The Experts below are selected from a list of 273 Experts worldwide ranked by ideXlab platform
Z. Wang - One of the best experts on this subject based on the ideXlab platform.
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A Prime Factor fast W transform algorithm
IEEE Transactions on Signal Processing, 1992Co-Authors: Z. WangAbstract:A method for converting any nesting DFT algorithm to the type-I discrete W transform (DWT-I) is introduced. A nesting algorithm that differs from either the Windograd Fourier transform algorithm (WFTA) or the Prime Factor FFT algorithm (PFA) is presented. New small-N DETs, which are suitable for this nesting algorithm, are developed based on using sparse matrix decomposition. The proposed algorithm is more efficient that either WFTA or PFA for large N, and it is more flexible for the choice of transform length, because 32 points are used. For 2D processing, the proposed algorithm is more efficient than the polynomial transform.
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A new nesting scheme of PFA (Prime Factor algorithm)
International Conference on Acoustics Speech and Signal Processing, 1990Co-Authors: B. Nong, Z. WangAbstract:A nesting scheme type of Prime Factor algorithm (PFA) is introduced. It takes advantage of both the PFA and the Winograd Fourier transform algorithm (WFTA) by developing a new nesting scheme and modifying the small-N discrete Fourier transform (DFT) algorithms. This new nesting scheme will not expand the data in the nesting multiplication part. It requires far fewer multiplications and fewer additions than the PFA. In addition, data transfer between the main array and the temporary array, which is needed by the WFTA, is avoided, and it can be implemented in place and in order.
Fang-yu Huang - One of the best experts on this subject based on the ideXlab platform.
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An efficient Prime-Factor algorithm for the discrete cosine transform and its hardware implementations
IEEE Transactions on Signal Processing, 1994Co-Authors: Fang-yu HuangAbstract:The Prime-Factor decomposition is a fast computational technique for many important digital signal processing operations, such as the convolution, the discrete Fourier transform, the discrete Hartley transform, and the discrete cosine transform (DCT). The authors present a new Prime-Factor algorithm for the DCT. They also design a Prime-Factor algorithm for the discrete sine transform based on the Prime-Factor DCT algorithm. Hardware implementations for the Prime-Factor DCT are also studied. They are especially interested in the hardware designs which are suitable for the VLSI implementations. They show three hardware designs for the Prime-Factor DCT, including a VLSI circuit fabricated directly according to the signal-flow graph, a linear systolic array, and a mesh-connected systolic array. These three designs show the trade-off between cost and performance. The methodology, which deals with general (N/sub 1//spl times/ N/sub 2/)-point DCTs, where N/sub 1/ and N/sub 2/ are mutually Prime, is illustrated by converting a 15-point DCT problem into a (3/spl times/5)-point 2D DCT problem.
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An efficient Prime-Factor algorithm for the discrete cosine transform and its hardware implementations
1993 IEEE International Conference on Acoustics Speech and Signal Processing, 1993Co-Authors: Fang-yu HuangAbstract:The input index mapping adopted is the Ruritanian mapping; the output index mapping is the same as B.G. Lee's (IEEE Trans. vol. ASSP.37, no.2, p.237-44, Feb. 1989). Hardware implementations for the Prime-Factor DCT are also studied. The methodology, which deals with general (N/sub 1/*N/sub 2/)-point DCTs, where N/sub 1/ and N/sub 2/ are mutually Prime, is illustrated by converting a 15-point DCT problem into a (3*5)-point 2-D DCT problem.
C. Goutis - One of the best experts on this subject based on the ideXlab platform.
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On the computation of the Prime Factor DST
Signal Processing, 1995Co-Authors: A. Tatsaki, T. Stouraitis, C. GoutisAbstract:Abstract In this paper a new algorithm based on Prime Factor decomposition for computing the discrete sine transform (DST) is presented. The proposed 1-D N-point DST algorithm is indirectly computed by using the DFT. The DST of odd length can be implemented on the existing VLSI architectures of the DFT, while the DST of even length can be implemented on slightly modified DFT architectures. A comparison of the algorithm with other fast ones points out its computational efficiency, which is mainly based on the advantages of the Prime Factor decomposition and the proper choice of the index mappings.
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Prime-Factor DCT algorithms
IEEE Transactions on Signal Processing, 1995Co-Authors: A. Tatsaki, T. Stouraitis, C. GoutisAbstract:In this correspondence, new algorithms are presented for computing the l-D and 2-D discrete cosine transform (DCT) of even length by using the discrete Fourier transform (DFT). A comparison of the proposed algorithms to other fast ones points out their computational efficiency, which is mainly based on the advantages of Prime-Factor decomposition and a proper choice of index mappings.
G.a. Mian - One of the best experts on this subject based on the ideXlab platform.
