Frequency Domain Methods For Nonlinear Analysis

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Frequency-domain Methods for Nonlinear Analysis

Author : Gennadi? Alekseevich Leonov
Publisher : World Scientific
ISBN 13 : 9789810221461
Total Pages : 522 pages
Book Rating : 4.2/5 (214 download)

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Book Synopsis Frequency-domain Methods for Nonlinear Analysis by : Gennadi? Alekseevich Leonov

Download or read book Frequency-domain Methods for Nonlinear Analysis written by Gennadi? Alekseevich Leonov and published by World Scientific. This book was released on 1996 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.

Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

Author : Leonov Gennady A
Publisher : World Scientific
ISBN 13 : 9814500909
Total Pages : 512 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Frequency-domain Methods For Nonlinear Analysis: Theory And Applications by : Leonov Gennady A

Download or read book Frequency-domain Methods For Nonlinear Analysis: Theory And Applications written by Leonov Gennady A and published by World Scientific. This book was released on 1996-05-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.

Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion

Author : Xingjian Jing
Publisher : Springer
ISBN 13 : 3319123912
Total Pages : 331 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion by : Xingjian Jing

Download or read book Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion written by Xingjian Jing and published by Springer. This book was released on 2015-02-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain. The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis and design method. Based on the parametric characteristic approach, nonlinear influence in the frequency domain can be investigated with a novel insight, i.e., alternating series, which is followed by some application results in vibration control. Magnitude bounds of frequency response functions of nonlinear systems can also be studied with a parametric characteristic approach, which result in novel parametric convergence criteria for any given parametric nonlinear model whose input-output relationship allows a convergent Volterra series expansion. This book targets those readers who are working in the areas related to nonlinear analysis and design, nonlinear signal processing, nonlinear system identification, nonlinear vibration control, and so on. It particularly serves as a good reference for those who are studying frequency domain methods for nonlinear systems.

Analysis and Control of Nonlinear Systems with Stationary Sets

Author : Jinzhi Wang
Publisher : World Scientific
ISBN 13 : 9812814698
Total Pages : 334 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Analysis and Control of Nonlinear Systems with Stationary Sets by : Jinzhi Wang

Download or read book Analysis and Control of Nonlinear Systems with Stationary Sets written by Jinzhi Wang and published by World Scientific. This book was released on 2009 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear systems with stationary sets are important because they cover a lot of practical systems in engineering. Previous analysis has been based on the frequency-domain for this class of systems. However, few results on robustness analysis and controller design for these systems are easily available. This book presents the analysis as well as methods based on the global properties of systems with stationary sets in a unified time-domain and frequency-domain framework. The focus is on multi-input and multi-output systems, compared to previous publications which considered only single-input and single-output systems. The control methods presented in this book will be valuable for research on nonlinear systems with stationary sets.

Analysis and Design of Nonlinear Systems in the Frequency Domain

Author : Yunpeng Zhu
Publisher :
ISBN 13 : 9783030708344
Total Pages : 0 pages
Book Rating : 4.7/5 (83 download)

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Book Synopsis Analysis and Design of Nonlinear Systems in the Frequency Domain by : Yunpeng Zhu

Download or read book Analysis and Design of Nonlinear Systems in the Frequency Domain written by Yunpeng Zhu and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the development of three novel approaches to build up a framework for the frequency domain analysis and design of nonlinear systems. The concepts are derived from Volterra series representation of nonlinear systems which are described by nonlinear difference or differential equations. Occupying the middle ground between traditional linear approaches and more complex nonlinear system theories, the book will help readers to have a good start to analyse and exploit the nonlinearities. Analysis and Design of Nonlinear Systems in the Frequency Domain provides clear illustrations and examples at the beginning and the end of each chapter, respectively, making it of interest to both academics and practicing engineers.

Nonlinear System Identification

Author : Stephen A. Billings
Publisher : John Wiley & Sons
ISBN 13 : 1118535553
Total Pages : 611 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Nonlinear System Identification by : Stephen A. Billings

Download or read book Nonlinear System Identification written by Stephen A. Billings and published by John Wiley & Sons. This book was released on 2013-07-29 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.

