Fourier Transformation for Pedestrians PDF Download

Author: Tilman Butz
Publisher: Springer
ISBN: 3319169858
Category : Science
Languages : en
Pages : 250

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Book Description
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.

Author: Eleanor Chu
Publisher: CRC Press
ISBN: 1420063642
Category : Mathematics
Languages : en
Pages : 423

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Book Description
Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform

Author: Lokenath Debnath
Publisher: Birkhäuser
ISBN: 3319594338
Category : Mathematics
Languages : en
Pages : 227

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Book Description
This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.

Author: Firdous A. Shah
Publisher: CRC Press
ISBN: 100077161X
Category : Mathematics
Languages : en
Pages : 502

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Book Description
Wavelet Transforms: Kith and Kin serves as an introduction to contemporary aspects of time-frequency analysis encompassing the theories of Fourier transforms, wavelet transforms and their respective offshoots. This book is the first of its kind totally devoted to the treatment of continuous signals and it systematically encompasses the theory of Fourier transforms, wavelet transforms, geometrical wavelet transforms and their ramifications. The authors intend to motivate and stimulate interest among mathematicians, computer scientists, engineers and physical, chemical and biological scientists. The text is written from the ground up with target readers being senior undergraduate and first-year graduate students and it can serve as a reference for professionals in mathematics, engineering and applied sciences. Features Flexibility in the book’s organization enables instructors to select chapters appropriate to courses of different lengths, emphasis and levels of difficulty Self-contained, the text provides an impetus to the contemporary developments in the signal processing aspects of wavelet theory at the forefront of research A large number of worked-out examples are included Every major concept is presented with explanations, limitations and subsequent developments, with emphasis on applications in science and engineering A wide range of exercises are incoporated in varying levels from elementary to challenging so readers may develop both manipulative skills in theory wavelets and deeper insight Answers and hints for selected exercises appear at the end The origin of the theory of wavelet transforms dates back to the 1980s as an outcome of the intriguing efforts of mathematicians, physicists and engineers. Owing to the lucid mathematical framework and versatile applicability, the theory of wavelet transforms is now a nucleus of shared aspirations and ideas.

Author: Karl-Heinz Spatschek
Publisher: John Wiley & Sons
ISBN: 352763813X
Category : Science
Languages : en
Pages : 642

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Book Description
Filling the gap for a treatment of the subject as an advanced course in theoretical physics with a huge potential for future applications, this monograph discusses aspects of these applications and provides theoretical methods and tools for their investigation. Throughout this coherent and up-to-date work the main emphasis is on classical plasmas at high-temperatures, drawing on the experienced author's specialist background. As such, it covers the key areas of magnetic fusion plasma, laser-plasma-interaction and astrophysical plasmas, while also including nonlinear waves and phenomena. For master and PhD students as well as researchers interested in the theoretical foundations of plasma models.

Author: Dimitrij Tschodu
Publisher: Springer Nature
ISBN: 3658328134
Category : Science
Languages : en
Pages : 72

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Book Description
The present essential contains a number of tips for the successful completion of physics studies. What makes it special is the inspiring style of the author, who studied physics himself and knows what he is talking about. Whether it's keeping lecture notes, working on exercise problems or effectively preparing for exams - this book motivates physics students even in difficult phases of their studies and encourages potential first-year students to dare to study natural sciences. This Springer essential is a translation of the original German 1st edition essentials, Wie man effektiv und nachhaltig Physik studiert by Dimitrij Tschodu, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

Author: Ulrich Kubitscheck
Publisher: John Wiley & Sons
ISBN: 3527687726
Category : Medical
Languages : en
Pages : 508

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Book Description
Zu dem Thema gibt es viele Publikationen, die von Experten für Experten geschrieben wurden. Dieses Buch wendet sich insbesondere an Studenten höherer Semester und Forscher, denen das Hintergrundwissen der Physik fehlt, um neuartige Verfahren der Fluoreszenzmikroskopie zu verstehen. Die zweite Auflage wartet mit neuen Kapiteln und einer erweiterten Einführung auf. Der Schwerpunkt liegt auf der hochauflösenden und Einzelmolekül-Mikroskopie. Jedes Kapitel wurde von einem anerkannten Experten des Fachgebiets geschrieben und sorgfältig überarbeitet, um so die Entwicklungen der letzten Jahre wiederzugeben.

