The Information Super Highway concept has gained great popularity recently. If the super highway is to be realised it will almost certainly be built mainly using optical fibres. The British Telecoms research group in this area has long been acknowledged as a leading force in developing optical communications technology. In this book they set out the technology necessary to build the super highway of the future.

The study of vibrations and waves is central to physics and engineering disciplines.This text contains a detailed treatment of vibrations and waves at an introductory level suitable for second and third year students. It builds on first year physics and emphasizes understanding of vibratory motion and waves based on first principles. Since waves appear in almost all branches of physics and engineering, readers will be exposed to many different types of waves; this study aims to draw together their similarities, by examining them in a common language. The book is divided into three parts: Part I contains a preliminary chapter that serves as a review of relevant ideas of mechanics and complex numbers. Part II is devoted to a detailed discussion of vibrations of mechanical systems. This part covers simple harmonic oscillator, coupled oscillators, normal coordinates, beaded string, continuous string, and Fourier series. It concludes with a presentation of stationary solutions of driven finite systems. Part III is concerned with waves, focusing on the discussion of common aspects of all types of waves, and the applications to sound, electromagnetic, and matter waves are illustrated. Finally, relevant examples are provided at the end of the chapters to illustrate the main ideas, and better the reader's understanding.

One of the great twentieth-century achievements in the mechanics of fluids was the full elucidation of the physics of shock waves and the later comprehensive development of understanding of how shock waves propagate (i) through otherwise undisturbed fluid and (ii) in interaction either with solid bodies or with independently generated fluid flows. The interaction problems (ii) were soon found to raise some very special difficulties (beginning with the common formation of "Mach stems" in shock-wave reflection) yet they also turned out to possess enormous scientific interest as well as being highly important in practical applications. For all these reasons the appearance of this book on "Interaction of Shock Waves" by one of the world's major contributors to knowledge in that field is most particularly to be welcomed. It covers all those approaches to the subject which have been found fruitful, and most satisfactorily goes into comprehensive detail about each. At last the important achievements of the leading research workers, experimental as well as theoretical, on shockwave interaction problems are brought together in a single convenient and well written volume. I warmly congratulate the author and the publisher on having performed, for the benefit of everyone interested in the mechanics of fluids, this immensely valuable service.

The origin ofthe International Acoustical Imaging Symposium series can be traced to 1967, when a meeting on acoustical holography was held in C alifornia. In those days, acoustical holography was at the leading edge of research but, as the importance of this subject waned, so the title of the series was changed from Acoustical Holography to Acoustical Imaging in 1978. The early Symposia were held at various venues in the United States. In 1980. the series became international, with the Symposium that year taking place in Cannes in France. The pattern now is to try to met alternately in the USA and in another part of the world so that active researchers everywhere can conveniently attend at a reasonably high frequency. It was a great privilege for us in Bristol in the United Kingdom to be chosen to host the 25th Symposium, which convened on 19 March 2000 and spread over four days. We were blessed not only by good weather, but also by the attendance ofnearly 100 pa rticipants who came from 17 c ountries. A large number of papers were accepted for presentation, either orally or as posters. Whether an oral presentation or a poster, all were considered to have equal merit, and no distinction is made between them in the published proceedings. There were no parallel sessions, so every participant could attend every presentation. The re sultant disciplinary cross fertilisation maintained the t radition of past Symposia.

A great number of scientists in European research institutions is involved in one or more aspects of the multidisciplinary field of signal processing. This book contains concise descriptions of the activities and interests of 379 signal proces sing laboratories from 17 European countries. Its purpose is twofold: to facilitate communications between institutions and individual scientists within the signal pro cessing community - and to give an expose of the combined European signal processing research effort. This publication is the result of a survey which was made in the fall of 1983 by the European Association for Signal Processing EURASIP. EURASIP is a non-profit professional organization which aims at the improvement of communications between groups and individuals working in the field of signal pro cessing in Europe or elsewhere, and to exchange and disseminate information in the field allover the world. EURASIP arranges workshops and conferences, e.g., the European Signal Processing Conferences EUSIPCO, and publishes the journals SIGNAL PROCESSING and SPEECH COMMUNICATION."

