Journal ArticleDOI
A second improved digit-reversal permutation algorithm for fast transforms
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A fourth theorem is given, indicating an alternate order of generating the index pairs for swapping, and a second permutation algorithm results, which uses the same principles as the first and differs principally in that in its innermost loop, one of the pair of indexes is usually generated by an integer increment.Abstract:
Based on three previously published theorems and an algorithm for the digit-reversal permutation required by fast transform algorithms, a fourth theorem is given, indicating an alternate order of generating the index pairs for swapping, and a second permutation algorithm results. This algorithm uses the same principles as the first and differs principally in that in its innermost loop, one of the pair of indexes is usually generated by an integer increment (i:=i+n). This will result in slightly faster execution on most computers. >read more
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Multidigit multiplication for mathematicians
TL;DR: In this article , a survey of techniques for multiplying elements of various commutative rings is presented, including dual Karatsuba multiplication, dual Toom multiplication and dual FFT.
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Programs for signal recovery from noisy data using the maximum likelihood principle I. General description
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Transforming real-valued sequences: fast Fourier versus fast Hartley transform algorithms
TL;DR: Five programs for efficient computation of DFT of real-valued data are analyzed with respect to their operation counts vis-a-vis run times on weak and powerful floating-point processors and the Bruun (1978) algorithm turns out to be a "best" performer.
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New FFT bit-reversal algorithm
Juan M. Rius,R. De Porrata-Doria +1 more
TL;DR: Presents a very short, simple, easy to understand bit-reversal algorithm for radix-2 fast Fourier transform (FFT), which is, furthermore, easily extendable to Radix-M and Yong's technique, which is comparable to that of the fastest algorithms.
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Efficient input-reordering algorithms for fast DCT
TL;DR: Three fast input reordering algorithms are proposed that result in fewer data transfers, reduced storage requirements and an average speed increase of 37% in the DCT computation.
References
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TL;DR: Several methods are described for modifying Cholesky factors and a new algorithm is presented for modifying the complete orthogonal factorization of a general matrix, from which the conventional QR factors are obtained as a special case.