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Discrete sine transform

About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.


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Book
01 Sep 1987

215 citations

Proceedings ArticleDOI
15 Mar 1999
TL;DR: This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions and supports confidence that it will be accepted as the definitive definition of this transform.
Abstract: We propose and consolidate a definition of the discrete fractional Fourier transform which generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform (FRT) generalizes the continuous ordinary Fourier Transform. This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The fact that this definition satisfies all the desirable properties expected of the discrete FRT, supports our confidence that it will be accepted as the definitive definition of this transform.

210 citations

Journal ArticleDOI
TL;DR: In this paper, the authors have evaluated and adopted a spectral transform called the discrete cosine transform (DCT), which is a widely used transform for compression of digital images such as MPEG and JPEG, but its use for atmospheric spectral analysis has not yet received widespread attention.
Abstract: For most atmospheric fields, the larger part of the spatial variance is contained in the planetary scales. When examined over a limited area, these atmospheric fields exhibit an aperiodic structure, with large trends across the domain. Trying to use a standard (periodic) Fourier transform on regional domains results in the aliasing of largescale variance into shorter scales, thus destroying all usefulness of spectra at large wavenumbers. With the objective of solving this particular problem, the authors have evaluated and adopted a spectral transform called the discrete cosine transform (DCT). The DCT is a widely used transform for compression of digital images such as MPEG and JPEG, but its use for atmospheric spectral analysis has not yet received widespread attention. First, it is shown how the DCT can be employed for producing power spectra from two-dimensional atmospheric fields and how this technique compares favorably with the more conventional technique that consists of detrending the data before applying a periodic Fourier transform. Second, it is shown that the DCT can be used advantageously for extracting information at specific spatial scales by spectrally filtering the atmospheric fields. Examples of applications using data produced by a regional climate model are displayed. In particular, it is demonstrated how the 2D-DCT spectral decomposition is successfully used for calculating kinetic energy spectra and for separating mesoscale features from large scales.

208 citations

Book
01 Jan 1983
TL;DR: This paper presents a meta-modelling framework for system modeling and analysis in the Time Domain of Discrete-Time Signals and Systems using the Fourier Transform, and some of the techniques used in this framework are described.
Abstract: 1. Signal and System Modeling Concepts. 2. System Modeling and Analysis in the Time Domain. 3. The Fourier Series. 4. The Fourier Transform and Its Applications. 5. The Laplace Transformation. 6. Applications of the Laplace Transform. 7. State-Variable Techniques. 8. Discrete-Time Signals and Systems. 9. Analysis and Design of Digital Filters. 10. The Discrete Fourier Transform and Fast Fourier Transform Algorithms. Appendix A: Comments and Hints on Using MATLAB. Appendix B: Functions of a Complex Variable--Summary of Important Definitions and Theorems. Appendix C: Matrix Algebra. Appendix D: Analog Filters. Appendix E: Mathematical Tables. Appendix F: Answers to Selected Problems. Appendix G: Index of MATLAB Functions Used. Index.

201 citations

Journal ArticleDOI
TL;DR: Presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation, and proposes orthogonal and periodic basic discrete wavelets to get a correct invertibility of this procedure.
Abstract: Presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation. This is done by defining a purely invertible discrete transform, representing a signal either in the time or in the time-frequency domain, as simply as possible with the conventional discrete Fourier transform between the time and the frequency domains. The wavelet concept has been used to build this transform. To get a correct invertibility of this procedure, the authors have proposed orthogonal and periodic basic discrete wavelets. The properties of such a transform are described, and examples on brain-evoked potential signals are given to illustrate the time-frequency filtering possibilities. >

194 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20234
202234
202124
202021
201925
201833