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A family of MD FFT algorithms of complexity intermediate between the MD Cooley-Tukey FFT and the MD Prime-Factor FFT
1993 IEEE International Symposium on Circuits and Systems, 1993Co-Authors: R. Bernardini, G. Cortelazzo, G.a. MianAbstract:Twiddle-Factors elimination in the multidimensional fast Fourier transform (FFT) is approached using changes of basis, either in the signal or in the transform domain, as tools for generating FFT algorithms. The approach brings a new technique for the computation of the twiddle-Factor free multidimensional FFT which is applicable to a range of situations considerably broader than that allowed by the multidimensional Prime Factor FFT of Guessoum and Merserau. The approach allows the determination of a family of FFT algorithms with computational complexity intermediate between that of the M-D Cooley-tukey FFT and that of the M-D Prime Factor FFT.
Guoan Bi - One of the best experts on this subject based on the ideXlab platform.
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Prime Factor Algorithm for Multidimensional Discrete
2020Co-Authors: Guoan Bi, Yonghong Zeng, Yan Qiu ChenAbstract:A Prime-Factor fast algorithm is proposed for the computa- tion of the multidimensional forward and inverse discrete cosine transform (DCT). By using an example of two-dimensional (2-D) DCT, it shows that an -dimensional DCT can be obtained from a dimensional DCT with a post-processing stage. Efficient method for input/output mapping is re- ported to substantially reduce the computational overhead associated with the Prime-Factor algorithm. The discrete cosine transform is an important tool in digital signal processing for various applications. Multidimensional DCT is widely used for image and video applications (1), (13)-(17). In particular, ap- plications of three dimensions (3-D) or higher of DCT for image pro- cessing were reported in (15)-(17). Computational complexity for such applications becomes prohibitive even with current advanced proces- sors. Fast algorithms were reported to reduce the computational and structural complexity (see (1)-(10), for example). The Prime-Factor algorithm (PFA) was generally considered to be computationally ef- ficient because twiddle Factors between computational stages can be eliminated. The basic principle of the Prime-Factor algorithm is to con- vert an -dimensional DCT into dimensional DCT of reduced di- mensional sizes. A mapping process is generally needed to convert the -dimensional input array into a -dimensional array for the DCT computation. When , for example, most reported work focused on converting a 1-D DCT into a 2-D DCT (3)-(5), (7), (8). It was also reported that the 2-D DCT could be calculated by using polynomial transform computation (10), which achieved a reduction of arithmetic operations compared with other fast algorithms. By using a 2-D dis- crete Fourier transform (DFT), a Prime-Factor fast algorithm for DCT computation was reported (11). It was shown that the 2-D DFT could be achieved from a number of 1-D DFTs with a postprocessing stage. To achieve computational savings compared with the row-column al- gorithm, the required number of 1-D DFTs had to be smaller than (12). Although substantial savings in terms of the required number of arithmetic operations were achieved due to efficient computation of the DFT, this algorithm suffered a substantially computational overhead for a two-stage input/output mapping process. The mapping process is generally undesirable because it complicates the computational struc- ture and requires modulo and other arithmetic operations, which im- poses a substantially computational overhead. By using tabulation or matrix manipulation, several methods were proposed to deal with the mapping process (see (5)-(7), for example). These methods are not straightforward and difficult to use particularly for large Prime fac- tors and multidimensional computation. It is important to simplify the
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Prime Factor algorithm for multidimensional discrete cosine transform
IEEE Transactions on Signal Processing, 2001Co-Authors: Guoan Bi, Yonghong Zeng, Yen Qiu ChenAbstract:A Prime Factor fast algorithm is proposed for the computation of the multidimensional forward and inverse discrete cosine transform (DCT). By using an example of a two-dimensional (2-D) DCT, it shows that an r-dimensional DCT can be obtained from a 2r dimensional DCT with a post-processing stage, efficient method for input/output mapping is reported to substantially reduce the computational overhead associated with the Prime Factor algorithm.
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Prime Factor algorithm of discrete cosine transform
2000 10th European Signal Processing Conference, 2000Co-Authors: Guoan Bi, Yonghong ZengAbstract:Prime Factor fast algorithms are computationally efficient for various discrete transforms. However, they generally need an index mapping process to convert one-dimensional input sequence into a two-dimensional array, which results in a substantially computational overhead and an irregular computational structure. This letter attempts to minimize the computation overhead by a simple and general mapping procedure.
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Prime-Factor algorithms for generalised discrete Hartley transform
Electronics Letters, 1999Co-Authors: Guoan Bi, Chao LuAbstract:A Prime Factor fast algorithm for the type-II generalised discrete Hartley transform is presented. In addition to reducing the number of arithmetic operations and achieving a regular computational structure, a simple index mapping method is proposed to minimise the overall implementation complexity.
