Homework II Fast Discrete Cosine Transform Jain-Yi Lu ( 呂健益 ) Visual Communications Laboratory Department of Communication Engineering National Central University ChungLi, Taiwan

 Implement Fast Discrete Cosine Transform  Implement Fast Discrete Cosine Inverse Transform 2

3 N : 1-D Sequence Length : 0,1,2…N-1 (u=0 -> DC) f(x) : Spatial Domain Intensity C(u) : Frequency Domain intensity            )12( cos)()()( N x N ux xfuauC  u

DCT Spatial Domain Frequency Domain Spatial Domain IDCT 4

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 W. H. Chen, C. H. Smith and S. C. Fralick, “A Fast Computational Algorithm for the Discrete Cosine Transform,” IEEE Trans. Communications, Vol. COM- 25, No. 9, September

Stage1 Stage2 Stage3 Stage4 Initial Signal Result 7

Stage1 Stage2 Stage3 Stage4 8

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Stage1 Stage2 Stage3 Stage4 11

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 We will provide grayscale Lena 512×512 pixels image.  Your program (Image size, bugs, some questions) (2 points)  The accuracy (2 points)  Computation perplexity (Bonus)  Other comment (Bonus) 13

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