Image Processing Toolbox User's Guide |

**The DCT Transform Matrix **

The Image Processing Toolbox offers two different ways to compute the DCT. The first method is to use the function `dct2`

. `dct2`

uses an FFT-based algorithm for speedy computation with large inputs. The second method is to use the DCT *transform matrix*, which is returned by the function `dctmtx`

and might be more efficient for small square inputs, such as 8-by-8 or 16-by-16. The M-by-M transform matrix `T`

is given by

For an M-by-M matrix `A`

, `T*A`

is an M-by-M matrix whose columns contain the one-dimensional DCT of the columns of `A`

. The two-dimensional DCT of `A`

can be computed as `B=T*A*T'`

. Since `T`

is a real orthonormal matrix, its inverse is the same as its transpose. Therefore, the inverse two-dimensional DCT of `B`

is given by `T'*B*T`

.

Discrete Cosine Transform | DCT and Image Compression |

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