FourierMatrix

FourierMatrix[n]
returns an n×n Fourier matrix.

Details and OptionsDetails and Options

  • FourierMatrix of order n returns a list of the length-n discrete Fourier transform's basis sequences.
  • Each entry of the Fourier matrix is by default defined as .
  • Rows of the FourierMatrix are basis sequences of the discrete Fourier transform.
  • The result F of FourierMatrix[n] is symmetric and unitary, meaning that is Conjugate[F].
  • The result of FourierMatrix[n].list is equivalent to Fourier[list] when list has length n. However, the computation of Fourier[list] is much faster and has less numerical error. »
  • With the setting FourierParameters->{a, b}, entry of the Fourier matrix is defined as . The default setting is FourierParameters->{0, 1}.
  • FourierMatrix[..., WorkingPrecision->p] gives a matrix with entries of precision p.
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