**Download Discrete Cosine And Sine Transforms Book PDF**

Download full Discrete Cosine And Sine Transforms books PDF, EPUB, Tuebl, Textbook, Mobi or read online Discrete Cosine And Sine Transforms anytime and anywhere on any device. Get free access to the library by create an account, fast download and ads free. We cannot guarantee that every book is in the library.

## Discrete Cosine and Sine Transforms

- Author : Vladimir Britanak,Patrick C. Yip,K. R Rao
- Publisher :Unknown
- Release Date :2010-07-28
- Total pages :368
- ISBN : 0080464645

**Summary :** The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Loéve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Loéve transform (KLT) Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations Comprehensive list of additional references reflecting recent/latest developments in the efficient implementations of DCTs and DSTs mainly one-, two-, three- and multi-dimensional fast DCT/DST algorithms including the recent active research topics for the time period from 1990 up to now

## Discrete Cosine and Sine Transforms

- Author : Vladimir Britanak,Pat C. Yip,Ping Yip,Kamisetty Ramamohan Rao
- Publisher :Unknown
- Release Date :2007
- Total pages :349
- ISBN : 0123736242

**Summary :** The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhunen-Loéve transform (KLT), with the emphasis on fast algorithms (one-dimensional and two-dimensional) and integer approximations of DCTs and DSTs for their efficient implementations in the integer domain. DCTs and DSTs are real-valued transforms that map integer-valued signals to floating-point coefficients. To eliminate the floating-point operations, various methods of integer approximations have been proposed to construct and flexibly generate a family of integer DCT and DST transforms with arbitrary accuracy and performance. The integer DCTs/DSTs with low-cost and low-powered implementation can replace the corresponding real-valued transforms in wireless and satellite communication systems as well as portable computing applications. The book is essentially a detailed excursion on orthogonal/orthonormal DCT and DST matrices, their matrix factorizations and integer aproximations. It is hoped that the book will serve as a valuable reference for industry, academia and research institutes in developing integer DCTs and DSTs as well as an inspiration source for further advanced research. Key Features - Presentation of the complete set of DCTs and DSTs in context of entire class of discrete unitary sinusoidal transforms: the origin, definitions, general mathematical properties, mutual relationships and relations to the optimal Karhunen-Loéve transform (KLT). - Unified treatment with the fast implementations of DCTs and DSTs: the fast rotation-based algorithms derived in the form of recursive sparse matrix factorizations of a transform matrix including one- and two-dimensional cases. - Detailed presentation of various methods and design approaches to integer approximation of DCTs and DSTs utilizing the basic concepts of linear algebra, matrix theory and matrix computations leading to their efficient multiplierless real-time implementations, or in general reversible integer-to-integer implementations. - Comprehensive list of additional references reflecting recent/latest developments in the efficient implementations of DCTs and DSTs mainly one-, two-, three- and multi-dimensional fast DCT/DST algorithms including the recent active research topics for the time period from 1990 up to now.

## Discrete Cosine Transform, Second Edition

- Author : Humberto Ochoa-Dominguez,K. R. Rao
- Publisher :Unknown
- Release Date :2019-04-18
- Total pages :358
- ISBN : 9781351396486

**Summary :** Many new DCT-like transforms have been proposed since the first edition of this book. For example, the integer DCT that yields integer transform coefficients, the directional DCT to take advantage of several directions of the image and the steerable DCT. The advent of higher dimensional frames such as UHDTV and 4K-TV demand for small and large transform blocks to encode small or large similar areas respectively in an efficient way. Therefore, a new updated book on DCT, adapted to the modern days, considering the new advances in this area and targeted for students, researchers and the industry is a necessity.

## Linear Difference Equations with Discrete Transform Methods

- Author : A.J. Jerri
- Publisher :Unknown
- Release Date :2013-03-09
- Total pages :442
- ISBN : 9781475756579

**Summary :** This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is in tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar meth ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solv ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other meth ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended eas ily to solve partial difference equations associated with initial and/or boundary value problems.

