TMtx.IFFT2DToReal Methods

Summary

Inverse two-dimensional Fast Fourier Transformation from complex to real.

Class
TMtx

Declaration

Function IFFT2DToReal(Mtx: TMtx; NoScale: boolean = False): TMtx;

Description

Transformation is applied on source Mtx matrix and results are saved in the calling matrix. Source matrix must be real, if TDenseMtxVec.FFTStorageFormat was set to fsfPack or to fsfPack. Check the storage format requirements to see how the complex numbers are to be stored in a real matrix. Source matrix must be complex, if TDenseMtxVec.FFTStorageFormat was set to fsfCCS. The source matrix will not be changed. The calling matrix becomes real. Size of the calling matrix will be set to [Mtx.Rows,Mtx.Cols], if TDenseMtxVec.FFTStorageFormat was set to fsfPack or to fsfPack. Size of calling matrix will be set to [Mtx.Rows, 2*Mtx.Cols], if TDenseMtxVec.FFTStorageFormat is set to fsfCCS. All element are involved into the inverse transformation, but the number of reconstructed elements depends on the property TDenseMtxVec.FFTStorageFormat. If that property is set to fsfPerm or to fsfPack, then all elements will be reconstructed after inverse transformation. If that property is set to fsfCCS (which is default), then the number of elements which will be reconstructed depends on the property TDenseMtxVec.FFTOddLength and these rules will be followed:

- Number of source columns and rows must be more than one. An exception will be raised otherwise;
- if TDenseMtxVec.FFTOddLength is set to False, elements in range [0..Cols-2] x [0..Rows-2] will be reconstructed;
- if TDenseMtxVec.FFTOddLength is set to True, elements in range [0..Cols-1] x [0..Rows-2] will be reconstructed;
- Here Cols and Rows are the number of columns and rows of the calling matrix after the inverse transformation.
NOTE: Both properties FFTStorageFormat and TDenseMtxVec.FFTOddLength must be set to the same values for forward and inverse transformation to get reversible results. NoScale parameter allows the scaling to be turned off.

See Also
FFT2D
FFT2DFromReal
IFFT2D

Declaration

Function IFFT2DToReal(NoScale: boolean = False): TMtx;

Summary

Inverse two-dimentional Fast Fourier Transformation from complex to real.

Description

Transformation is applied in-place. Source matrix Complex property must be false, if TDenseMtxVec.FFTStorageFormat was set to fsfPack or to fsfPack. Source matrix Complex property must be True, if TDenseMtxVec.FFTStorageFormat was set to fsfCCS. The calling matrix becomes real. Size of the calling matrix is not changed if TDenseMtxVec.FFTStorageFormat was set to fsfPack or to fsfPack. Size of calling matrix will be set to [Rows, 2*Cols], if TDenseMtxVec.FFTStorageFormat is set to fsfCCS, i.e. matrix changes TMtxVec.Complex property, but does not reallocate storage for elements. All elements are involved into inverse transformation, but number of reconstructed elements depends on the property TDenseMtxVec.FFTStorageFormat. If that property is set to fsfPerm or to fsfPack, then all elements will be reconstructed after inverse transformation. If that property is set to fsfCCS (which is default), then the number of element's which will be reconstructed depends on the property TDenseMtxVec.FFTOddLength and these rules will be followed:

- Number of source columns and rows must be more than one. Exception will be raised otherwise;
- if TDenseMtxVec.FFTOddLength is set to False, elements in range [0..Cols-2] x [0..Rows-2] will be reconstructed;
- if TDenseMtxVec.FFTOddLength is set to True, elements in range [0..Cols-1] x [0..Rows-2] will be reconstructed;
- Here Cols and Rows are the number of columns and rows of the calling matrix after the inverse transformation.
NOTE: Both properties TDenseMtxVec.FFTStorageFormat and TDenseMtxVec.FFTOddLength must be set to the same values for forward and inverse transformation to get reversible results. NoScale parameter allows the scaling to be turned off.

See Also
FFT2D
FFT2DFromReal
IFFT2D

Example 1

      var a: TMtx;
      begin
        CreateIt(a);
        try
          a.SetIt (4,4,False,
                   [1,  2,  3,  4,
                   -5,  6, -7,  8,
                    9, 12,-11, 10,
                   16,-15,-14,  0]);

          a.FFTStorageFormat := fsfCCS;
          a.FFTOddLength := TRUE;

          // the next elements are involved into transformation
              [1, 2, 3,
              -5, 6, -7]

          a.FFT2DFromReal;
          // result will be
          // [(0,0), (-6, -10.39),
          //  (0,0), (3, 12.12),
          //  (12,12), (-11,10),
          //  (0,-15), (-14,0)]

          a.IFFT2DToReal;
          // [ 1,  2,  3, 0
          //  -5,  6, -7, 0
          //  12, 12,-11, 10
          //   0,-15,-14, 0]

          // the next elements are reconstructed 
          // [ 1, 2, 3,  undef,
          //  -5, 6, -7, undef,
          //  undef, undef, undef, undef,
          //  undef, undef, undef, undef]
          //
          // if a.FFTOddLength is set to False,
          // then range of reconstruction would be one column less, i.e.
          // [ 1, 2, undef, undef,
          //  -5, 6, undef, undef,
          //  undef, undef, undef, undef,
          //  undef, undef, undef, undef]

        finally
          FreeIt(a);
        end;
      end;