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Topic: List of Fourier-related transforms

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List of Fourier-related transforms - Wikipedia, the free encyclopedia This is a list of linear transformations of functions related to the Fourier transform. The usage of all of these transforms is greatly facilitated by the existence of efficient algorithms based on a fast Fourier transform (FFT). Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. en.wikipedia.org /wiki/List_of_Fourier-related_transforms   (276 words)

Mathematical Transforms The discrete-time Fourier transform is related to the Z transform, and can under certain circumstances be viewed as a special case of the Z transform, with convergence inside the unit circle. Because of the similarities between this transform and the Z transform, the implementation in Signals and Systems simply adds rules for those cases where the discrete-time Fourier transform is different, then call the Z transform with the appropriate variable substitution for all other cases. For convenience, the forward and inverse discrete Fourier transforms have a syntax that allows a numeric vector to be passed directly to the transform function, generating a vector output. documents.wolfram.com /applications/signals/MathematicalTransforms.html   (3315 words)

Modified discrete cosine transform - Wikipedia, the free encyclopedia As a lapped transform, the MDCT is a bit unusual compared to other Fourier-related transforms in that it has half as many outputs as inputs (instead of the same number). The modified discrete cosine transform (MDCT) is a Fourier-related transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are 50% overlapped. In principle, x and y could have different window functions, and the window function could also change from one block to the next (especially for the case where data blocks of different sizes are combined), but for simplicity we consider the common case of identical window functions for equal-sized blocks. www.encyclopedia-online.info /MDCT   (1374 words)

Fourier analysis In mathematics, the discrete Fourier transform (DFT), sometimes called the finite Fourier transform, is a Fourier transform widely employed in Digital signal processing and related fields to analyze the frequencies contained in a sampled signal (information theory), solve partial differential equations, and to perform other operations such as convolutions. Such shifted transforms are most often used for symmetric data, to represent different boundary symmetries, and for real-symmetric data they correspond to different forms of the discrete Discrete cosine transform and Discrete sine transform transforms. The discrete Fourier transform can be viewed as a special case of the z-transform, evaluated on the unit circle in the complex plane. read-and-go.hopto.org /Fourier-analysis   (1912 words)

Fourier Transforms in Quantum Physics Fourier transforms are used in many branches of physics and engineering to relate functions described in terms of conjugate variables. A list of the more useful sites we have found to date is given below: you could also go to the library or get out your old math books, but this is more fun. The first search of the web that we did under (Fourier + transform) gave 8358 entries, more than we really need for this course.... venables.asu.edu /quant/fourier.html   (410 words)

Part I: Fourier Transforms and Sampling A unique feature of the discrete Fourier transform, in contrast to the Fourier transform, is that both resulting representations are periodic: f(t) repeats with a period equal to the total sample time N The Fourier Series is a limiting case of the discrete Fourier transform, where the sample interval A Fourier transform is a linear relationship, but this should not be confused with possible non-linearities in the system that produces f(t). www.silcom.com /~aludwig/Signal_processing/Signal_processing.htm   (2731 words)

E-mail List and FTP Site for Fractional Transforms Moderation of the list is not envisaged unless the kind of traffic appearing in the list shows moderation to be absolutely necessary - something that I wouldn't expect to happen for a long time. This is a normal policy in this kind of lists. To request to be included in the list, please send an e-mail message to "frt-request@inesc.pt", indicating your name, e-mail address, regular-mail address and the reasons for your interest to be included. www.csc.fi /math_topics/Mail/NANET95/msg00542.html   (405 words)

2D Fourier Transforms using Java, Part 2 Performing a forward Fourier transform on this surface produces a pair of peaks in the wavenumber spectrum that are symmetrical about the origin at approximately 45 degrees relative to the horizontal axis. Listing 1 also determines and displays the dimensions of the incoming 2D array of data to be transformed. If you understand the material that I have previously published on Fourier transforms in one dimension, this code and these concepts should be a straightforward extension from one dimension to two dimensions. www.developer.com /java/other/article.php/3526241   (9158 words)

FFTW Home Page A preprint on a new FFT algorithm that, following James Van Buskirk, improves upon previous records for the arithmetic complexity of the DFT and related transforms, is: Steven G. Johnson and Matteo Frigo, "A modified split-radix FFT with reduced arithmetic complexity", submitted for publication in April 2005. FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. For general questions about Fourier transforms, see our www.fftw.org   (912 words)

