TVec.FFTFromReal Methods

Summary

The forward Fast Fourier Transformation (FFT) from real to complex.

Class
TVec

Declaration

Function FFTFromReal(Vec: TVec): TVec;

Description

Calculate the FFT from all Vec elements and store the result in the calling vector. TMtxVec.Length of the calling vector is set to match the length of the result. The

Declaration

Function FFTFromReal: TVec;

Description

Calculates the forward Fast Fourier Transformation (FFT) from real to complex for the calling vector in-place. The transform should be used, when the conjugate symmetric part of the frequency spectrum is not desired. If the calling vector is complex an exception will be raised. The operation implicitly sets the calling vector Complex property to True. The highest performance will be achieved if the transform length will be a power of two. The transform length is equal to TMtxVec.Length, when the FFTStorageFormat is fsfPack or fsfPerm. The default storage format is fsfCCS.

In-place fsfCCS complication

The transform length in case of fsfCCS will be equal to Length-2, because the result is bigger than the source data by 2 real samples, if the source data is even. If the source data length is odd, then FFTOddLength must be set to True and only Length-1 samples will be used, but Length must of course in that case be even, or Length-1 will not be odd. The last two (one) samples in the vector will be ignored and will be overwritten with the result.

See Also
FFT
TDenseMtxVec.FFT
IFFT
TDenseMtxVec.IFFT

Example 1

        var a,b: TVec;
        begin
          CreateIt(a,b);
          try  //Even
            a.SetIt(false,[1,2,3,4]);
            b.FFTFromReal(a); // b = [(10, 0),( -2,2), (-2, 0)]
            a.SetIt(false,[1,2,3,4, 0, 0]); //result requires 3 complex (or 6 real values)
            a.FFTFromReal; // b = [(10, 0),( -2,2), (-2, 0)]

            //Odd length
            a.SetIt(false,[1,2,3]);

            b.FFTOddLength := True; //use only Length-1 samples
            b.FFTFromReal(a); // b = [(6,0),( -1.5,0.8660)] //result requires 2 complex (= 4 real numbers)

            a.SetIt(false,[1,2,3,0]);

            a.FFTOddLength := True; //use only Length-1 samples
            a.FFTFromReal; // b = [(6,0),( -1.5,0.8660)] //result requires 2 complex (= 4 real numbers)
          finally
            FreeIt(a,b);
          end;
        end;