FFT2D

MLModule

genre	Fourier
status	stable
author	Tobias Böhler
package	MeVisLab/Standard
dll	MLFourier
definition	MLFourier.def
keywords	FFT, DFT, fast, fourier, transformation, inverse, 2d, sande, tukey, cooke

Purpose

The module FFT2D computes a two-dimensional (2-D) Fast Fourier Transformation of the given input image, or the inverse FFT.

The FFT will only be computed from images that have dimensions of powers of two (e.g. 512, 256, 16). Width and height need not to be identical.

Details

The FFT will be computed using the Sande-Tukey algorithm, providing a stable and considerably fast method of computing the discrete Fourier Transform.

However, this requires the images to have dimensions of 2ⁿ.

Windows

Default Panel

Input Fields

input0

name: input0, type: Image

The input image.

In case of a FFT, the input image needs to be scalar and in case of an inverse FFT, the input image needs to be of complex type.

Output Fields

output0

name: output0, type: Image

Output image showing either the FFT (complex, phase, or spectrum) or the inverse FFT, depending on the Direction.

Parameter Fields

Field Index

2D computation: Bool

Center the FFT: Bool

Direction: Enum

Output Type: Enum

Scale Factor: Double

Use logarithmic scale: Bool

Visible Fields

Direction

name: direction, type: Enum, default: Forward

Defines the operation on the input image.

Values:

Title	Name	Description
Forward	Forward	Computes a FFT.
Inverse	Inverse	Computes the inverse FFT. Note that in this mode, the input image needs to be of type complex.

Use logarithmic scale

name: logarithmicValues, type: Bool, default: TRUE

If checked, the output values are being logarithmically scales for a better visualization (see Gonzales, Woods).

Scale Factor

name: logarithmicScaleFactor, type: Double, default: 0.5

Sets the logarithmic scale factor that is used if Use logarithmic scale is checked.

Center the FFT

name: centeredValues, type: Bool, default: TRUE

If checked, the FFT will be centered so that the origin will be set to (imageWidth/2), (imageHeight/2).

Since higher frequencies can be found around the origin, this allows an intuitive visualization, especially when the spectrum is displayed. This view is often used in image processing textbooks.

2D computation

name: yComputationOn, type: Bool, default: TRUE

If checked, a 2D FFT is performed.

Otherwise, a 1D FFT is performed for all voxel columns.

Output Type

name: outputType, type: Enum, default: Complex

Defines the output type.

Values:

Title	Name	Description
Complex	Complex	Complex data type.
Spectrum	Spectrum	Scalar data type.
Phase	Phase	Scalar data type.