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DCT and DST (+ inverse) in arbitrary dimension

version (8.53 KB) by Damien Garcia
Discrete cosine/sine transforms and their inverses


Updated 25 Nov 2011

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Y = DCTN(X) returns the discrete cosine transform (DCT) of X.

X = IDCTN(Y) returns the inverse discrete cosine transform (IDCT) of Y.

Y = DSTN(X) returns the discrete sine transform (DST) of X.

X = IDSTN(Y) returns the inverse discrete sine transform (IDST) of Y.

X and Y can be N-dimensional.

D = DSTMTX(k) returns the k-by-k DST transform matrix.

Faster DCT2 and IDCT2 are also included in the zip file.

Enter "help dctn", "help dstn", "help idctn", "help idstn" and "help dstmtx" in the Matlab command window for complete information.

RGB = imread('autumn.tif');
I = rgb2gray(RGB);
J = dstn(I);
imshow(log(abs(J)),[]), colormap(jet), colorbar

The commands below set values less than magnitude 10 in the DST matrix to zero, then reconstruct the image using the inverse DST.

J(abs(J)<10) = 0;
K = idstn(J);
figure, imshow(I)
figure, imshow(K,[0 255])


Cite As

Damien Garcia (2020). DCT and DST (+ inverse) in arbitrary dimension (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (5)

Does the output need to be revered so that it corresponds to the low frequency and going up? (I am a bit confused by what would be the corresponding omega after transformation.) Can you please help?


Works great. But the idctn is missing?

According to the author and the reference in IEEE, the definition of the DCT rather corresponds to what is called REDFT10 in fftw. I guess the DST corresponds to RODFT10. Matlab dst function rather uses the same definition as RODFT00.

Would be great if you could add the exact definition. Does dstn correspond to ?

Really useful otherwise :)

these function when used in >resize3d< allow faster volume resizing of large volumes with less memory usage


faster DCT2 and IDCT2 are also included

Faster DCT2 and IDCT2 are also included

DCT and IDCT have been added upon request

MATLAB Release Compatibility
Created with R2007b
Compatible with any release
Platform Compatibility
Windows macOS Linux