Editing Discrete cosine transform (section)

==Example of IDCT==
[[File:DCT filter comparison.png|thumb|right|An example showing eight different filters applied to a test image (top left) by multiplying its DCT spectrum (top right) with each filter.]]
Consider this 8x8 grayscale image of capital letter A.
[[File:letter-a-8x8.png|frame|center|Original size, scaled 10x (nearest neighbor), scaled 10x (bilinear).]]

[[File:dct-table.png|frame|center|Basis functions of the discrete cosine transformation with corresponding coefficients (specific for our image).
<br/>DCT of the image =
<math>
\begin{bmatrix}
6.1917 & -0.3411 & 1.2418  &  0.1492  &  0.1583  &  0.2742 &  -0.0724  &  0.0561 \\
0.2205 & 0.0214 & 0.4503  &  0.3947  & -0.7846 &  -0.4391  &  0.1001  & -0.2554 \\
1.0423 & 0.2214 & -1.0017 &  -0.2720  &  0.0789 &  -0.1952  &  0.2801  &  0.4713 \\
-0.2340 & -0.0392 & -0.2617 &  -0.2866 &   0.6351 &   0.3501 &  -0.1433  &  0.3550 \\
0.2750 & 0.0226 & 0.1229  &  0.2183  & -0.2583  & -0.0742  & -0.2042  & -0.5906 \\
0.0653 & 0.0428 & -0.4721 &  -0.2905  &  0.4745  &  0.2875  & -0.0284  & -0.1311 \\
0.3169 & 0.0541 & -0.1033 &  -0.0225  & -0.0056  &  0.1017  & -0.1650 &  -0.1500 \\
-0.2970 & -0.0627 & 0.1960 &   0.0644  & -0.1136 &  -0.1031 &   0.1887  &  0.1444 \\
\end{bmatrix}

</math>.]]

Each basis function is multiplied by its coefficient and then this product is added to the final image.

[[File:idct-animation.gif|frame|center|On the left is the final image. In the middle is the weighted function (multiplied by a coefficient) which is added to the final image. On the right is the current function and corresponding coefficient. Images are scaled (using bilinear interpolation) by factor 10×.]]