Hopf Bifurcation Analysis

Author : Jorge L Moiola
Publisher : World Scientific
ISBN 13 : 9814499102
Total Pages : 344 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Hopf Bifurcation Analysis by : Jorge L Moiola

Download or read book Hopf Bifurcation Analysis written by Jorge L Moiola and published by World Scientific. This book was released on 1996-04-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references. Contents: IntroductionThe Hopf Bifurcation TheoremContinuation of Bifurcation Curves on the Parameter PlaneDegenerate Bifurcations in the Space of System ParametersHigh-Order Hopf Bifurcation FormulasHopf Bifurcation in Nonlinear Systems with Time DelaysBirth of Multiple Limit CyclesAppendixReferencesArthur IndexSubject Index Readership: Nonlinear scientists, applied mathematicians, and systems engineers. keywords:Bifurcation;Harmonic Balance Approximation;Graphical Hopf Bifurcation;Degenerate Hopf Bifurcation;High-Order Hopf Bifurcation;Multiple Limit Cycles;Hopf;Frequency;Harmonic Balance;Feedback;Oscillations;Nonlinear;Delay;Limit Cycles;Degenerate Bifurcations

Advances on Analysis and Control of Vibrations

Author : Mauricio Zapateiro
Publisher : BoD – Books on Demand
ISBN 13 : 9535106996
Total Pages : 294 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Advances on Analysis and Control of Vibrations by : Mauricio Zapateiro

Download or read book Advances on Analysis and Control of Vibrations written by Mauricio Zapateiro and published by BoD – Books on Demand. This book was released on 2012-09-05 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vibration is a phenomenon that we can perceive in many systems. Their effects are as diverse as the personal discomfort that can produce the unevenness of a road or the collapse of a building or a bridge during an earthquake. This book is a compendium of research works on vibration analysis and control. It goes through new methodologies that help us understand and mitigate this phenomenon. This book is divided into two sections. The first one is devoted to new advances on vibration analysis while the second part is a series of case studies that illustrate novel techniques on vibration control. The applications are varied and include areas such as vehicle suspension systems, wind turbines and civil engineering structures.

Analysis and Control of Nonlinear Systems with Stationary Sets

Author :
Publisher :
ISBN 13 : 981447097X
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Analysis and Control of Nonlinear Systems with Stationary Sets by :

Download or read book Analysis and Control of Nonlinear Systems with Stationary Sets written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Condition Monitoring and Nonlinear Frequency Analysis Based Fault Detection of Mechanical Vibration Systems

Author : Hogir Rafiq
Publisher : Springer Nature
ISBN 13 : 365842480X
Total Pages : 206 pages
Book Rating : 4.6/5 (584 download)

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Book Synopsis Condition Monitoring and Nonlinear Frequency Analysis Based Fault Detection of Mechanical Vibration Systems by : Hogir Rafiq

Download or read book Condition Monitoring and Nonlinear Frequency Analysis Based Fault Detection of Mechanical Vibration Systems written by Hogir Rafiq and published by Springer Nature. This book was released on 2023-08-26 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hogir Rafiq proposes two approaches, the signal processing based condition monitoring approaches with applications to fault detection in gear systems, and application of deep mathematical and system theoretical methods to fault detection. The author develops the multivariate empirical mode decomposition (MEMD) algorithm to enhance the capability of extracting fault features and theoretical problems in nonlinear frequency analysis methods, respectively. The effectiveness has been demonstrated by an experimental study on a wind turbine gearbox test rig.

The RF and Microwave Handbook - 3 Volume Set

Author : Mike Golio
Publisher : CRC Press
ISBN 13 : 1439833230
Total Pages : 2208 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis The RF and Microwave Handbook - 3 Volume Set by : Mike Golio

Download or read book The RF and Microwave Handbook - 3 Volume Set written by Mike Golio and published by CRC Press. This book was released on 2018-10-08 with total page 2208 pages. Available in PDF, EPUB and Kindle. Book excerpt: By 1990 the wireless revolution had begun. In late 2000, Mike Golio gave the world a significant tool to use in this revolution: The RF and Microwave Handbook. Since then, wireless technology spread across the globe with unprecedented speed, fueled by 3G and 4G mobile technology and the proliferation of wireless LANs. Updated to reflect this tremendous growth, the second edition of this widely embraced, bestselling handbook divides its coverage conveniently into a set of three books, each focused on a particular aspect of the technology. Six new chapters cover WiMAX, broadband cable, bit error ratio (BER) testing, high-power PAs (power amplifiers), heterojunction bipolar transistors (HBTs), as well as an overview of microwave engineering. Over 100 contributors, with diverse backgrounds in academic, industrial, government, manufacturing, design, and research reflect the breadth and depth of the field. This eclectic mix of contributors ensures that the coverage balances fundamental technical issues with the important business and marketing constraints that define commercial RF and microwave engineering. Focused chapters filled with formulas, charts, graphs, diagrams, and tables make the information easy to locate and apply to practical cases. The new format, three tightly focused volumes, provides not only increased information but also ease of use. You can find the information you need quickly, without wading through material you don’t immediately need, giving you access to the caliber of data you have come to expect in a much more user-friendly format.

