Function Repository Resource:

FourierShiftInverse

Source Notebook

Invert a zero-frequency shift

Contributed by: Yong-an Lu

ResourceFunction["FourierShiftInverse"][data]

rearranges a zero-frequency-shifted Fourier transform data back to the original transform output.

ResourceFunction["FourierShiftInverse"][data, dim]

operates along the dimension dim of data.

Details and Options

ResourceFunction["FourierShiftInverse"] is the inverse of the resource function FourierShift.

In optics, the zero-frequency term appears in the center of spectrum.

ResourceFunction["FourierShiftInverse"] typically works with InverseFourier.

InverseFourier assumes that the zero-frequency term appears at position 1 in the input list.

Examples

Basic Examples (5)

Swap the left and right halves of a vector:

In[1]:=

Out[1]=

If a vector has an odd number of elements, then the middle element is considered part of the right half of the vector:

In[2]:=

Out[2]=

Swap the first quadrant of the matrix with the third, and the second quadrant with the fourth:

In[3]:=

$ResourceFunction["FourierShiftInverse"][\!$\* TagBox[ RowBox[{"(", "", GridBox[{ {"1", "2", "3", "4"}, {"5", "6", "7", "8"}, {"9", "10", "11", "12"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]$] // MatrixForm$

Out[3]=

Swap halves of each column of matrix:

In[4]:=

Out[4]=

Swap halves of each row of matrix:

In[5]:=

Out[5]=

Scope (2)

FourierShiftInverse can be applied to a multidimensional array:

In[6]:=

$ResourceFunction["FourierShiftInverse"][\!\(\* TagBox[ RowBox[{"(", "", GridBox[{ { RowBox[{"(", "", GridBox[{ {"1", "2"}, {"3", "4"}, {"5", "6"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "", ")"}], RowBox[{"(", "", GridBox[{ {"7", "8"}, {"9", "10"}, {"11", "12"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "", ")"}]}, { RowBox[{"(", "", GridBox[{ {"13", "14"}, {"15", "16"}, {"17", "18"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "", ")"}], RowBox[{"(", "", GridBox[{ {"19", "20"}, {"21", "22"}, {"23", "24"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "", ")"}]} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\)] // MatrixForm$