Within nonlinear spatio-temporal dynamics, active lattice systems are of relevance to the study of multi-dimensional dynamical systems and the theory of nonlinear waves and dis- sipative structures of extended systems. In this book, the authors deal with basic concepts and models, with methodolo- gies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition bet- ween order and chaos is crucial for synergetic behavior and evolution. The results described in the book have both in- ter- and trans-disciplinary features and a fundamental cha- racter. It is a textbook for graduate courses in nonlinear sciences, including physics, biophysics, biomathematics, bioengineering, neurodynamics, electrical and electronic engineering, mathematical economics, and computer sciences.

This book reports on the 13th International Workshop on Railway Noise (IWRN13), held on September 16-20, 2019, in Ghent, Belgium. It gathers original peer-reviewed papers describing the latest developments in railway noise and vibration, as well as state-of-the-art reviews written by authoritative experts in the field. The different papers cover a broad range of railway noise and vibration topics, such as rolling noise, wheel squeal, noise perception, prediction methods, measurements and monitoring, and vehicle interior noise. Further topics include rail roughness, rail corrugation and grinding, high-speed rail and aerodynamic noise, structure-borne noise, ground-borne noise and vibration, and resilient track forms. Policy, criteria and regulation are also discussed. Offering extensive and timely information to both scientists and engineers, this book will help them in their daily efforts to identify, understand and solve problems related to railway noise and vibration, and to achieve the ultimate goal of reducing the environmental impact of railway systems.

After alm ost three scores of years of basic and applied research, the field of speech processing is, at present, undergoing a rapid growth in terms of both performance and applications and this is fueHed by the advances being made in the areas of microelectronics, computation and algorithm design.Speech processing relates to three aspects of voice communications: -Speech Coding and transmission which is mainly concerned with man-to man voice communication. -Speech Synthesis which deals with machine-to-man communication. -Speech Recognition which is related to man-to-machine communication. Widespread application and use of low-bit rate voice codec.>, synthesizers and recognizers which are all speech processing products requires ideaHy internationally accepted quality assessment and evaluation methods as weH as speech processing standards so that they may be interconnected and used independently of their designers and manufacturers without costly interfaces. This book presents, in a tutorial manner, both fundamental and applied aspects of the above topics which have been prepared by weH-known specialists in their respective areas. The book is based on lectures which were sponsored by AGARD/NATO and delivered by the authors, in several NATO countries, to audiences consisting mainly of academic and industrial R&D engineers and physicists as weH as civil and military C3I systems planners and designers."

This collection brings together the fundamental research in shock focussing and sonoluminescence. The authors report on their studies on shock focussing and related bubble dynamics, as well as their applications in medical science. The destructive action of cavitation bubbles collapsing near boundaries is treated with special reference to kidney stones, demonstrating the capacity of bubbles for causing damage to materials. It is also shown that the shock theory of sonoluminescence plays an important part, as do converging shock and thermal waves emanating from sonoluminescing gas bubbles and upscaling single-bubble sonoluminescence. The book also addresses the current status of shock measurement technique and correlated clinical findings. The interdisciplinary approach of this book makes it relevant for medical doctors, technical researchers of lithotripsy and gas dynamicists.

This book focuses on the mathematical potential and computational efficiency of the Boundary Element Method (BEM) for modeling seismic wave propagation in either continuous or discrete inhomogeneous elastic/viscoelastic, isotropic/anisotropic media containing multiple cavities, cracks, inclusions and surface topography. BEM models may take into account the entire seismic wave path from the seismic source through the geological deposits all the way up to the local site under consideration. The general presentation of the theoretical basis of elastodynamics for inhomogeneous and heterogeneous continua in the first part is followed by the analytical derivation of fundamental solutions and Green's functions for the governing field equations by the usage of Fourier and Radon transforms. The numerical implementation of the BEM is for antiplane in the second part as well as for plane strain boundary value problems in the third part. Verification studies and parametric analysis appear throughout the book, as do both recent references and seminal ones from the past. Since the background of the authors is in solid mechanics and mathematical physics, the presented BEM formulations are valid for many areas such as civil engineering, geophysics, material science and all others concerning elastic wave propagation through inhomogeneous and heterogeneous media. The material presented in this book is suitable for self-study. The book is written at a level suitable for advanced undergraduates or beginning graduate students in solid mechanics, computational mechanics and fracture mechanics.

