FFT

MLModule

genre	Fourier
authors	Markus Hüllebrand, Ola Friman
package	FMEwork/ReleaseMeVis
dll	MLFFT
definition	MLFFT.def
keywords	fft, dft, fourier, complex, transformation, spectrum, phase

Purpose

The FFT module calculates a discrete n-D fourier transform of the given image.

Usage

The scalar volume to be processed is attached to input0.

Details

A separable fast Fourier transform is applied along the image dimensions indicated by the user. The discrete nD FFT is computed using the kissFFT library, version 1.2.8. by Mark Borgerding. The fourier transform is computed for a sequence of N real or complex numbers x₀,…,x_N-1. The sequence is transformed into X₀,…,X_N-1 according to the formula:

where i is the imaginary unit.

The inverse DFT is given by the formula:

According to the user indicated output type either the complex result, it’s real or imaginary component, the magnitude,

or the phase,

will be computed.

In order to perform a windowed FFT the following windows have been provided and can be selected in the Filter field. The windowing is applied before the transformation, and should only be used when calculating the (forward) FFT.

• Cosine window:

• von Hann window:

• Hamming window:

• Exponential window:

• Kaiser window:

• Sine Bell window:

• Sine Bell

• Lanczos window:

• Blackman window:

The default parameters have been selected from Matlab.

If Shift frequency center is selected the low frequencies can be reordered to the center of the spectrum. By selecting is the same as the fftshift in Matlab. Therefore the image is swapped iteratively along each dimension. In 2D this leads to a swapping of the first quadrant with the third and the second quadrant with the fourth.

Windows

Default Panel

Input Fields

input0

name: input0, type: Image

input0 must be a scalar volume or complex volume, as it will be implicitly cast to a complex data type. The dimensions of input0 can be chosen arbitrarily.

Output Fields

output0

name: output0, type: Image

The output is the result of the FFT as described above. Depending of the Output Type (see below) the datatype of the output image is either std::complex<MLdouble> or MLdouble.

Parameter Fields

Field Index

Calculate inverse FFT: Bool	Size u: Integer
Frequency unit: Enum	Size x: Integer
Keep sizes: Bool	Size y: Integer
Output: Enum	Size z: Integer
preProcessOnly: Bool	Window: Enum
Shift Frequency Center: Bool	x: Bool
Size c: Integer
Size t: Integer

Visible Fields

x

name: xDim, type: Bool, default: TRUE

Select the dimensions to process for the FFT. The page size in this dimension will be set to the image extent.

Size x

name: xDimSize, type: Integer, default: 0

Size y

name: yDimSize, type: Integer, default: 0

Size z

name: zDimSize, type: Integer, default: 0

Size c

name: cDimSize, type: Integer, default: 0

Size t

name: tDimSize, type: Integer, default: 0

Size u

name: uDimSize, type: Integer, default: 0

Calculate inverse FFT

name: calculateInverse, type: Bool, default: FALSE

Output

name: outputType, type: Enum, default: Complex

Values:

Title	Name
Complex	Complex
Magnitude	Magnitude
Phase	Phase
Real	Real
Imaginary	Imaginary

Shift Frequency Center

name: shiftFrequencyCenter, type: Bool, default: TRUE

Reorders frequencies to have low frequencies in center

Window

name: windowFunction, type: Enum, default: None

Values:

Title	Name
None	None
Cosine	Cosine
von Hann	vonHann
Hamming	Hamming
Exponential	Exponential
Gaussian	Gaussian
Sine Bell	SineBell
Sine Bell Square	SineBellSquare
Tukey	Tukey
Lanczos	Lanczos
Blackman	Blackman

Frequency unit

name: frequencyUnit, type: Enum, default: Keep original

Values:

Title	Name
Keep original	Keep original
Radians/Voxel	Radians/Voxel
Periods/Millimeter	Periods/Millimeter

Keep sizes

name: keepFFTSize, type: Bool, default: FALSE

Hidden Fields

preProcessOnly

name: preProcessOnly, type: Bool, default: FALSE