Discrete Cosine Transform (DCT)
Discrete Cosine Transform (DCT)
Discrete Cosine Transform (DCT)
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The implementation of the 2D-I<strong>DCT</strong><br />
Let the 8-point 1-D <strong>DCT</strong> of input data<br />
f(x) be:<br />
S<br />
8<br />
( u)<br />
=<br />
C<br />
2<br />
u<br />
7<br />
∑<br />
x=<br />
0<br />
( 2x<br />
+ 1)<br />
πu<br />
f ( x)<br />
cos<br />
16<br />
First the 1-D <strong>DCT</strong> is applied to all the<br />
rows of the 2-D input f(y,x):<br />
S<br />
8r<br />
( y,<br />
u)<br />
=<br />
C<br />
2<br />
u<br />
7<br />
∑<br />
x=<br />
0<br />
( 2x<br />
+ 1)<br />
πu<br />
f ( y,<br />
x)<br />
cos<br />
16<br />
(1)<br />
(2)<br />
14
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