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The Fractional Fourier Transform

Author: Haldun M. Ozaktas

Publisher: John Wiley & Sons

Published: 2001-02-08

Total Pages: 546

ISBN-13:

The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how the fractional Fourier transform has allowed the generalization of the Fourier transform and the notion of the frequency transform. It will serve as the standard reference on Fourier transforms for many years to come.

Fractional Fourier Transform Techniques for Speech Enhancement

Author: Prajna Kunche

Publisher: Springer Nature

Published: 2020-04-16

Total Pages: 110

ISBN-13: 3030427463

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This book explains speech enhancement in the Fractional Fourier Transform (FRFT) domain and investigates the use of different FRFT algorithms in both single channel and multi-channel enhancement systems, which has proven to be an ideal time frequency analysis tool in many speech signal processing applications. The authors discuss the complexities involved in the highly non- stationary signal processing and the concepts of FRFT for speech enhancement applications. The book explains the fundamentals of FRFT as well as its implementation in speech enhancement. Theories of different FRFT methods are also discussed. The book lets readers understand the new fractional domains to prepare them to develop new algorithms. A comprehensive literature survey regarding the topic is also made available to the reader.

The Sparse Fourier Transform

Author: Haitham Hassanieh

Publisher: Morgan & Claypool

Published: 2018-02-27

Total Pages: 279

ISBN-13: 1947487051

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The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications. The fastest algorithm for computing the Fourier transform is the Fast Fourier Transform (FFT), which runs in near-linear time making it an indispensable tool for many applications. However, today, the runtime of the FFT algorithm is no longer fast enough especially for big data problems where each dataset can be few terabytes. Hence, faster algorithms that run in sublinear time, i.e., do not even sample all the data points, have become necessary. This book addresses the above problem by developing the Sparse Fourier Transform algorithms and building practical systems that use these algorithms to solve key problems in six different applications: wireless networks; mobile systems; computer graphics; medical imaging; biochemistry; and digital circuits. This is a revised version of the thesis that won the 2016 ACM Doctoral Dissertation Award.

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

Fractional Processes and Fractional-Order Signal Processing

Author: Hu Sheng

Publisher: Springer Science & Business Media

Published: 2011-10-20

Total Pages: 310

ISBN-13: 144712233X

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Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; introduces FOSP techniques and the fractional signals and fractional systems point of view; details real-world-application examples of FOSP techniques to demonstrate their utility; and provides important background material on Mittag–Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.

Linear Canonical Transforms

Author: John J. Healy

Publisher: Springer

Published: 2015-11-26

Total Pages: 463

ISBN-13: 1493930281

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This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

Local Fractional Integral Transforms and Their Applications

Author: Xiao Jun Yang

Publisher: Academic Press

Published: 2015-10-22

Total Pages: 262

ISBN-13: 0128040327

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Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods

Algorithms for Discrete Fourier Transform and Convolution

Author: Richard Tolimieri

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 363

ISBN-13: 1475738544

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This easily accessible book provides a broad view of the latest developments in the field of fast digital signal processing algorithms. It bridges the gap between DSP algorithms and their implementation on a variety of serial and super computers.

Intelligent Computing Theories and Application

Author: De-Shuang Huang

Publisher: Springer Nature

Published: 2020-10-13

Total Pages: 614

ISBN-13: 3030607992

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This two-volume set of LNCS 12463 and LNCS 12464 constitutes - in conjunction with the volume LNAI 12465 - the refereed proceedings of the 16th International Conference on Intelligent Computing, ICIC 2020, held in Bari, Italy, in October 2020. The 162 full papers of the three proceedings volumes were carefully reviewed and selected from 457 submissions. The ICIC theme unifies the picture of contemporary intelligent computing techniques as an integral concept that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. The theme for this conference is “Advanced Intelligent Computing Methodologies and Applications.” Papers related to this theme are especially solicited, addressing theories, methodologies, and applications in science and technology.

Optical Pattern Recognition

Author: Francis T. S. Yu

Publisher: Cambridge University Press

Published: 1998-06-28

Total Pages: 460

ISBN-13: 9780521465175

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A comprehensive review of optical pattern recognition techniques and implementations, for graduate students and researchers.