Discrete Cosine Transform (DCT)
Discrete Cosine Transform (DCT)
Discrete Cosine Transform (DCT)
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Fast 1-D <strong>DCT</strong> Algorithms<br />
Define<br />
Eqn. (1) can be written as:<br />
Since<br />
2πux<br />
πu<br />
α = , β = , and H = α + β.<br />
16 16<br />
7<br />
7<br />
Cu<br />
( 2x<br />
+ 1)<br />
πu<br />
Cu<br />
S8 ( u)<br />
= ∑ f ( x)<br />
cos = ∑ f ( x)<br />
cos( α + β )<br />
2<br />
16 2<br />
2cos<br />
x=<br />
0<br />
H cos β = 2cos(<br />
α + β ) cos β =<br />
↑<br />
( HW )<br />
x=<br />
0<br />
2xπu<br />
2(<br />
15 − x)<br />
πu<br />
cos + cos<br />
16 16<br />
16
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