Showing papers on "Rader's FFT algorithm published in 2000"
08 Aug 2000
TL;DR: A new FFT pruning algorithm where the number of nonzero inputs or desired outputs can be arbitrary, and the implementation is similar to the FFT algorithms that use in-place computation, with a small alteration.
Abstract: The efficiency of the fast Fourier transform may be increased by removing operations on input values which are zero, and on output values which are not required; this procedure is known as FFT pruning algorithm. Up to now some algorithms have been proposed considering decimation-in-time (DIT) or decimation-in-frequency (DIF) procedures, and considering that for a N = 2/sup M/ input points of the FFT only quantities equals to 2/sup k/ (to an integer k), of nonzero input or desired output points are required. In this paper we propose a new FFT pruning algorithm where the number of nonzero inputs or desired outputs can be arbitrary. The idea of the proposed algorithm works well with DIT as well as DIEF procedures, and the implementation is similar to the FFT algorithms that use in-place computation, with a small alteration.
49 citations
TL;DR: Although the proposed algorithm does not reach the theoretical lower bound for the number of multiplications, the algorithm possesses the regular structure of the Cooley-Tukey FFT algorithms, therefore, the FFT implementation principles can also be applied to the discrete cosine transform.
Abstract: Modification to the architecture-oriented fast algorithm for discrete cosine transform of type II from Astola and Akopian (see ibid., vol.47, no.4, p.1109-24, April 1999) is presented, which results in a constant geometry algorithm with simplified parameterized node structure. Although the proposed algorithm does not reach the theoretical lower bound for the number of multiplications, the algorithm possesses the regular structure of the Cooley-Tukey FFT algorithms. Therefore, the FFT implementation principles can also be applied to the discrete cosine transform.
39 citations
TL;DR: The use of wavelets for the solution of convolution equations is studied as a possible alternative to the well-established Fast Fourier Transform technique and of so-called vaguelettes for the representations of the given data leads to an algorithm which is even faster than FFT.
Abstract: The use of wavelets for the solution of convolution equations is studied as a possible alternative to the well-established Fast Fourier Transform (FFT) technique. Two possible solution strategies are investigated: (1) The use of wavelets for the representation of both the given data and the unknown solution. This leads to an algorithm with good de-noising and data-compression properties. In terms of computational efficiency this algorithm is inferior to FFT. (2) The use of wavelets for the representation of the unknown solution and of so-called vaguelettes for the representations of the given data. This leads to an algorithm which is even faster than FFT.
8 citations
21 Aug 2000
TL;DR: A new approach for computing DFT of arbitrary length is proposed, which is based on the arithmetic Fourier transform (AFT), which needs only /spl Oscr/(N) multiplications and has a simple computational structure, so it can be easily performed in parallel and it is very suitable for VLSI design.
Abstract: A new approach for computing DFT of arbitrary length is proposed, which is based on the arithmetic Fourier transform (AFT). The algorithm needs only /spl Oscr/(N) multiplications and has a simple computational structure, so it can be easily performed in parallel and it is very suitable for VLSI design. The algorithm is faster than the classical FFT when the length of the DFT contains relatively large factors. It is especially efficient for computing the DFT of prime length, where FFT does not work. The algorithm is competitive with the FFT in term of accuracy. A method to enhance the accuracy of the algorithm is also proposed for cases when higher accuracy is required.
6 citations
TL;DR: This work proposes effective implementations in the case of multi-dimensional radix-2 FFT for the recent RISC workstation and the vector-type supercomputer, respectively.
5 citations
18 Jun 2000
TL;DR: A high-performance parallel three-dimensional fast Fourier transform (FFT) algorithm on clusters of vector symmetric multiprocessor (SMP) nodes that can be altered into a multirow FFT algorithm to expand the innermost loop length is proposed.
Abstract: In this paper, we propose a high-performance parallel three-dimensional fast Fourier transform (FFT) algorithm on clusters of vector symmetric multiprocessor (SMP) nodes. The three-dimensional FFT algorithm can be altered into a multirow FFT algorithm to expand the innermost loop length. We use the multirow FFT algorithm to implement the parallel three-dimensional FFT algorithm. Performance results of three-dimensional power-of-two FFTs on clusters of (pseudo) vector SMP nodes, Hitachi SR8000, are reported. We succeeded in obtaining performance of about 40 GFLOPS on a 16-node Hitachi SR8000.
5 citations
TL;DR: This work proposes an original multidimensional fast Fourier transform (FFT) algorithm where the computation is first organized into multiplier-free butterflies and then completed by 1-D FFTs, finding that its total computational cost decreases as the signal space dimensions increase and its efficiency is superior to that of any other multiddimensional FFT algorithm.