This book treats important topics in "Acoustic Echo and Noise Control" and reports the latest developments. Methods for enhancing the quality of transmitted speech signals are gaining growing attention in universities and in industrial development laboratories. This book, written by an international team of highly qualified experts, concentrates on the modern and advanced methods.

The study of multiphase flow through porous media is undergoing intense development, mostly due to the recent introduction of new methods. After the profound changes induced by percolation in the eighties, attention is nowadays focused on the pore scale. The physical situation is complex and only recently have tools become available that allow significant progress to be made in the area. This volume on Multiphase Flow in Porous Media, which is also being published as a special issue of the journal Transport in Porous Media, contains contributions on the lattice-Boltzmann technique, the renormalization technique, and semi-phenomenological studies at the pore level. Attention is mostly focused on two- and three-phase flows. These techniques are of tremendous importance for the numerous applications of multiphase flows in oil fields, unsaturated soils, the chemical industry, and environmental sciences.

The book presents a broad-scope analysis of piezoelectric electromechanical transducers and the related aspects of practical transducer design for underwater applications. It uses an energy method for analyzing transducer problems that provides the physical insight important for the understanding of electromechanical devices. Application of the method is first illustrated with transducer examples that can be modeled as systems with a single degree of freedom, (such as spheres, short cylinders, bars and flexural disks and plates made of piezoelectric ceramics). Thereupon, transducers are modeled as devices with multiple degrees of freedom. In all these cases, results of modeling are presented in the form of equivalent electromechanical circuits convenient for the calculation of the transducers' operational characteristics. Special focus is made on the effects of coupled vibrations in mechanical systems on transducer performance. The book also provides extensive coverage of acoustic radiation including acoustic interaction between the transducers. The book is inherently multidisciplinary. It provides essential background regarding the vibration of elastic passive and piezoelectric bodies, piezoelectricity, acoustic radiation, and transducer characterization. Scientists and engineers working in the field of electroacoustics and those involved in education in the field will find this material useful not only for underwater acoustics, but also for electromechanics, energy conversion and medical ultrasonics. Part I contains an introduction to the energy method illustrated with examples of one degree of freedom transducers. It is self-sufficient and can be read independently.

158 2. Wiener Filtering 159 3. Speech Enhancement by Short-Time Spectral Modification 3. 1 Short-Time Fourier Analysis and Synthesis 159 160 3. 2 Short-Time Wiener Filter 161 3. 3 Power Subtraction 3. 4 Magnitude Subtraction 162 3. 5 Parametric Wiener Filtering 163 164 3. 6 Review and Discussion Averaging Techniques for Envelope Estimation 169 4. 169 4. 1 Moving Average 170 4. 2 Single-Pole Recursion 170 4. 3 Two-Sided Single-Pole Recursion 4. 4 Nonlinear Data Processing 171 5. Example Implementation 172 5. 1 Subband Filter Bank Architecture 172 173 5. 2 A-Posteriori-SNR Voice Activity Detector 5. 3 Example 175 6. Conclusion 175 Part IV Microphone Arrays 10 Superdirectional Microphone Arrays 181 Gary W. Elko 1. Introduction 181 2. Differential Microphone Arrays 182 3. Array Directional Gain 192 4. Optimal Arrays for Spherically Isotropic Fields 193 4. 1 Maximum Gain for Omnidirectional Microphones 193 4. 2 Maximum Directivity Index for Differential Microphones 195 4. 3 Maximimum Front-to-Back Ratio 197 4. 4 Minimum Peak Directional Response 200 4. 5 Beamwidth 201 5. Design Examples 201 5. 1 First-Order Designs 202 5. 2 Second-Order Designs 207 5. 3 Third-Order Designs 216 5. 4 Higher-Order designs 221 6. Optimal Arrays for Cylindrically Isotropic Fields 222 6. 1 Maximum Gain for Omnidirectional Microphones 222 6. 2 Optimal Weights for Maximum Directional Gain 224 6. 3 Solution for Optimal Weights for Maximum Front-to-Back Ratio for Cylindrical Noise 225 7. Sensitivity to Microphone Mismatch and Noise 230 8.

