Discrete Cosine Transform (DCT)
Discrete Cosine Transform (DCT)
Discrete Cosine Transform (DCT)
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<strong>DCT</strong>-II:<br />
f<br />
j<br />
=<br />
∑ − n 1<br />
k = 0<br />
x<br />
k<br />
π<br />
cos[ j(<br />
k +<br />
n<br />
1<br />
)]<br />
2<br />
Some authors further multiply the f o term by<br />
1/<br />
2<br />
(see below for the corresponding<br />
change in <strong>DCT</strong>-III) . This makes the <strong>DCT</strong>-II<br />
matrix orthogonal (up to a scale factor), but<br />
breaks the direct correspondence with a realeven<br />
DFT of half-shifted input.<br />
7