Author: Timothy G. Feeman
Publisher: Springer
ISBN: 3319226657
Category : Mathematics
Languages : en
Pages : 205

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Book Description
The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. Extending the ideas of the acclaimed first edition, new material has been adeed to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering, and more. Copious examples and exercises, new computer-based exercises, and additional graphics have been added to further delineate concepts. The use of technology has been revamped throughout with the incorporation of the open source programming environment R to illustrate examples and composition of graphics. All R code is available as extra source material on SpringerLink. From the reviews of the first edition: “This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics to a real-world problem. ...T his book is well written. It serves its purpose of focusing a variety of mathematical topics onto a real-world application that is in its essence mathematics.” –The Journal of Nuclear Medicine, Vol. 51 (12), December, 2010 “This new book by Timothy Feeman, truly intended to be a beginner’s guide, makes the subject accessible to undergraduates with a working knowledge of multivariable calculus and some experience with vectors and matrix methods. ...author handles the material with clarity and grace...” –The Mathematical Association of America, February, 2010

Author: Jundong Wu
Publisher: Springer Nature
ISBN: 9819908906
Category : Technology & Engineering
Languages : en
Pages : 304

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Book Description
This book investigates in detail cutting-edge technologies of underactuated manipulator control, which is a frontier topic in robotics that possesses great significance in energy conservation as well as fault tolerance for industrial applications. It is also the crucial technology associated with systems in special environments, including underwater or aerospace environments. So far, the topic of underactuated manipulator control has attracted engineers and scientists from various disciplines, such as applied physics, material, automation and robotics. Pursuing a holistic approach, the book establishes a fundamental framework for this topic, while emphasizing the importance of design and optimization in the control of underactuated manipulators. Chapters of the book cover a wide variety of manipulator systems, including vertical underactuated manipulator, planar underactuated manipulator with first-order nonholonomic constraint, planar underactuated manipulator with second-order nonholonomic constraint and flexible underactuated manipulator. The book is intended for undergraduate and graduate students that are interested in underactuated manipulators, researchers that investigate the design and optimization for controllers of underactuated manipulators and engineers working with underactuated systems.

Author: Stefan Welzel
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832523456
Category : Science
Languages : en
Pages : 198

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Book Description
Infrared laser absorption spectroscopy (IRLAS) employing both tuneable diode and quantum cascade lasers (TDLs, QCLs) has been applied with both high sensitivity and high time resolution to plasma diagnostics and trace gas measurements. TDLAS combined with a conventional White type multiple pass cell was used to detect up to 13 constituent molecular species in low pressure Ar/H2/N2/O2 and Ar/CH4/N2/O2 microwave discharges, among them the main products such as H2O, NH3, NO and CO, HCN respectively. The hydroxyl radical has been measured in the mid infrared (MIR) spectral range in-situ in both plasmas yielding number densities of between 1011 ... 1012 cm-3. Strong indications of surface dominated formation of either NH3 or N2O and NO were found in the H2-N2-O2 system. In methane containing plasmas a transition between deposition and etching conditions and generally an incomplete oxidation of the precursor were observed. The application of QCLs for IRLAS under low pressure conditions employing the most common tuning approaches has been investigated in detail. A new method of analysing absorption features quantitatively when the rapid passage effect is present is proposed. If power saturation is negligible, integrating the undisturbed half of the line profile yields accurate number densities without calibrating the system. By means of a time resolved analysis of individual chirped QCL pulses the main reasons for increased effective laser line widths could be identified. Apart from the well-known frequency down chirp non-linear absorption phenomena and bandwidth limitations of the detection system may significantly degrade the performance and accuracy of inter pulse spectrometers. The minimum analogue bandwidth of the entire system should normally not fall below 250 MHz. QCLAS using pulsed lasers has been used for highly time resolved measurements in reactive plasmas for the first time enabling a time resolution down to about 100 ns to be achieved. A temperature increase of typically less than 50 K has been established for pulsed DC discharges containing Ar/N2 and traces of NO. The main NO production and depletion reactions have been identified from a comparison of model calculations and time resolved measurements in plasma pulses of up to 100 ms. Considerable NO struction is observed after 5 ... 10 ms due to the impact of N atoms. Finally, thermoelectrically cooled pulsed and continuous wave (cw) QCLs have been employed for high finesse cavity absorption spectroscopy in the MIR. Cavity ring down spectroscopy (CRDS) has been performed with pulsed QCLs and was found to be limited by the intrinsic frequency chirp of the laser suppressing an efficient intensity build-up inside the cavity. Consequently the accuracy and advantage of an absolute internal absorption calibration is not achievable. A room temperature cw QCL was used in a complementary cavity enhanced absorption spectroscopy (CEAS) configuration which was equipped with different cavities of up to 1.3 m length. This spectrometer yielded path lengths of up to 4 km and a noise equivalent absorption down to 4 x 10-8 cm-1Hz-1/2. The corresponding molecular concentration detection limit (e.g. for CH4, N2O and C2H2 at 1303 cm-1/7.66 Aem) was generally below 1 x 1010 cm-3 for 1 s integration times and one order of magnitude less for 30 s integration times. The main limiting factor for achieving even higher sensitivity is the residual mode noise of the cavity. Employing a 0.5 m long cavity the achieved sensitivity was good enough for the selective measurement of trace atmospheric constituents at 2.2 mbar.