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# Topic: Fourier transform

 PlanetMath: Fourier transform So when looking a transform up in a table you should find out how it is defined in that table. The Fourier transform has some important properties, that can be used when solving differential equations. This is version 13 of Fourier transform, born on 2002-04-07, modified 2006-10-30. www.planetmath.org /encyclopedia/FourierTransform.html   (198 words)

 Image Transforms - Fourier Transform The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent. The logarithm of the magnitude of its Fourier transform is homepages.inf.ed.ac.uk /rbf/HIPR2/fourier.htm   (2177 words)

 The Discrete Fourier Transform Fourier analysis is a family of mathematical techniques, all based on decomposing signals into sinusoids. The discrete Fourier transform (DFT) is the family member used with digitized signals. This is the first of four chapters on the real DFT, a version of the discrete Fourier transform that uses real numbers to represent the input and output signals. www.dspguide.com /ch8.htm   (111 words)

 FFTW Home Page 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. The slides from the 7/28/98 talk "The Fastest Fourier Transform in the West," by M. Frigo, are also available, along with the slides from a shorter 1/14/98 talk on the same subject by S. Johnson. 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 fewer arithmetic operations", IEEE Trans. www.fftw.org   (992 words)

 Introduction to the Fourier Transform The Fourier Transform (in this case, the 2D Fourier Transform) is the series expansion of an image function (over the 2D space domain) in terms of "cosine" image (orthonormal) basis functions. By the way, you may have heard of the FFT and wondered if was different from the FT. FFT stands for "Fast" Fourier Transform and is simply a fast algorithm for computing the Fourier Transform. The major effect to notice is that in the transform of the degraded goofy the high frequencies in the horizontal direction have been significantly attenuated. www.cs.unm.edu /~brayer/vision/fourier.html   (2405 words)

 Fourier Transform Properties The Fourier transform is the mathematical relationship between these two representations. If a signal is modified in one domain, it will also be changed in the other domain, although usually not in the same way. These relationships are called properties of the Fourier Transform, how a mathematical change in one domain results in a mathematical change in the other domain. www.dspguide.com /ch10.htm   (128 words)

 The Fourier Transform Our ears do it by mechanical means, mathematicians do it using Fourier transforms, and computers do it using FFT. As you know, sound is vibration that propagates through air (or any other medium; don't be fooled by cheap science fiction movies--sound cannot cross the vacuum of empty space). With your Windows computer, you can collaborate with anyone, anywhere using Email, LAN, or VPN -- no server required. www.relisoft.com /Science/Physics/sound.html   (775 words)

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