<Dl> <Dd> G u, v = 1 4 α (u) α (v) ∑ x = 0 7 ∑ y = 0 7 g x, y cos ⁡ ((2 x + 1) u π 16) cos ⁡ ((2 y + 1) v π 16) (\ displaystyle \ G_ (u, v) = (\ frac (1) (4)) \ alpha (u) \ alpha (v) \ sum _ (x = 0) ^ (7) \ sum _ (y = 0) ^ (7) g_ (x, y) \ cos \ left ((\ frac ((2x + 1) u \ pi) (16)) \ right) \ cos \ left ((\ frac ((2y + 1) v \ pi) (16)) \ right)) </Dd> </Dl> <Dd> G u, v = 1 4 α (u) α (v) ∑ x = 0 7 ∑ y = 0 7 g x, y cos ⁡ ((2 x + 1) u π 16) cos ⁡ ((2 y + 1) v π 16) (\ displaystyle \ G_ (u, v) = (\ frac (1) (4)) \ alpha (u) \ alpha (v) \ sum _ (x = 0) ^ (7) \ sum _ (y = 0) ^ (7) g_ (x, y) \ cos \ left ((\ frac ((2x + 1) u \ pi) (16)) \ right) \ cos \ left ((\ frac ((2y + 1) v \ pi) (16)) \ right)) </Dd> <Ul> <Li> u (\ displaystyle \ u) is the horizontal spatial frequency, for the integers 0 ≤ u <8 (\ displaystyle \ 0 \ leq u <8). </Li> <Li> v (\ displaystyle \ v) is the vertical spatial frequency, for the integers 0 ≤ v <8 (\ displaystyle \ 0 \ leq v <8). </Li> <Li> α (u) = (1 2, if u = 0 1, otherwise (\ displaystyle \ alpha (u) = (\ begin (cases) (\ frac (1) (\ sqrt (2))), & (\ mbox (if)) u = 0 \ \ 1, & (\ mbox (otherwise)) \ end (cases))) is a normalizing scale factor to make the transformation orthonormal </Li> <Li> g x, y (\ displaystyle \ g_ (x, y)) is the pixel value at coordinates (x, y) (\ displaystyle \ (x, y)) </Li> <Li> G u, v (\ displaystyle \ G_ (u, v)) is the DCT coefficient at coordinates (u, v). (\ displaystyle \ (u, v).) </Li> </Ul> <Li> u (\ displaystyle \ u) is the horizontal spatial frequency, for the integers 0 ≤ u <8 (\ displaystyle \ 0 \ leq u <8). </Li>

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