Information is a core concept in animal communication: individuals routinely produce, acquire, process and store information, which provides the basis for their social life. This book focuses on how animal acoustic signals code information and how this coding can be shaped by various environmental and social constraints. Taking birds and mammals, including humans, as models, the authors explore such topics as communication strategies for "public" and "private" signaling, static and dynamic signaling, the diversity of coded information and the way information is decoded by the receiver. The book appeals to a wide audience, ranging from bioacousticians, ethologists and ecologists to evolutionary biologists. Intended for students and researchers alike, it promotes the idea that Shannon and Weaver's Mathematical Theory of Communication still represents a strong framework for understanding all aspects of the communication process, including its dynamic dimensions.

This open access textbook, like Rayleigh's classic Theory of Sound, focuses on experiments and on approximation techniques rather than mathematical rigor. The second edition has benefited from comments and corrections provided by many acousticians, in particular those who have used the first edition in undergraduate and graduate courses. For example, phasor notation has been added to clearly distinguish complex variables, and there is a new section on radiation from an unbaffled piston. Drawing on over 40 years of teaching experience at UCLA, the Naval Postgraduate School, and Penn State, the author presents a uniform methodology, based on hydrodynamic fundamentals for analysis of lumped-element systems and wave propagation that can accommodate dissipative mechanisms and geometrically-complex media. Five chapters on vibration and elastic waves highlight modern applications, including viscoelasticity and resonance techniques for measurement of elastic moduli, while introducing analytical techniques and approximation strategies that are revisited in nine subsequent chapters describing all aspects of generation, transmission, scattering, and reception of waves in fluids. Problems integrate multiple concepts, and several include experimental data to provide experience in choosing optimal strategies for extraction of experimental results and their uncertainties. Fundamental physical principles that do not ordinarily appear in other acoustics textbooks, like adiabatic invariance, similitude, the Kramers-Kronig relations, and the equipartition theorem, are shown to provide independent tests of results obtained from numerical solutions, commercial software, and simulations. Thanks to the Veneklasen Research Foundation, this popular textbook is now open access, making the e-book available for free download worldwide. Provides graduate-level treatment of acoustics and vibration suitable for use in courses, for self-study, and as a reference Highlights fundamental physical principles that can provide independent tests of the validity of numerical solutions, commercial software, and computer simulations Demonstrates approximation techniques that greatly simplify the mathematics without a substantial decrease in accuracy Incorporates a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation Emphasizes actual applications as examples of topics explained in the text Includes realistic end-of-chapter problems, some including experimental data, as well as a Solutions Manual for instructors. Features "Talk Like an Acoustician" boxes to highlight key terms introduced in the text.

This fully updated edition of the classic reference in its field keeps professionals current with the latest technology and techniques in transmission of digital signals. Unlike other references on the subject, this volume is written specifically for engineers and focuses on practical systems and their application in actual design and implementation. It covers systems used throughout the world in chapters detailing the latest on basic system design, baseband transmissions, and digital radio and cable systems. Every chapter from the previous edition has been updated, and new information has been added on: Fiber-optic transmission and digital transmission networks; New digital transmission networks - including private-line, public, and personal communication networks - and integrated services digital networks; Trellis-coded modulation, spread spectrum, digital cross-connect systems, and source codes. Areas covered include analog-to-digital conversion, time-division multiplexing, digital modulation, network synchronization, and how to test, monitor, and control transmission systems. Extensive design examples and references drawn from common carriers, manufacturers, and the author's own experience clarify real-life applications in actual systems. The latest standards published by the CCITT, CCIR, and ANSI are provided, and many new sample problems in each chapter build understanding and expertise. Since digital transmission is used by virtually all communications systems today, this new edition is an essential refeence for all engineers, operators, supervisors, and managers who work in systems testing, operations, maintenance, planning, and research and development. It will also meet the needs of students taking digital communications courses.

This book explores the fascinating and intimate relationship between music and physics. Over millennia, the playing of, and listening to music have stimulated creativity and curiosity in people all around the globe. Beginning with the basics, the authors first address the tonal systems of European-type music, comparing them with those of other, distant cultures. They analyze the physical principles of common musical instruments with emphasis on sound creation and particularly charisma. Modern research on the psychology of musical perception - the field known as psychoacoustics - is also described. The sound of orchestras in concert halls is discussed, and its psychoacoustic effects are explained. Finally, the authors touch upon the role of music for our mind and society. Throughout the book, interesting stories and anecdotes give insights into the musical activities of physicists and their interaction with composers and musicians.

