FourierDSTMatrix

FourierDSTMatrix[n]

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

FourierDSTMatrix[n,m]

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

Details and Options

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

Examples

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Basic Examples  (1)

A DST matrix:

Scope  (1)

The discrete sine transform's basis sequences of length 128:

Options  (1)

WorkingPrecision  (1)

Use machine precision:

Use arbitrary precision:

Properties & Relations  (2)

DST matrix multiplied by a vector is equivalent to the discrete sine transform of that vector:

FourierDST is much faster than the matrix-based computation:

Discrete sine transform matrix of type 1 is its own inverse:

Discrete sine transform matrix of type 3 is an inverse of the type 2 matrix:

Discrete sine transform matrix of type 4 is its own inverse:

Introduced in 2012
 (9.0)