NDLI: Fast Computation of MD-DCT-IV/MD-DST-IV by MD-DWT or MD-DCT-II

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Zeng, Yonghong Lin, Zhiping Cheng, Lizhi Bi, Guoan
Copyright Year	2003
Abstract	This paper reveals relationships between the type-IV multidimensional discrete cosine transform (MD-DCT-IV) and the type-II multidimensional discrete cosine transform (MD-DCT-II) or the multidimensional discrete W transform (MD-DWT). Based on the relationships, MD-DCT-IV can be efficiently computed by using the fast algorithms for MD-DCT-II or MD-DWT-III or MD-DWT-III. Efficient method for implementation of the post-addition or pre-addition process is also presented. Compared to the widely used row-column method, considerable savings on the number of arithmetic operations are achieved. For example, the number of multiplications for computing an r-dimensional DCT-IV is only about $\frac{1}{r}$ times that needed by the row-column method, and the number of additions is also reduced. Numerical experiments are made to test the computational time and roundoff errors. They show that the proposed fast algorithms save time.
Starting Page	1903
Ending Page	1918
Page Count	16
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827501394830
e-ISSN	10957197
Issue Number	6
Volume Number	24
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	discrete cosine transform fast algorithm Discrete and fast Fourier transforms multidimensional discrete W transform
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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