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Recently developed fast cosine transform (FCT) algorithms
require fewer operations than any other known general algorithm.
Similar to related fast transform algorithms (e.g., the FFT), these
algorithms permute the data before, during, or after the computation
of the transform. The choice of this permutation may be an important
consideration in reducing the complexity of the permutation algorithm.
In this paper, we derive the complexity to generate the permutation
mappings used in these FCT algorithms for power-of-2 data sets by
representing them as linear index transformations and translating them
into combinational circuits. Moreover, we show that one of these
permutations not only allows efficient implementation, but is also
self-invertible, i.e., we can use the same circuit to generate the
permutation mapping for both the fast cosine transform and its
inverse, like the bit-reversal permutation used by FFT algorithms.
These results may be useful to designers of low-level algorithms for
implementing fast cosine transforms.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Sean S. B. Moore and Leonard F. Wisniewski, "Complexity Analysis of Two Permutations Used by Fast Cosine Transform Algorithms ." Dartmouth Computer Science Technical Report PCS-TR95-266, October 1995.
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