A Student's Guide to Fourier Transforms : With Applications in Physics and Engineering This book provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. Beginning with a brief description of the basic ideas and theorems, the power of the technique is then illustrated by reference to a variety of applications in optics, spectroscopy, telecommunications, acoustics, and computer science. www.allbookstores.com /book/0521468299   (212 words)

sofpat.txt The list does however reflect the nature of software patenting in the United States, and does include software patents from all categories of software for which patents are being sought. The list is not all inclusive, since it depends on what I consider to be a software patent. A series of diskettes with more detailed information on each software patent listed below (full title, number, assignee, abstract, classification, application date) are available at a cost of $595. www.ibiblio.org /patents/txt/sofpat.txt   (1011 words)

FFT Links DFT Introduction by Paul Bourke, describing the discrete Fourier transform in terms of the continuous transform, with examples of the transforms of various functions. Picture Book of Fourier Transforms by Kevin Cowtan gives an interesting graphical tutorial on the interpretation of 2D FFT output, with a special emphasis on crystallography. FFT Sources: This is the list of all the codes that we included in benchFFT, along with links to where they may be downloaded. www.fftw.org /links.html   (986 words)

GNU Scientific Library -- Reference Manual - Fast Fourier Transforms (FFTs) Fast fourier transform algorithms use a divide-and-conquer strategy to factorize the matrix W into smaller sub-matrices, corresponding to the integer factors of the length N. If N can be factorized into a product of integers f_1 f_2... Allowing for the wrap-around of negative times at t=128, and working in units of k/N, the DFT approximates the continuum fourier transform, giving a modulated \sin function. Recursion relations could be used to compute the lookup table faster, but if an application performs many FFTs of the same length then computing the wavetable is a one-off overhead which does not affect the final throughput. panoramix.ift.uni.wroc.pl /knowledge/gsl-ref/gsl-ref_14.html   (3377 words)

Fourier and other Integral Transforms Along with a new Fourier transform algorithm, symbolic integral transforms, which had previously been part of the standard add-ons, have now been moved to the kernel. The fast Fourier transform algorithms also play a part in the multiplication of very high-precision numbers; beyond a certain level of precision, they allow for faster multiplication than the Karatsuba algorithm Mathematica otherwise uses for high-precision multiplication. We can test it by having it transform a matrix containing a quarter of a million random elements. www.wolfram.com /products/mathematica/newin4/new_fourier.html   (117 words)

Powell's Books - Fourier Transforms (Dover Books on Mathematics) by Ian N Sneddon Text presents theory of Fourier transforms and related topics applicable to boundary value problems of physics and engineering. Hankel transforms of the derivatives of a function. Powell's Books - Fourier Transforms (Dover Books on Mathematics) by Ian N Sneddon www.powells.com /cgi-bin/biblio?inkey=4-0486685225-2   (342 words)

Commonly Used Keywords in CIS Authors may also use this list to select keywords that have commonly been used before in CIS, so that the indexing of their article will be somewhat consistent with previous related literature. All keywords assigned by CIS editors appear first, followed by a list of keywords (in brackets) drawn directly from authors. There are about seven thousand unique phrases listed here; the entire list (including words used only once) includes about 24 thousand phrases. www.statindex.org /CIS/homepage/keywords.html   (184 words)

Statistics on the Web Lists a couple of texts as "related book titles", but it's unclear if these books actually refer to this package, or if they just cover some of the methods implemented by the program. List of papers by UCLA Stat faculty, some software demos, and an interesting Hypertext Intro Stat Textbook (currently under construction). A nice list of Java applets from around the web which can be used to explore or illustrate statistical concepts. my.execpc.com /~helberg/statistics.html   (4923 words)

Category:Computer vision - Unipedia Listed here are subjects relating to the field of computer vision and machine vision. While computer vision is seen as an academic discipline, the closely related field of machine vision is focused on its engineering applications. The purpose of computer vision is to program a computer to "understand" a scene or features in an image. www.unipedia.info /Category:Computer_vision.html   (177 words)

Time: Hitoshi Kitada's Home Page The second law of thermodynamics, related to the phenomenological experience of time as explained by science, can be restated to say nature abhors differences, i.e., gradients. Now we are in a position to give a solution of unifying quantum mechanics (QM) and classical mechanics (CM) governed by special theory of relativity, which I have arrived at on February 15, 2001, whose precise formulation is given in time IX paper. The general contours of the relation of quantum theory and relativity theory should be made more explicite: I think this will strengthen the position. www.kitada.com   (7039 words)