## Discrete Cosine Transform

- Author : K. Ramamohan Rao,P. Yip
- Publisher :Unknown
- Release Date :2014-06-28
- Total pages :512
- ISBN : 9780080925349

**Summary :** This is the first comprehensive treatment of the theoretical aspects of the discrete cosine transform (DCT), which is being recommended by various standards organizations, such as the CCITT, ISO etc., as the primary compression tool in digital image coding. The main purpose of the book is to provide a complete source for the user of this signal processing tool, where both the basics and the applications are detailed. An extensive bibliography covers both the theory and applications of the DCT. The novice will find the book useful in its self-contained treatment of the theory of the DCT, the detailed description of various algorithms supported by computer programs and the range of possible applications, including codecs used for teleconferencing, videophone, progressive image transmission, and broadcast TV. The more advanced user will appreciate the extensive references. Tables describing ASIC VLSI chips for implementing DCT, and motion estimation and details on image compression boards are also provided.

## Signal Analysis and Prediction

- Author : Ales Prochazka,Nicholas Kingsbury,P.J.W. Payner,J. Uhlir
- Publisher :Unknown
- Release Date :1998-12-23
- Total pages :502
- ISBN : 0817640428

**Summary :** Methods of signal analysis represent a broad research topic with applications in many disciplines, including engineering, technology, biomedicine, seismography, eco nometrics, and many others based upon the processing of observed variables. Even though these applications are widely different, the mathematical background be hind them is similar and includes the use of the discrete Fourier transform and z-transform for signal analysis, and both linear and non-linear methods for signal identification, modelling, prediction, segmentation, and classification. These meth ods are in many cases closely related to optimization problems, statistical methods, and artificial neural networks. This book incorporates a collection of research papers based upon selected contri butions presented at the First European Conference on Signal Analysis and Predic tion (ECSAP-97) in Prague, Czech Republic, held June 24-27, 1997 at the Strahov Monastery. Even though the Conference was intended as a European Conference, at first initiated by the European Association for Signal Processing (EURASIP), it was very gratifying that it also drew significant support from other important scientific societies, including the lEE, Signal Processing Society of IEEE, and the Acoustical Society of America. The organizing committee was pleased that the re sponse from the academic community to participate at this Conference was very large; 128 summaries written by 242 authors from 36 countries were received. In addition, the Conference qualified under the Continuing Professional Development Scheme to provide PD units for participants and contributors.

## Orthogonal Transforms for Digital Signal Processing

- Author : N. Ahmed,K.R. Rao
- Publisher :Unknown
- Release Date :2012-12-06
- Total pages :264
- ISBN : 9783642454509

**Summary :** This book is intended for those wishing to acquire a working knowledge of orthogonal transforms in the area of digital signal processing. The authors hope that their introduction will enhance the opportunities for interdiscipli nary work in this field. The book consists of ten chapters. The first seven chapters are devoted to the study of the background, motivation and development of orthogonal transforms, the prerequisites for which are a basic knowledge of Fourier series transform (e.g., via a course in differential equations) and matrix al gebra. The last three chapters are relatively specialized in that they are di rected toward certain applications of orthogonal transforms in digital signal processing. As such, a knowlegde of discrete probability theory is an essential additional prerequisite. A basic knowledge of communication theory would be helpful, although not essential. Much of the material presented here has evolved from graduate level courses offered by the Departments of Electrical Engineering at Kansas State University and the University of Texas at Arlington, during the past five years. With advanced graduate students, all the material was covered in one semester. In the case of first year graduate students, the material in the first seven chapters was covered in one semester. This was followed by a prob lems project-oriented course directed toward specific applications, using the material in the last three chapters as a basis.

## Digital Television

- Author : Walter Fischer
- Publisher :Unknown
- Release Date :2004-03-05
- Total pages :384
- ISBN : 3540011552

**Summary :** Digital Television deals with all present-day TV transmission methods, i.e. MPEG, DVB, ATSC and ISDB-T. The DVD Video is also discussed to some extent. The discussion is focussed on dealing with these subjects in as practical a way as possible. Although mathematical formulations are used, they are in most cases only utilized to supplement the text. The book also contains chapters dealing with basic concepts such as digital modulation or transformations into the frequency domain. A major emphasis is placed on the measuring techniques used on these various digital TV signals. Practical examples and hints concerning measurement are provided. The book starts with the analog TV baseband signal and then continues with the MPEG-2 data stream, digital video, digital audio and the compression methods. After an excursion into the digital modulation methods, all the mentioned transmission methods are discussed in detail. Interspersed between these are found the chapters on the relevant measuring technique.

