Mathematica > Mathematics and Algorithms > Calculus > Integral Transforms > Fourier Analysis > FourierDCT
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FourierDCT

FourierDCT[list]
finds the Fourier discrete cosine transform of a list of real numbers.

FourierDCT[list, m]
finds the Fourier discrete cosine transform of type m.

DetailsDetails

  • Possible types m of discrete cosine transform for a list of length giving a result are:
  • 1.DCT-I
    2.DCT-II
    3.DCT-III
    4.DCT-IV
  • FourierDCT[list] is equivalent to FourierDCT[list, 2].
  • The inverse discrete cosine transforms for types 1, 2, 3, and 4 are types 1, 3, 2, and 4, respectively.
  • The list given in FourierDCT[list] can be nested to represent an array of data in any number of dimensions.
  • The array of data must be rectangular.
  • If the elements of list are exact numbers, FourierDCT begins by applying N to them.
  • FourierDCT can be used on SparseArray objects.

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

Find a discrete cosine transform:

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Out[1]=

Find the inverse discrete cosine transform:

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Find a discrete cosine transform of type 1 (DCT-I):

In[1]:=
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Out[1]=

Find the inverse discrete cosine transform:

In[2]:=
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Out[2]=

Scope (2)Scope (2)

Generalizations & Extensions (2)Generalizations & Extensions (2)

Applications (3)Applications (3)

Properties & Relations (3)Properties & Relations (3)

Possible Issues (1)Possible Issues (1)

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