This book is devoted to recent developments in the field of rotating fluids, in particular the study of Taylor--Couette flow, spherical Couette flow, planar Couette flow, as well as rotating annulus flow. Besides a comprehensive overview of the current state of the art, possible future directions in this research field are investigated. The first part of this volume presents several new results in the classical Taylor--Couette system covering diverse theoretical, experimental and numerical work on bifurcation theory, influence of boundary conditions, counter-rotating flows, spiral vortices and many others. The second part focuses on spherical Couette flows, including isothermal flows, thermal convective motion, as well as magnetohydrodynamics in spherical shells. The remaining parts are devoted to Goertler vortices, rotating annulus flows, as well as superfluid Couette flows. The present book will be of interest to all researchers and graduate students working actively in the field.

A great deal of modern communications equipment is being converted from analog to digital technology. This timely book explains many of the important concepts related to digital signal processing in easy-to-understand discussions of communications techniques, data transmission, filters, and hardware. Readers are given practical information on how to apply theory and algorithms to the design of radio receivers and transmitters. Among the areas discussed are analog to digital conversion - with emphasis on noise and distortion performance; manipulation of complex signals - positive and negative frequencies, plus Hilbert transformers; digital filters - guidelines for performance in communications, plus decimation and interpolation; hardware - multiplier accumulators, fast Fourier transform processors, digital signal processors, data flow techniques in equipment, and hardware simulation and testing; and speech processing - linear predictive coding (LPC), code excited linear predictive coding (CELP), and how to digitize speech at low data rates. Development of algorithms for oscillators, detectors, modulators, automatic gain control circuits, and other devices is clearly explained. Specific algorithms are provided for AM modulation, frequency modulation, FM detection, threshold extension, audio compression, automatic gain control, and squelch circuitry. Explanations of basic concepts of digital signal processing and data transmission are accompanied by reviews of signal representations, sampling, convolution, and z-transforms. Extensive real-world examples contribute to expertise in many facets of incorporating digital technology into devices. This hands-on treatment of DSP will helpcommunications engineers upgrade their skills in digital signal processing and make a smooth transition into the design of more advanced systems. It also meets the needs of students who want to bolster their knowledge in communications.

