Higher Order Spectra Analysis: A Non-Linear Signal Processing Framework
In response to the recent growth of interest in polyspectra, this timely text provides an introduction to signal processing methods that are based on polyspectra and cumulants concepts. The emphasis of the book is placed on the presentation of signal processing tools for use in situations where the more common power spectrum estimation techniques fall short. This manual will be valuable to practicing engineers who need an introduction to polyspectra from a signal processing perspective.
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In response to the recent growth of interest in polyspectra, this timely text provides an introduction to signal processing methods that are based on polyspectra and cumulants concepts.The emphasis of the book is placed on the presentation of signal processing tools for use in situations where the more common power spectrum estimation techniques fall short.This manual will be valuable to practicing engineers who need an introduction to polyspectra from a signal processing perspective.
PrefaceList of SymbolsCh. 1Introduction1Ch. 2Cumulant Spectra of Stochastic Signals72.2Moments and Cumulants72.3Cumulant Spectra202.4Cumulant Spectra of Non-Gaussian Linear Processes372.5Detecting and Identifying Nonlinear Processes58Ch. 3Moment Spectra of Deterministic Signals713.2Moments of Energy Signals783.3Moment Spectra of a Periodic Energy Signals843.4Moments of Power Signals1003.5Moment Spectra of Periodic Power Signals107Ch. 4Conventional Methods for the Estimation of Higher-Order Spectra1234.2Indirect Class of Conventional Methods1244.3Direct Class of Conventional Methods1324.4Complex Demodulates Class of Conventional Methods1414.5Statistical Properties of Conventional Methods1424.6Test for Aliasing with the Bispectrum1474.7Bispectrum Computation on Polar Rasters149Ch. 5Higher-Order Cepstra (Polycepstra)1635.2The Complex Cepstrum of Deterministic Energy Signals1645.3The Differential Cepstrum of Deterministic Energy Signals1695.4The Power Cepstrum of Deterministic and Stochastic Signals1725.5The Bicepstrum and Tricepstrum of Deterministic and Stochastic Signals1775.6The Cepstrum of Bicoherency1875.7Higher-Order Spectrum Factorization and Index for Linearity1915.8Inverse Filter Reconstruction1935.9The Cross-Bicepstrum of Deterministic and Stochastic Signals2005.10Analytic Performance Evaluation of the Complex Cepstrum and Bicepstrum209Ch. 6Nonparametric Methods for Signal Recovery From Higher-Order Spectra2196.2Magnitude and Phase Estimation From Higher-Order Spectra2206.3Phase Recovery Algorithms2206.4Phase and Magnitude Algorithms Based on Polyspectra/Polycepstra Properties2306.5Signal Reconstruction From Only the Phase of the Bispectrum2376.6Signal Reconstruction From the Bispectrum Based on the Method of POCS2496.7Blind Deconvolution Using BIRA253Ch. 7Parametric Methods for the Estimation of Higher-Order Spectra2657.2MA Methods2667.3Noncausal AR Methods2787.4ARMA Methods2827.5Model Order Determination295Ch. 8Direction of Arrival Estimation and Analysis of Transient Signals3138.2Time Delay Estimation3148.3Bearing Estimation with Higher-Order Statistics3378.4Parameter Estimation of Transient Signals3668.5Detection of Transient Signals371Ch. 9Adaptive Filtering with Higher-Order Statistics3839.2Adaptive Filtering with Second-Order Statistics3849.3The LMF and RLF Algorithm3909.4Adaptive IIR Algorithms Based on HOS3979.5Adaptive Lattice Linear Prediction Using Cumulants4029.6Adaptive MA Model Estimation Via Noncausal AR Approximations4069.7Adaptive Time Delay Estimation4149.8Adaptive Blind Equalization Algorithms418Ch. 10Detection and Characterization of Nonlinearities in Time Series44710.1General Volterra Systems44810.2Second-Order Volterra Filters44810.3The Identification of a Particular Nonlinear Time Series System45510.4Quadratic Phase Coupling45910.5Cubic Phase Coupling482Ch. 11Time-Frequency Distributions Based on Higher-Order Spectra48711.2Wigner-Ville Distribution (WD)48811.3Cohen's General Class of Time-Frequency Distributions49111.4Wigner Higher-Order Moment Spectra: Continuous Case49411.5Wigner Polyspectra: Discrete Case50311.6Applications of Wigner Higher-Order Spectra512Ch. 12Current and Future Trends525Index529
