14,583 research outputs found
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and
discrete sine transform (DST-IV), as well as for the modified discrete cosine
transform (MDCT) and its inverse, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact
count is strictly lowered for all N > 4. These results are derived by
considering the DCT to be a special case of a DFT of length 8N, with certain
symmetries, and then pruning redundant operations from a recent improved fast
Fourier transform algorithm (based on a recursive rescaling of the
conjugate-pair split radix algorithm). The improved algorithms for DST-IV and
MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page
Signal Flow Graph Approach to Efficient DST I-IV Algorithms
In this paper, fast and efficient discrete sine transformation (DST)
algorithms are presented based on the factorization of sparse, scaled
orthogonal, rotation, rotation-reflection, and butterfly matrices. These
algorithms are completely recursive and solely based on DST I-IV. The presented
algorithms have low arithmetic cost compared to the known fast DST algorithms.
Furthermore, the language of signal flow graph representation of digital
structures is used to describe these efficient and recursive DST algorithms
having points signal flow graph for DST-I and points signal flow
graphs for DST II-IV
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
We present algorithms for the discrete cosine transform (DCT) and discrete
sine transform (DST), of types II and III, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~ 2N log_2 N to ~ (17/9) N log_2 N for a power-of-two transform size N.
Furthermore, we show that a further N multiplications may be saved by a certain
rescaling of the inputs or outputs, generalizing a well-known technique for N=8
by Arai et al. These results are derived by considering the DCT to be a special
case of a DFT of length 4N, with certain symmetries, and then pruning redundant
operations from a recent improved fast Fourier transform algorithm (based on a
recursive rescaling of the conjugate-pair split radix algorithm). The improved
algorithms for DCT-III, DST-II, and DST-III follow immediately from the
improved count for the DCT-II.Comment: 9 page
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