Sound, devoid of meaning, would not matter to us. It is the information sound conveys that helps the brain to understand its environment. Sound and its underlying meaning are always associated with time and space. There is no sound without spatial properties, and the brain always organizes this information within a temporal-spatial framework. This book is devoted to understanding the importance of meaning for spatial and related further aspects of hearing, including cross-modal inference. People, when exposed to acoustic stimuli, do not react directly to what they hear but rather to what they hear means to them. This semiotic maxim may not always apply, for instance, when the reactions are reflexive. But, where it does apply, it poses a major challenge to the builders of models of the auditory system. Take, for example, an auditory model that is meant to be implemented on a robotic agent for autonomous search-&-rescue actions. Or think of a system that can perform judgments on the sound quality of multimedia-reproduction systems. It becomes immediately clear that such a system needs * Cognitive capabilities, including substantial inherent knowledge * The ability to integrate information across different sensory modalities To realize these functions, the auditory system provides a pair of sensory organs, the two ears, and the means to perform adequate preprocessing of the signals provided by the ears. This is realized in the subcortical parts of the auditory system. In the title of a prior book, the term Binaural Listening is used to indicate a focus on sub-cortical functions. Psychoacoustics and auditory signal processing contribute substantially to this area. The preprocessed signals are then forwarded to the cortical parts of the auditory system where, among other things, recognition, classification, localization, scene analysis, assignment of meaning, quality assessment, and action planning take place. Also, information from different sensory modalities is integrated at this level. Between sub-cortical and cortical regions of the auditory system, numerous feedback loops exist that ultimately support the high complexity and plasticity of the auditory system. The current book concentrates on these cognitive functions. Instead of processing signals, processing symbols is now the predominant modeling task. Substantial contributions to the field draw upon the knowledge acquired by cognitive psychology. The keyword Binaural Understanding in the book title characterizes this shift. Both books, The Technology of Binaural Listening and the current one, have been stimulated and supported by AABBA, an open research group devoted to the development and application of models of binaural hearing. The current book is dedicated to technologies that help explain, facilitate, apply, and support various aspects of binaural understanding. It is organized into five parts, each containing three to six chapters in order to provide a comprehensive overview of this emerging area. Each chapter was thoroughly reviewed by at least two anonymous, external experts. The first part deals with the psychophysical and physiological effects of Forming and Interpreting Aural Objects as well as the underlying models. The fundamental concepts of reflexive and reflective auditory feedback are introduced. Mechanisms of binaural attention and attention switching are covered-as well as how auditory Gestalt rules facilitate binaural understanding. A general blackboard architecture is introduced as an example of how machines can learn to form and interpret aural objects to simulate human cognitive listening. The second part, Configuring and Understanding Aural Space, focuses on the human understanding of complex three-dimensional environments-covering the psychological and biological fundamentals of auditory space formation. This part further addresses the human mechanisms used to process information and interact in complex reverberant environments, such as concert halls and forests, and additionally examines how the auditory system can learn to understand and adapt to these environments. The third part is dedicated to Processing Cross-Modal Inference and highlights the fundamental human mechanisms used to integrate auditory cues with cues from other modalities to localize and form perceptual objects. This part also provides a general framework for understanding how complex multimodal scenes can be simulated and rendered. The fourth part, Evaluating Aural-scene Quality and Speech Understanding, focuses on the object-forming aspects of binaural listening and understanding. It addresses cognitive mechanisms involved in both the understanding of speech and the processing of nonverbal information such as Sound Quality and Quality-of- Experience. The aesthetic judgment of rooms is also discussed in this context. Models that simulate underlying human processes and performance are covered in addition to techniques for rendering virtual environments that can then be used to test these models. The fifth part deals with the Application of Cognitive Mechanisms to Audio Technology. It highlights how cognitive mechanisms can be utilized to create spatial auditory illusions using binaural and other 3D-audio technologies. Further, it covers how cognitive binaural technologies can be applied to improve human performance in auditory displays and to develop new auditory technologies for interactive robots. The book concludes with the application of cognitive binaural technologies to the next generation of hearing aids.

In this thesis, the author develops new high-power millimeter wave techniques for measuring the hyperfine structure of positronium (Ps-HFS) directly for the first time in the world. Indirect measurement of Ps-HFS in the literature might have systematic uncertainties related to the use of a static magnetic field. Development of the millimeter wave devices supports the precise determination of Ps-HFS by directly measuring the Breit-Wigner resonant transition from o-Ps to p-Ps without the magnetic field. At the same time, the width of the measured Breit-Wigner resonance directly provides the lifetime of p-Ps. This measurement is the first precise spectroscopic experiment involving the magnetic dipole transition and high-power millimeter waves. The development of a gyrotron and a Fabry-Perot cavity is described as providing an effective power of over 20 kW, which is required to cause the direct transition from o-Ps to p-Ps. Those values measured by the newly developed millimeter wave device pave the way for examining the discrepancy observed between conventional indirect experiments on Ps-HFS and the theoretical predictions of Quantum Electrodynamics.

This book presents a technical solution to ensuring the noise immunity of navigation systems in civil aviation aircrafts at the stages of their terminal procedures. It highlights instrumental precision approaches to landing and landing in automatic mode using satellite and inertial radio navigation systems and ground-based augmentation used as the primary means, in accordance with the ICAO requirements. The book is intended for engineering and technical specialists engaged in the development, manufacture and operation of on-board radio electronic systems of aircrafts and ground-based radio engineering support for flights, as well as graduate students and senior students of radio engineering specialties. It is also useful for professionals whose activities are related to air traffic control.

Recent Developments in Time-Frequency Analysis brings together in one place important contributions and up-to-date research results in this fast moving area. Recent Developments in Time-Frequency Analysis serves as an excellent reference, providing insight into some of the most challenging research issues in the field.

This is an introduction to noise, describing fundamental noise sources and basic circuit analysis, discussing characterization of low-frequency noise and offering practical advice that bridges concepts of noise theory and modelling, characterization, CMOS technology and circuits. The text offers the latest research, reviewing the most recent publications and conference presentations. The book concludes with an introduction to noise in analog/RF circuits and describes how low-frequency noise can affect these circuits.