Discrete and Continuous Fourier Transforms
Discrete and Continuous Fourier Transforms

Author: Eleanor Chu

Publisher: CRC Press

Published: 2008-03-19

Total Pages: 423

ISBN-13: 1420063642

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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

Spectral Audio Signal Processing
Spectral Audio Signal Processing

Author: Julius Orion Smith

Publisher:

Published: 2007

Total Pages: 654

ISBN-13:

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"Spectral Audio Signal Processing is the fourth book in the music signal processing series by Julius O. Smith. One can say that human hearing occurs in terms of spectral models. As a result, spectral models are especially useful in audio applications. For example, with the right spectral model, one can discard most of the information contained in a sound waveform without changing how it sounds. This is the basis of modern audio compression techniques."--Publisher's description.

Mathematics of the Discrete Fourier Transform (DFT)
Mathematics of the Discrete Fourier Transform (DFT)

Author: Julius O. Smith

Publisher: Julius Smith

Published: 2008

Total Pages: 323

ISBN-13: 097456074X

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"The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover

The Discrete Fourier Transform
The Discrete Fourier Transform

Author: D. Sundararajan

Publisher: World Scientific

Published: 2001

Total Pages: 400

ISBN-13: 9789812810298

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This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and WalshOCoHadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Errata(s). Preface, Page viii. OC www.wspc.com/others/software/4610/OCO. The above links should be replaced with. OC www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zipOCO. Contents: The Discrete Sinusoid; The Discrete Fourier Transform; Properties of the DFT; Fundamentals of the PM DFT Algorithms; The u X 1 PM DFT Algorithms; The 2 X 2 PM DFT Algorithms; DFT Algorithms for Real Data OCo I; DFT Algorithms for Real Data OCo II; Two-Dimensional Discrete Fourier Transform; Aliasing and Other Effects; The Continuous-Time Fourier Series; The Continuous-Time Fourier Transform; Convolution and Correlation; Discrete Cosine Transform; Discrete WalshOCoHadamard Transform. Readership: Upper level undergraduate students, graduates, researchers and lecturers in engineering and applied mathematics."

Theory of Discrete and Continuous Fourier Analysis
Theory of Discrete and Continuous Fourier Analysis

Author: H. Joseph Weaver

Publisher: Wiley-Interscience

Published: 1989-01-17

Total Pages: 328

ISBN-13:

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A companion volume to Weaver's Applications of Discrete and Continuous Fourier Analysis (Wiley, 1983). Addresses the theoretical and analytical aspects of Fourier analysis, including topics usually found only in more advanced treatises. Provides background information before going on to cover such topics as existence of the inner product, distribution theory, Fourier series representation of complex functions, properties and behavior of the Fourier transform, Fourier transform of a distribution, physical interpretation of convolution, the fast Fourier transform, sampling a function, and much more. Includes exercises, problems, applications, over 150 illustrations, and a Fourier transform FORTRAN subroutine.

The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing
The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing

Author: Sonali Bagchi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 216

ISBN-13: 1461549256

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The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.

The DFT
The DFT

Author: William L. Briggs

Publisher: SIAM

Published: 1995-01-01

Total Pages: 446

ISBN-13: 0898713420

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This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.

Essential Radio Astronomy
Essential Radio Astronomy

Author: James J. Condon

Publisher: Princeton University Press

Published: 2016-04-05

Total Pages: 376

ISBN-13: 069113779X

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The ideal text for a one-semester course in radio astronomy Essential Radio Astronomy is the only textbook on the subject specifically designed for a one-semester introductory course for advanced undergraduates or graduate students in astronomy and astrophysics. It starts from first principles in order to fill gaps in students' backgrounds, make teaching easier for professors who are not expert radio astronomers, and provide a useful reference to the essential equations used by practitioners. This unique textbook reflects the fact that students of multiwavelength astronomy typically can afford to spend only one semester studying the observational techniques particular to each wavelength band. Essential Radio Astronomy presents only the most crucial concepts—succinctly and accessibly. It covers the general principles behind radio telescopes, receivers, and digital backends without getting bogged down in engineering details. Emphasizing the physical processes in radio sources, the book's approach is shaped by the view that radio astrophysics owes more to thermodynamics than electromagnetism. Proven in the classroom and generously illustrated throughout, Essential Radio Astronomy is an invaluable resource for students and researchers alike. The only textbook specifically designed for a one-semester course in radio astronomy Starts from first principles Makes teaching easier for astronomy professors who are not expert radio astronomers Emphasizes the physical processes in radio sources Covers the principles behind radio telescopes and receivers Provides the essential equations and fundamental constants used by practitioners Supplementary website includes lecture notes, problem sets, exams, and links to interactive demonstrations An online illustration package is available to professors

Music Through Fourier Space
Music Through Fourier Space

Author: Emmanuel Amiot

Publisher: Springer

Published: 2016-10-26

Total Pages: 214

ISBN-13: 3319455818

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This book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients. This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.