FFT

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Perform forward discrete Fourier transform along selected dimensions using the Fast Fourier Transform (FFT) algorithm. The (non-centered) forward discrete Fourier transform along a specific dimension is defined as

\(X(...,k ,...) = Z \cdot \sum_{j=0}^{n-1} x(..., j, ...) e^{-i2\pi kj/n}\),

where \(Z\) is a normalization constant.

Inputs

Input

Input(s)

Type: Image, Numeric Array, List, Required, Single

Outputs

Output

Output(s)

Type: Image, Numeric Array

Settings

Centered Boolean

True if the center of the frequency spectrum is placed at the center index. I.e. \(c = N - \lfloor N/2 \rfloor\). Otherwise the center frequency will be placed at the 0 index.

Dimensions Integers

The dimensions over which the FFT is performed.

Normalization Selection

The type of normalization:

Ortho - Make the Fourier transform unitary. Sets the scaling factor \(Z = \frac{1}{\sqrt{n}}\).
Backward Sets the scaling factor \(Z = 1\).
Forward Sets the scaling factor \(Z = \frac{1}{n}\).

Values: Ortho (1/sqrt(n)), Backward (None), Forward (1/n)

FFT