Fourier space


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Fourier space

[‚fu̇r·ē‚ā ‚spās]
(mathematics)
The space in which the Fourier transform of a function is defined.
References in periodicals archive ?
Because it isn't a frequency dependent noise, but rather random, it can't be done in Fourier space. That is noise removal will be done using the spatial domain.
The resulting dataset represents the k-space (or Fourier space) of the image.
Lewitt, "Constrained fourier space method for compensation of missing data in emission computed tomography," IEEE Transactions on Medical Imaging, vol.
These latter methods are especially well suited to handle a large number of projections thanks to their computational speed and their accuracy when the angular coverage of the set of projections fully fills the 3D Fourier space, which is currently normally the case in SPA (a word of caution should be expressed in those cases in which subsequent rounds of 3D classification significantly reduce the number of images per 3D class).
Thus, (4) can be transformed into the discrete Fourier space as follows:
This scattered field data or the projection data from multiple angles can be used to populate the Fourier space of the object (ROI).
As can be seen from the equivalent Fourier transform (Figure 2), the Fourier space cannot distinguish between the two types of signals.
They also look at the closely related well-established boundary element method, showing how it can be viewed as the counterpart in the physical space of the numerical implementation of the unified transform, which is formulated in the spectral or Fourier space. ([umlaut] Ringgold, Inc., Portland, OR)
Their strategy was as follows: Represent the equations (2) as a Galerkin system in Fourier space with a basis {[e.sup.2[pi]ikx]}k[member of][Z.sup.3].
All of the convolutions are carried out via multiplication in Fourier space, per the convolution theorem (see Appendix A, Sec.
However, one of the major numerical issues in dealing with field-material interactions in a spectral basis is the observation that a simple product equation in real space is not always accurately reproduced by a convolution in Fourier space if one or both representations of the product variables have a finite (or truncated) Fourier expansion (as is the case in numerical implementations).
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