Discrete Cosine Transform (DCT)

More documents

Recommendations

Info

We can re-write (5) as 4 C u πu cos S 16 When j 8 = ( u) = −1 15 2kπu 16 ∑ f ( k) cos = Re{ ∑ k= 0 k= 0 2kπu − j 16 Decaese the 16-point DFT is defined by F 16 ( u) = 15 ∑ k = 0 f ( k) e 2kπu − j 16 15 f ( k) e } 18
We have the following <strong>DCT</strong> v.s. DFT relationship 4 C u u cos 16 π : only the first 8 values S ( u) = Re{ F ( u)} are needed. 8 Instead of performing an I<strong>DCT</strong> an IDFT of twice the length is performed. IDFT can be implemented by IFFT with complexity O(NlogN)! 16 19
Page 1 and 2: Discrete Cosine Transform (DCT) 1
Page 3 and 4: Two related transform are the discr
Page 5 and 6: Formulation: DCT is a linear and i
Page 7 and 8: DCT-II: f j = ∑ − n 1 k = 0 x k
Page 9 and 10: DCT-IV: f j = ∑ − n 1 k = 0 x k
Page 11 and 12: Inverse Transforms: IDCT-I is DCT-
Page 13 and 14: References: 1. Rao and Yip, Discre
Page 15 and 16: Then the 1-D DCT is applied to the
Page 17: 4 C u πu cos S 16 8 ( u) = 7 ∑ x
Page 21 and 22: Let X M = (f(0), f(1), f(2), f(3),
Page 23 and 24: F M = X M x (1/8)T M Because cosα
Page 25 and 26: 25 X M = F M x (8T M -1 ) = FM x L
Page 27 and 28: 27 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Page 29 and 30: 29 So the IDFT can be performed by
Page 31 and 32: 31 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪
Page 33: If you count the operations you wil

Discrete Cosine Transform (DCT)

Create successful ePaper yourself

Delete template?

Save as template?