Discrete Cosine Transform (DCT)

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DCT is a Fourier-related transform similar to DFT, but using only real numbers. It is equivalent to a DFT roughly twice the transform length, operating on real data with “Even symmetry” (since Fourier transform of a real and even function is real and even). The most common variant of DCT is the type- II DCT and its inverse is the type-III DCT. 2
Two related transform are the discrete sine transform (DST), which is equivalent to a DFT of “Real and odd” functions, and the modified DCT (MDCT), which is based on a DCT of overlapping data. The other interesting transform is the discrete Hartley transform (DHT) in which Even part of DHT = Real part of DFT Odd part of DHT = Imaginary part of DFT 3
Page 1: Discrete Cosine Transform (DCT) 1
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 and 18: 4 C u πu cos S 16 8 ( u) = 7 ∑ x
Page 19 and 20: We have the following DCT v.s. DFT
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)

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