Uncertainty Modeling in Vibration, Control and Fuzzy Analysis of Structural Systems

Author : Bilal M. Ayyub
Publisher : World Scientific
ISBN 13 : 9810231342
Total Pages : 382 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Uncertainty Modeling in Vibration, Control and Fuzzy Analysis of Structural Systems by : Bilal M. Ayyub

Download or read book Uncertainty Modeling in Vibration, Control and Fuzzy Analysis of Structural Systems written by Bilal M. Ayyub and published by World Scientific. This book was released on 1997 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of the current state of uncertainty modeling in vibration, control, and fuzzy analysis of structural and mechanical systems. It is a coherent compendium written by leading experts and offers the reader a sampling of exciting research areas in several fast-growing branches in this field. Uncertainty modeling and analysis are becoming an integral part of system definition and modeling in many fields. The book consists of ten chapters that report the work of researchers, scientists and engineers on theoretical developments and diversified applications in engineering systems. They deal with modeling for vibration, control, and fuzzy analysis of structural and mechanical systems under uncertain conditions. The book designed for readers who are familiar with the fundamentals and wish to study a particular topic or use the book as an authoritative reference. It gives readers a sophisticated toolbox for tackling modeling problems in mechanical and structural systems in real-world situations. The book is part of a series on Stability, Vibration and Control of Structures, and provides vital information in these areas.

Hopf Bifurcation Analysis

Author : Jorge L. Moiola
Publisher : World Scientific
ISBN 13 : 9789810226282
Total Pages : 354 pages
Book Rating : 4.2/5 (262 download)

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Book Synopsis Hopf Bifurcation Analysis by : Jorge L. Moiola

Download or read book Hopf Bifurcation Analysis written by Jorge L. Moiola and published by World Scientific. This book was released on 1996 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.

System Identification

Author : Rik Pintelon
Publisher : John Wiley & Sons
ISBN 13 : 0471660957
Total Pages : 644 pages
Book Rating : 4.4/5 (716 download)

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Book Synopsis System Identification by : Rik Pintelon

Download or read book System Identification written by Rik Pintelon and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electrical Engineering System Identification A Frequency Domain Approach How does one model a linear dynamic system from noisy data? This book presents a general approach to this problem, with both practical examples and theoretical discussions that give the reader a sound understanding of the subject and of the pitfalls that might occur on the road from raw data to validated model. The emphasis is on robust methods that can be used with a minimum of user interaction. Readers in many fields of engineering will gain knowledge about: * Choice of experimental setup and experiment design * Automatic characterization of disturbing noise * Generation of a good plant model * Detection, qualification, and quantification of nonlinear distortions * Identification of continuous- and discrete-time models * Improved model validation tools and from the theoretical side about: * System identification * Interrelations between time- and frequency-domain approaches * Stochastic properties of the estimators * Stochastic analysis System Identification: A Frequency Domain Approach is written for practicing engineers and scientists who do not want to delve into mathematical details of proofs. Also, it is written for researchers who wish to learn more about the theoretical aspects of the proofs. Several of the introductory chapters are suitable for undergraduates. Each chapter begins with an abstract and ends with exercises, and examples are given throughout.

Discontinuous Control Systems

Author : Igor Boiko
Publisher : Springer Science & Business Media
ISBN 13 : 0817647538
Total Pages : 212 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Discontinuous Control Systems by : Igor Boiko

Download or read book Discontinuous Control Systems written by Igor Boiko and published by Springer Science & Business Media. This book was released on 2008-11-18 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides new insight on the problem of closed-loop performance and oscillations in discontinuous control systems, covering the class of systems that do not necessarily have low-pass filtering properties. The author provides a practical, yet rigorous and exact approach to analysis and design of discontinuous control systems via application of a novel frequency-domain tool: the locus of a perturbed relay system. Presented are a number of practical examples applying the theory to analysis and design of discontinuous control systems from various branches of engineering, including electro-mechanical systems, process control, and electronics. Discontinuous Control Systems is intended for readers who have knowledge of linear control theory and will be of interest to graduate students, researchers, and practicing engineers involved in systems analysis and design.

Frequency-domain Approach To Hopf Bifurcation Analysis: Continuous Time-delayed Systems

Author : Franco Sebastian Gentile
Publisher : World Scientific
ISBN 13 : 9811205485
Total Pages : 393 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Frequency-domain Approach To Hopf Bifurcation Analysis: Continuous Time-delayed Systems by : Franco Sebastian Gentile

Download or read book Frequency-domain Approach To Hopf Bifurcation Analysis: Continuous Time-delayed Systems written by Franco Sebastian Gentile and published by World Scientific. This book was released on 2019-10-07 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations.The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed.

Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis

Author : György Terdik
Publisher : Springer Science & Business Media
ISBN 13 : 1461215528
Total Pages : 275 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis by : György Terdik

Download or read book Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis written by György Terdik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Itô integrals and finally chaotic Wiener-Itô spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.