FourierDCTMatrix

FourierDCTMatrix[n]

returns an n×n discrete cosine transform matrix of type 2.

FourierDCTMatrix[n,m]

returns an n×n discrete cosine transform matrix of type m.

Details and Options

  • Each entry Frs of the discrete cosine transform matrix of type m is computed as:
  • 1.DCT-I
    2.DCT-II
    3.DCT-III
    4.DCT-IV
  • The discrete cosine transform matrices of types 1, 2, 3, and 4 have inverses of type 1, 3, 2, and 4, respectively. »
  • Rows of the FourierDCTMatrix are basis sequences of the discrete cosine transform.
  • The result of FourierDCTMatrix[n].list is equivalent to FourierDCT[list] when list has length n. However, the computation of FourierDCT[list] is much faster and has less numerical error. »
  • FourierDCTMatrix[,WorkingPrecision->p] gives a matrix with entries of precision p.

Examples

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Basic Examples  (1)

A DCT matrix:

In[1]:=
Click for copyable input
Out[1]//MatrixForm=

Scope  (1)

Options  (1)

Applications  (1)

Properties & Relations  (2)

See Also

FourierMatrix  FourierDSTMatrix  HadamardMatrix  FourierDCT

Introduced in 2012
(9.0)