## Integral and Discrete Transforms with Applications and Error Analysis

- Author : Abdul Jerri
- Publisher :Unknown
- Release Date :1992-06-11
- Total pages :848
- ISBN : 0824782526

**Summary :** This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

## The Transform and Data Compression Handbook

- Author : Kamisetty Ramam Rao,Patrick C. Yip
- Publisher :Unknown
- Release Date :2018-10-03
- Total pages :408
- ISBN : 9781420037388

**Summary :** Data compression is one of the main contributing factors in the explosive growth in information technology. Without it, a number of consumer and commercial products, such as DVD, videophone, digital camera, MP3, video-streaming and wireless PCS, would have been virtually impossible. Transforming the data to a frequency or other domain enables even more efficient compression. By illustrating this intimate link, The Transform and Data Compression Handbook serves as a much-needed handbook for a wide range of researchers and engineers. The authors describe various discrete transforms and their applications in different disciplines. They cover techniques, such as adaptive quantization and entropy coding, that result in significant reduction in bit rates when applied to the transform coefficients. With clear and concise presentations of the ideas and concepts, as well as detailed descriptions of the algorithms, the authors provide important insight into the applications and their limitations. Data compression is an essential step towards the efficient storage and transmission of information. The Transform and Data Compression Handbook provides a wealth of information regarding different discrete transforms and demonstrates their power and practicality in data compression.

## Transforms and Applications Handbook

- Author : Alexander D. Poularikas
- Publisher :Unknown
- Release Date :2018-09-03
- Total pages :911
- ISBN : 9781420066531

**Summary :** Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.

## The DFT

- Author : William L. Briggs,Van Emden Henson
- Publisher :Unknown
- Release Date :1995-01-01
- Total pages :434
- ISBN : 9780898713428

**Summary :** 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.

## Transforms and Applications Handbook

- Author : Alexander D. Poularikas
- Publisher :Unknown
- Release Date :2018-09-03
- Total pages :911
- ISBN : 9781420066531

**Summary :** Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.

## Fast Fourier Transforms

- Author : James S. Walker
- Publisher :Unknown
- Release Date :2017-11-22
- Total pages :464
- ISBN : 9781351448871

**Summary :** This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :

## Quantitative Methods of Data Analysis for the Physical Sciences and Engineering

- Author : Douglas G. Martinson
- Publisher :Unknown
- Release Date :2018-09-30
- Total pages :598
- ISBN : 9781107029767

**Summary :** Provides thorough and comprehensive coverage of new and important quantitative methods in data science, for graduate students and practitioners.

## Handbook of Formulas and Tables for Signal Processing

- Author : Alexander D. Poularikas
- Publisher :Unknown
- Release Date :1998-09-29
- Total pages :864
- ISBN : 1420049704

**Summary :** Signal processing is a broad and timeless area. The term "signal" includes audio, video, speech, image, communication, geophysical, sonar, radar, medical, and more. Signal processing applies to the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals. Handbook of Formulas and Tables for Signal Processing a must-have reference for all engineering professionals involved in signal and image processing. Collecting the most useful formulas and tables - such as integral tables, formulas of algebra, formulas of trigonometry - the text includes: Material for the deterministic and statistical signal processing areas Examples explaining the use of the given formula Numerous definitions Many figures that have been added to special chapters Handbook of Formulas and Tables for Signal Processing brings together - in one textbook - all the equations necessary for signal and image processing for professionals transforming anything from a physical to a manipulated form, creating a new standard for any person starting a future in the broad, extensive area of research.

## Discrete Cosine Transform, Second Edition

- Author : Humberto Ochoa-Dominguez,K. R. Rao
- Publisher :Unknown
- Release Date :2019-04-18
- Total pages :358
- ISBN : 9781351396479

**Summary :** Many new DCT-like transforms have been proposed since the first edition of this book. For example, the integer DCT that yields integer transform coefficients, the directional DCT to take advantage of several directions of the image and the steerable DCT. The advent of higher dimensional frames such as UHDTV and 4K-TV demand for small and large transform blocks to encode small or large similar areas respectively in an efficient way. Therefore, a new updated book on DCT, adapted to the modern days, considering the new advances in this area and targeted for students, researchers and the industry is a necessity.

## The Discrete Fourier Transform

- Author : D. Sundararajan
- Publisher :Unknown
- Release Date :2001
- Total pages :374
- ISBN : 9789810245214

**Summary :** 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 Walsh-Hadamard 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?www.wspc.com/others/software/4610/?The above links should be replaced with?www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zip?

