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.

Their strategy was as follows: Represent the equations (2) as a Galerkin system in

Fourier space with a basis {[e.

We remark that in

Fourier space, the following symbols

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).

This

Fourier space algorithm is more efficient than real space FBP if the number of projections is sufficiently large.

This effectively provides information on response at one selected point in

Fourier space, or its multiples.

Walter Norfleet of MIT has concluded that a technique based on identification of the part shape's local sensitivity to each individual pin's position is more efficient than an incremental correction method, or a method in which the correction is calculated in

Fourier space.

We use a method to estimate local orientations in the n-dimensional space from the covariance matrix of the gradient, which can be implemented either in the image space or in the

Fourier space.

Fornberg and Driscoll [16] gave an interesting generalization of this approach by splitting also the linear part of the equation in

Fourier space in regimes of high, medium, and low frequencies, and to use different numerical schemes for the respective regimes.

During evaluations of the Fourier transforms for one, two and three dimensions, a diagonal linear integral operator was found to be implicit in the 3-D

Fourier space of the scattering potential.

The Inverse Filter algorithm is a one-step deconvolution technique performed in

Fourier space by dividing the captured image by the pointspread function.