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Unformatted text preview: 3. 2D Unitary DFT (25 points) Let the 2D unitary DFT of the 2D matrix Φ be Γ as indicated below. As is customary, the origin is the upper left element. 2 D DFT a b c d A B C D e f g h E F G H i j k l I J K L m n o p M N O P Φ = →Γ = Find the 2D unitary IDFT (not the forward DFT) of the matrix Ψ below in terms of the elements of Φ . Ψ = * * * * * * * * * * * * * * * * A B C D E F G H I J K L M N O P 4. DCT (25 points) Let the 1D unitary DCT of the 1D vector ( ) [ ] u n a b c d e f g h = be given by [ ] ( ) v k A B C D E F G H = . The underbars under the a and A indicate the origin locations; e.g. the n=0 and k=0 positions, respectively. Find the DCT of ( ) [ ] y n h g f e d c b a = in terms of the elements of ( ) v k ....
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 Fall '10
 Villasenor
 Image processing, Computer Graphics

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