Spatial FFT
Use a Spatial FFT () dataset to compute the spatial Fourier transform of a variable or expression. You can add a Spatial FFT dataset by right-clicking the Datasets node and choose Spatial FFT from the More Datasets submenu.
Data
From the Dataset list, choose the dataset to use a the input for the spatial FFT.
Transformation
Click the Preview Spatial Samples button to get a plot of the spatial resolution in the Graphics window.
From the Resolution list, choose Automatic (the default) to have the spatial sampling resolution set up automatically, or choose Manual to specify the sampling resolution using integers larger than 2 in the Nx, Ny, and (in 3D) Nz fields under Sampling resolution.
From the Layout list under Spatial layout, choose Normal (the default), Periodic, or Use zero padding. For the last layout option, specify paddings as integer values (zero or larger) in the x padding, y padding, and (in 3D) z padding fields.
If the geometry is a unit cell of a periodic pattern, the last samples of each dimension must be ignored to make the samples periodic. To have more resolution in the frequency domain you then need to pad the spatial domain with zeros. This option should be used when the transformation is followed by frequency domain filtration that helps having higher resolution in the frequency domain.
Under Fourier space variables, the default variable names for the fx, fy, and (in 3D) fz Fourier space variables are sfft1fx, sffft1fy, and sfft1z for a Spatial FFT 1 dataset. If desired, enter other variable names.
From the Domain list, choose Frequency (the default), corresponding to the spatial frequencies, Negative frequency, to use the opposite sign convention used for electromagnetic waves, for example, or Index, having the axes values as the 0-based DFT indices. The following equation describes the DFT transform:
where .
In the equation for the DFT transform above, d can be up to 3 as it is the dimensionality of the Fourier space. The ki indices are integers that are the indices of the transformed space corresponding to the axis values when Domain is set to Index. If you set Domain to Frequency or Negative frequency, the axis values are shifted and scaled to match spatial frequencies. If you choose Negative frequency, is used, which is the convention used for electromagnetic waves.
The Mask DC check box is selected by default to set the DC value (zero frequency component) to zero. This is usually necessary because this value is too high and overwhelms the rest of the spectrum. If you want to include the DC value, clear this check box.
Quality
From the Resolution list, choose Extra fine, Finer, Fine, Normal (the default), Coarse, No refinement, or Custom. A higher resolution means that elements are split into smaller patches during rendering. If you chose Custom, enter a refinement as a positive integer pin the Element refinement field.
If you have the Structural Mechanics Module, see Wave Propagation in Rock Under Blast Loads: Application Library path Structural_Mechanics_Module/Elastic_Waves/blasting_rock.
If you have the Wave Optics Module, see Fresnel Lens:
Application Library path Wave_Optics_Module/Verification_Examples/fresnel_lens.