Showing papers on "Cyclotomic fast Fourier transform published in 1985"

Fast 2-D discrete cosine transform

Abstract: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented. First, the mapping into a 2-D discrete Fourier transform (DFT) of a real signal is improved. Then an usual polynomial transform approach is used in order to map the 2-D DFT into a reduced size 2-D DFT and one dimensional odd DFT's. Finally, optimized odd DFT algorithms for real signals are developped. All together, a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.

Fast Hartley transform algorithm

Abstract: The discrete Hartley transform is a new tool for the analysis, design and implementation of digital signal processing algorithms and systems. It is strictly symmetrical concerning the transformation and its inverse. A new fast Hartley transform algorithm has been developed. Applied to real signals, it is faster than a real fast Fourier transform, especially in the case of the inverse transformation. The speed of operation for a fast convolution can thus be increased.

A comparison of the time involved in computing fast Hartley and fast Fourier transforms

Abstract: It is shown that the DFT of a real sequence, formed via the Fast Hartley Transform, can be computed at most only 2 times faster than by using a complex Fast Fourier Transform. However, more sophisticated FFT algorithms exist which give the same speedup factor. A simple FHT subroutine is presented to illustrate the similarity of the FHT and FFT butterflies in their simplest forms.

Fast Fourier transform calculation of electron density maps

Abstract: This chapter has described the mathematical basis of the fast Fourier transform as applied to the calculation of crystallographic Fourier syntheses. The relationship between real space and reciprocal space symmetry operators has been described. Finally, program organizations have been presented for performing general crystallographic Fourier transforms on computer systems ranging from the very largest systems down to minicomputers. Programs are available from the author, written in FORTRAN IV and in Ratfor, which are suitable for building blocks in these program designs.

A new discrete Fourier transform algorithm using butterfly structure fast convolution

Abstract: This paper proposes a new approach to computing the discrete Fourier transform (DFT) with the power of 2 length using the butterfly structure number theoretic transform (NTT). An algorithm breaking down the DFT matrix into circular matrices with the power of 2 size is newly introduced. The fast circular convolution, which is implemented by the NTT based on the butterfly structure, can provide significant reductions in the number of computations, as well as a simple and regular structure, The proposed algorithm can be successively implemented following a simple flowchart using the reduced size submatrices. Multiplicative complexity is reduced to about 21 percent of that by the classical FFT algorithm, preserving almost the same number of additions.

A fast pipelined DFT processor and its programming consideration

Abstract: A new discrete Fourier transform (DFT) processor with a pipelined structure has been developed. This processor is designed to optimise computation of the pair of operationsAx0 ±Bx1, which is mostly encountered in various fast DFT algorithms. For real-valued data and coefficients, the processor needs only two machine cycles to calculate the pair of operations. A straightforward multiple-stage transform algorithm has been proposed to implement real-valued prime-factor or radix-type transforms. About half of the computation can be saved by taking into account the fact that transform outputs are conjugate pairs for real inputs. The short Winograd Fourier transform algorithm is suggested as a basic building block for large transforms because it is more efficient than the fast Fourier transform.