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BUILT-IN MATHEMATICA SYMBOL
FourierMatrix
FourierMatrix[n]
returns an n×n Fourier matrix.
Details 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.
Examplesopen all
Basic Examples (1)
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