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Discrete cosine transform matrix


D = dctmtx(n)


D = dctmtx(n) returns the n-by-n DCT (discrete cosine transform) matrix. D*A is the DCT of the columns of A and D'*A is the inverse DCT of the columns of A (when A is n-by-n).

Class Support

n is an integer scalar of class double. D is returned as a matrix of class double.


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Read image into the workspace and cast it to class double.

A = im2double(imread('rice.png'));

Calculate discrete cosine transform matrix.

D = dctmtx(size(A,1));

Multiply the input image A by D to get the DCT of the columns of A and by D' to get the inverse DCT of the columsn of A.

dct = D*A*D';
figure, imshow(dct)


If A is square, the two-dimensional DCT of A can be computed as D*A*D'. This computation is sometimes faster than using dct2, especially if you are computing a large number of small DCTs, because D needs to be determined only once.

For example, in JPEG compression, the DCT of each 8-by-8 block is computed. To perform this computation, use dctmtx to determine D, and then calculate each DCT using D*A*D' (where A is each 8-by-8 block). This is faster than calling dct2 for each individual block.

See Also

Introduced before R2006a

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