Fourier Series and Transform Fourier and trigonometric transforms with complex coefficients regularly varying in mean. Fourier coefficients of Eisenstein series of one complex variable for the special linear group. Convergence for Fourier series solutions of the forced harmonic oscillator II Fay T. International Journal of Mathematical Education in Science and Technology, 1 May 2002, vol. math.fullerton.edu /mathews/c2003/FourierTransformBib/Links/FourierTransformBib_lnk_3.html   (2783 words)

Fourier-Related Transforms, Fast Algorithms and Applications This book discusses new applications of the Fourier transform which is one of the most pervasive ideas in mathematics. www.pcbcafe.com /BOOKS/view_book.php?isbn=0136244122   (54 words)

Amazon.ca: Books: Fourier Transforms in Spectroscopy This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. Addresses all topics related to Fourier transforms and their use in spectroscopy and spectral applications. This book contains a full blown theoretical treatment of how Fourier Transforms are used in spectroscopy. www.amazon.ca /exec/obidos/ASIN/3527402896   (425 words)

Amazon.com: Books: Fourier and Laplace Transforms Fourier and Laplace transforms provide a technique to solve differential equations which frequently occur when translating a physical problem into a mathematical model. This textbook describes in detail the various Fourier and Laplace transforms that are used to analyze problems in mathematics, the natural sciences and engineering. These transforms decompose complicated signals into elementary signals, and are widely used across the spectrum of science and engineering. www.amazon.com /exec/obidos/tg/detail/-/0521534410?v=glance   (571 words)

Software for Manipulating or Displaying NetCDF Data There are over 600 functions and procedures that include routines for use specifically with climate and model data computing, empirical orthogonal functions, Fourier coefficients, wavelets, singular value decomposition, 1-, 2-, and 3-dimensional interpolation, approximation, and regridding, and computer analysis of scalar and vector global geophysical quantities. Stretched rectangular grids (which occur when the stretching along a given coordinate is a function only of the value of that coordinate) can be accommodated by specifying one-dimensional arrays containing the grid-point locations along the stretched coordinate as part of the IVE input data. DX supports a number of non-graphical functions such as point-wise mathematical expressions (e.g., arithmetic, transcendental, boolean, type conversion, etc.), univariate statistics and image processing (e.g., transformation, filter, warp, edge detection, convolution, equalization, blending, morphological operations, etc.). www.unidata.ucar.edu /packages/netcdf/software.html   (9793 words)

Wiley::Handbook of Real-Time Fast Fourier Transforms : Algorithms to Product Testing Fast Fourier Transforms (FFTs) synthesize, recognize,enhance, compress, modify, or analyze signals in products such as Doppler weather radar, CT and MRI scans, AWACS radar, and satellite imaging radar. An all-in-one-source for implementing real-time FFT algorithms of any length, this book will be essential to engineers and other technical innovators who want to stay on the cutting edge of FFT technology. Copyright © 2000-2005 by John Wiley and Sons, Inc. or related companies. www3.interscience.wiley.com:8100 /WileyCDA/WileyTitle/productCd-0780310918.html   (376 words)

The Math Forum - Math Library - Fourier/Wavelets Extensions include the theory of singular integrals, Fourier transforms, and the study of the appropriate function spaces. A paper about Fourier transformations, which decompose or separate a waveform or function into sinusoids of different frequencies that sum to the original waveform. FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data. mathforum.org /library/topics/fourier   (2270 words)

Lexicon List of capitals and larger cities by country List of top-grossing movies in the United States and Canada List of NATO reporting names for hunter-killer and experimental submarines www.glink.net /more_l.html   (266 words)

Links to Other Astronomy and IDL related sites Stuart Colley at University College London (UCL) makes available some of his IDL software dealing with astronomical spectra, including procedures for merging echelle orders, Fourier CLEANing, and temporal variance spectrum (TVS) analysis. The IMAGE spacecraft was launched in March 2000 to study the Earth's magnetosphere, and IDL analysis software includes EUV_IMTOOL, a image processing widget for images from the Extreme Ultraviolet Imager (EUV), and software for the Far-Ultraviolet Imager (FUV). TARA is an IDL widget which was originally developed at Penn State University for for the pre-launch calibration of the AXAF CCD Imaging Spectrometer (ACIS), now aboard the Chandra X-ray observatory, but which is generally useful for studying event data. idlastro.gsfc.nasa.gov /other_url.html   (3364 words)

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