Topic
Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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01 Dec 2012
TL;DR: A correlation-based watermarking technique with the fast Fourier transforms (FFTs) for three-dimensional (3-D) mesh models with desirable properties, similar to a pseudonoise signal, is described.
Abstract: This paper describes a correlation-based watermarking technique with the fast Fourier transforms (FFTs) for three-dimensional (3-D) mesh models. For generating a watermark with desirable properties, similar to a pseudonoise (PN) signal, an impulse signal on a two-dimensional (2-D) space is spread through the FFT, multiplications of a complex sinusoid signal, and the inverse FFT. This system easily incorporate a frequency selectivity property, because zero-valued components in the multiplication block prevent the energy of the impulse signal at appropriate frequencies. As a result, the proposed approach requires no additional transform, such as the discrete cosine transform and wavelet transform. Since the amount of information that can be stored in the watermark depends on the size of a spread space, the elimination of the subband transform increases a payload of the watermark in a previous paper. The watermark, i.e., spread impulse signal, is embedded into 3-D data aligned by the principle component analysis (PCA). In the detection procedure, after realigning the watermarked mesh model through the PCA, we map the 3-D data on the 2-D space via block segmentation and averaging operation. The 2-D data are processed by the inverse system, i.e., the FFT, the division of the complex sinusoid signal, and the inverse FFT. From the resulting 2-D signal, we detect the position of the maximum value as a signature.
02 Jul 2003
TL;DR: In the paper it is shown that discrete Fourier transform can be computed using only 0(NlogN) operations even if N is prime, N is the transform size, and by introducing few modifications the worst case computational complexity of the algorithm can be reduced to circa 16Nlog/sub 2/(N) arithmetical operations.
Abstract: In the paper it is shown that discrete Fourier transform can be computed using only 0(NlogN) operations even if N is prime, N is the transform size. A fast algorithm working for any prime N is presented, which worst case computational complexity is below 32N log/sub 2/(N) arithmetical operations, which can be compared to less than 4Nlog/sub 2/(N) operations for the best existing FFT for N being power of number 2. It is shown, however that by introducing few modifications the worst case computational complexity of the algorithm can be reduced to circa 16Nlog/sub 2/(N) arithmetical operations. In this way an interesting theoretical result is obtained that computational complexities of the DFT for 'most' and 'least' convenient N values do not differ by more than factor 4.
01 Jan 2016
TL;DR: New algorithms for computing the Discrete Fourier Transform of n points are described, which use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions.
Abstract: New algorithms for computing the Discrete Fourier Transform of n points are described. For n in the range of a few tens to a few thousands these algorithms use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions. Computing the Discrete Fourier Transform (DFT) of n points:
20 Mar 1988
TL;DR: An alternative discrete-cosine-transform-based DWD processor is proposed where factorization is performed directly on the cosine matrix and compared in terms of computational complexity to radix-two,Radix-four, and radIX-2/4 FFT- based DWD processors.
Abstract: The symmetry of the discrete Wigner distribution (DWD) kernel input and the corresponding DWD output is used to develop an N-point DWD processor that outputs two DWD slices per N/2-point fast Fourier transform (FFT) subsystem. The overhead associated with FFT size reduction and kernel generation are shown to be less than that of the short-time Fourier transform magnitude (STFTM), given an equivalent reduction in FFT size, and the conclusion of double throughput for the DWD over that of the STFTM is validated. An alternative discrete-cosine-transform-based DWD processor is proposed where factorization is performed directly on the cosine matrix and compared in terms of computational complexity to radix-two, radix-four, and radix-2/4 FFT-based DWD processors. >
14 Apr 1991
TL;DR: A fast algorithm for computing the pseudo-Wigner distribution using the fast Hartley transform (FHT) is presented, and the computation complexity is reduced from three complex FFTs to three real FHTs.
Abstract: A fast algorithm for computing the pseudo-Wigner distribution using the fast Hartley transform (FHT) is presented. Unlike the conventional fast Fourier transform (FFT) approach, this algorithm performs entirely in the real domain. Many efficient FHT algorithms can be applied, and the computation complexity is reduced from three complex FFTs to three real FHTs. >