# 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.

# Details

• 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.

# Examples

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## Basic Examples(2)

Find a discrete cosine transform:

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Find the inverse discrete cosine transform:

 In[2]:=
 Out[2]=

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

 In[1]:=
 Out[1]=

Find the inverse discrete cosine transform:

 In[2]:=
 Out[2]=