signals, Correlation Functions, and Power Spectra | |

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Random Processes | |

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Stationary Random Processes | |

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Statistical (Ensemble) Averages | |

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Statistical Averages for Joint Random Processes | |

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Power Density Spectrum | |

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Discrete-Time Random Signals | |

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Time Averages for a Discrete-Time Random Process | |

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Mean-Ergodic Process | |

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Correlation-Ergodic Processes | |

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Innovations Representation of a Stationary Random Process | |

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Rational Power Spectra | |

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Relationships Between the Filter Parameters and the Autocorrelation Sequence | |

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Forward and Backward Linear Prediction | |

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Forward Linear Prediction | |

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Backward Linear Prediction | |

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The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors | |

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Relationship of an AR Process to Linear Prediction | |

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Solution of the Normal Equations | |

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The Levinson-Durbin Algorithm | |

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The Schur Algorithm | |

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Properties of the Linear Prediction-Error Filters | |

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AR Lattice and ARMA Lattice-Ladder Filters | |

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AR Lattice Structure | |

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ARMA Processes and Lattice-Ladder Filters | |

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Wiener Filters for Filtering and Prediction | |

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FIR Wiener Filter | |

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Orthogonality Principle in Linear Mean-Square Estimation | |

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IIR Wiener Filter | |

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Noncausal Wiener Filter | |

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Summary and References | |

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Problems | |

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Adaptive Filters | |

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Applications of Adaptive Filters | |

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System Identification or System Modeling | |

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Adaptive Channel Equalization | |

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Echo Cancellation in Data Transmission over Telephone Channels | |

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Suppression of Narrowband Interference in a Wideband Signal | |

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Adaptive Line Enhancer | |

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Adaptive Noise Cancelling | |

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Linear Predictive Coding of Speech Signals | |

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Adaptive Arrays | |

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Adaptive Direct-Form FIR Filters-The LMS Algorithm | |

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Minimum Mean-Square-Error Criterion | |

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The LMS Algorithm | |

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Related Stochastic Gradient Algorithms | |

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Properties of the LMS Algorithm | |

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Adaptive Direct-Form Filters-RLS Algorithms | |

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RLS Algorithm | |

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The LDU Factorization and Square-Root Algorithms | |

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Fast RLS Algorithms | |

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Properties of the Direct-Form RLS Algorithms | |

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Adaptive Lattice-Ladder Filters | |

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Recursive Least-Squares Lattice-Ladder Algorithms | |

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Other Lattice Algorithms | |

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Properties of Lattice-Ladder Algorithms | |

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Summary and References | |

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Problems | |

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Power Spectrum Estimation | |

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Estimation of Spectra from Finite-Duration Observations of Signals | |

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Computation of the Energy Density Spectrum | |

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Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram | |

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The Use of the DFT in Power Spectrum Estimation | |

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Nonparametric Methods for Power Spectrum Estimation | |

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The Bartlett Method: Averaging Periodograms | |

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The Welch Method: Averaging Modified Periodograms | |

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The Blackman and Tukey Method: Smoothing the Periodogram | |

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Performance Characteristics of Nonparametric Power Spectrum Estimators | |

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Computational Requirements of Nonparametric Power Spectrum Estimates | |

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Parametric Methods for Power Spectrum Estimation | |

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Relationships Between the Autocorrelation and the Model Parameters | |

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The Yule-Walker Method for the AR Model Parameters | |

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The Burg Method for the AR Model Parameters | |

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Unconstrained Least-Squares Method for the AR Model Parameters | |

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Sequential Estimation Methods for the AR Model Parameters | |

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Selection of AR Model Order | |

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MA Model for Power Spectrum Estimation | |

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ARMA Model for Power Spectrum Estimation | |

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Some Experimental Results | |

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Filter Bank Methods | |

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Filter Bank Realization of the Periodogram | |

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Minimum Variance Spectral Estimates | |

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Eigenanalysis Algorithms for Spectrum Estimation | |

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Pisarenko Harmonic Decomposition Method | |

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Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise | |

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MUSIC Algorithm | |

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ESPRIT Algorithm | |

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Order Selection Criteria | |

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Experimental Results | |

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Summary and References | |

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Problems | |

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Random Number Generators | |

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Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters | |

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References and Bibliography | |

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Answers to Selected Problems | |

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Index | |