Digital Signal Processing Reference
In-Depth Information
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Pixel (3, 2)
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Figure 12.3. Block of pixels used to compute DCT.
The tiles represent the video pixel block for each DCT coeffi-
cient. If
(0, 0) is non-zero, and the rest of the DCT coefficients
equal zero, the video will appear as the {0, 0} tile in
Figure 12.4
.
This particular tile is a constant value in all 64 pixel locations,
which is what is expected since all the DCT coefficients with some
cosine frequency content are zero.
If
F
F
(7, 7) is non-zero, and the rest of the DCT coefficients equal
zero, the video will appear as the {7, 7} tile in
Figure 12.4
, which
shows high frequency content in both vertical and horizontal
direction. The idea is that any block of eight by eight pixels, no
matter what the image, can be represented as the weighted sum
of these 64 tiles in
Figure 12.4
.
The DCT coefficients, and the video tiles they represent, form
a set of basis functions. From linear algebra, any set of function
values f(x,y) can be represented as a linear combination of the
basis functions.
The whole purpose of this is to provide an alternate repre-
sentation of any set of pixels, using the DCT basis functions. By
itself, this exchanges one set of 64 pixel values with a set of 64
Figure 12.4. DCT basis functions.