## Applications in Electronics Pervading Industry, Environment and Society

- Author : Sergio Saponara
- Publisher :Unknown
- Release Date :2021
- Total pages :229
- ISBN : 9783030372774

**Summary :**

## Discrete Fourier Analysis and Wavelets

- Author : S. Allen Broughton,Kurt Bryan
- Publisher :Unknown
- Release Date :2018-04-03
- Total pages :464
- ISBN : 9781119258247

**Summary :** Delivers an appropriate mix of theory and applications to help readers understand the process and problems of image and signal analysis Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing. Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; spectrograms; frames; filter banks; lifting schemes; and wavelets. Discrete Fourier Analysis and Wavelets introduces a new chapter on frames—a new technology in which signals, images, and other data are redundantly measured. This redundancy allows for more sophisticated signal analysis. The new coverage also expands upon the discussion on spectrograms using a frames approach. In addition, the book includes a new chapter on lifting schemes for wavelets and provides a variation on the original low-pass/high-pass filter bank approach to the design and implementation of wavelets. These new chapters also include appropriate exercises and MATLAB® projects for further experimentation and practice. • Features updated and revised content throughout, continues to emphasize discreteand digital methods, and utilizes MATLAB® to illustrate these concepts • Contains two new chapters on frames and lifting schemes, which take into account crucial new advances in the field of signal and image processing • Expands the discussion on spectrograms using a frames approach, which is an ideal method for reconstructing signals after information has been lost or corrupted (packet erasure) • Maintains a comprehensive treatment of linear signal processing for audio and image signals with a well-balanced and accessible selection of topics that appeal to a diverse audience within mathematics and engineering • Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods • Supplemented with a companion website containing solution sets and software exploration support for MATLAB and SciPy (Scientific Python) Thoroughly class-tested over the past fifteen years, Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing is an appropriately self-contained book ideal for a one-semester course on the subject. S. Allen Broughton, PhD, is Professor Emeritus of Mathematics at Rose-Hulman Institute of Technology. Dr. Broughton is a member of the American Mathematical Society (AMS) and the Society for the Industrial Applications of Mathematics (SIAM), and his research interests include the mathematics of image and signal processing, and wavelets. Kurt Bryan, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. Dr. Bryanis a member of MAA and SIAM and has authored over twenty peer-reviewed journal articles. div id="_mcePaste" style="position: absolute; left: -10000px; top: 0px; width: 1px; height: 1px; overflow: hidden;"Kurt Bryan, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. Dr. Bryanis a member of MAA and SIAM and has authored over twenty peer-reviewed journal articles.Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and r

## Fourier Analysis

- Author : Source Wikipedia
- Publisher :Unknown
- Release Date :2013-09
- Total pages :194
- ISBN : 1230550585

**Summary :** Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 192. Chapters: Nyquist-Shannon sampling theorem, Discrete cosine transform, Discrete Fourier transform, Bessel function, Dirac delta function, Autocorrelation, Laplace's equation, Convolution, Topological group, Banach algebra, List of Fourier-related transforms, Frequency spectrum, Haar measure, Laplace transform, Fourier transform spectroscopy, Convolution theorem, Harmonic function, Basis function, Periodic function, Whittaker-Shannon interpolation formula, Fundamental frequency, Laplace operator, Modified discrete cosine transform, Fourier optics, Spherical harmonics, LTI system theory, Window function, Pontryagin duality, Multiplier, Discrete-time Fourier transform, Modulus of continuity, Sobolev space, Almost periodic function, Carleson's theorem, Ewald summation, Relations between Fourier transforms and Fourier series, Poisson summation formula, Analytic signal, Reciprocal lattice, Fractional Fourier transform, Solid harmonics, Spin-weighted spherical harmonics, Short-time Fourier transform, Uncertainty principle for the short-time Fourier transform, Riesz-Thorin theorem, Discrete Hartley transform, Linear canonical transformation, SigSpec, Discrete sine transform, Chirplet transform, Homogeneous distribution, Peter-Weyl theorem, Bilinear time-frequency distribution, Metaplectic group, Bloch wave - MoM method, Marcinkiewicz interpolation theorem, Spectral leakage, Orthonormal basis, Paley-Wiener theorem, Overlap-add method, FBI transform, Unit circle, Fourier inversion theorem, DFT matrix, Poisson kernel, Interpolation space, Littlewood-Paley theory, Motions in the time-frequency distribution, List of cycles, Parametrix, A derivation of the discrete Fourier transform, Parseval's theorem, Number-theoretic transform, Compact group, Overlap-save method, Set of uniqueness, Multitaper, Convolution power, ..