Abstract: This work proposes an original multidimensional fast Fourier transform (FFT) algorithm where the computation is first organized into multiplier-free butterflies and then completed by 1-D FFTs. The properties of well-known 1-D FFT algorithms blend in quite nicely with those of the proposed multidimensional FFT scheme, extending their computational and structural characteristics to it. Strong points of the proposed method are that its total computational cost decreases as the signal space dimensions increase and that its efficiency is superior to that of any other multidimensional FFT algorithm.
4 citations
TL;DR: A new algorithm is presented for the type-II, -III and -IV discrete W transforms which involves the simple conversion of a length-N discrete W transform into a length -N discrete Hartley transform.
Abstract: A new algorithm is presented for the type-II, -III and -IV discrete W transforms which involves the simple conversion of a length-N discrete W transform into a length-N discrete Hartley transform. The total number of additional arithmetic operations introduced by the conversion is less than 5N.
3 citations
Journal Article•
TL;DR: The precedures of DCT (discrete cosine transform) and FFT (fast Fourier transform) which map integers to integers by using lifting scheme and the butterfly configuration of FFT are described.
Abstract: In this paper, the authors describe the precedures of DCT (discrete cosine transform) and FFT (fast Fourier transform) which map integers to integers by using lifting scheme and the butterfly configuration of FFT. The transform is reversible, fast and suitable for the lossless image compressions.
3 citations
Journal Article•
TL;DR: A new algorithm for the computation of Discrete Cosine Transform with odd prime length using cyclic or skew cyclic convolutions, which has low computational complexity, simple and regular structure.
Abstract: This paper proposes a new algorithm for the computation of Discrete Cosine Transform (DCT) with odd prime length using cyclic or skew cyclic convolutions. The algorithm separates DCT coefficients into three parts: DC coefficients, even and odd indexed DCT coefficients. According to the number theory a new index mapping operation is defined. By means of the index mapping operation,the even indexed part is converted to a cyclic convolution, and the odd indexed part is converted to a cyclic or skew cyclic convolution depending on its length. Since efficient and fast cyclic convolution algorithms are available in the literature, the algorithm has low computational complexity, simple and regular structure.
3 citations
01 Jan 2000
TL;DR: A new Fourier analysis technique called the arithmetic Fourier transform (AFT) is used to compute DFT, which needs only O(N) multiplications and opens up a new approach for the fast computation of DFT.
Abstract: The Discrete Fourier Transform (DFT) plays an important role in digital signal processing and many other fields.In this paper,a new Fourier analysis technique called the arithmetic Fourier transform (AFT) is used to compute DFT.This algorithm needs only O(N) multiplications.The process of the algorithm is simple and it has a unified formula,which overcomes the disadvantage of the traditional fast method that has a complex program containing too many subroutines.The algorithm can be easily performed in parallel,especially suitable for VLSI designing.For a DFT at a length that contains big prime factors,especially for a DFT at a prime length,it is faster than the traditional FFT method.The algorithm opens up a new approach for the fast computation of DFT.
Journal Article•
TL;DR: It is some application cases and the DFT is superior to FFT, and its fast implementation method—Fast Fourier Transform is better.
Abstract: This paper analyzes the calculation magnitudes of Discrete Fourier Transform(DFT)and its fast implementation method—Fast Fourier Transform(FFT), and makes a thorough comparison between their characteristics in actual application. In conclusion, it is some application cases and the DFT is superior to FFT.
Journal Article•
TL;DR: Computer emputer emulation shows that this FFT parallel algorithm is efficient, high speed, and also adapted for real-time process system.
Abstract: Compared to Discrete Fourier Transform(DFT),Fast Fourier Transform(FFT)is improved by 1 to 2 steps in speed,but when the sequence length of discrete signal is too large,FFT can not satisfy the requirements of the real-time system.A parallel algorithm for FFT on shared-memory multi-computer system is detailed in this paper,and its performance is analyzed.Computer emputer emulation shows that this FFT parallel algorithm is efficient,high speed,and also adapted for real-time process system.
01 Jan 2000
TL;DR: This work proposes an original multidimensional fast Fourier transform (FFT) algorithm where the computation is first organized into multiplier-free butterflies and then completed by 1-D FFT's.
Abstract: This work proposes an original multidimensional fast Fourier transform (FFT) algorithm where the computation is first organized into multiplier-free butterflies and then completed by 1-D FFT's. The proper- ties of well-known 1-D FFT algorithms blend in quite nicely with those of the proposed multidimensional FFT scheme, extending their computa- tional and structural characteristics to it. Strong points of the proposed method are that its total computational cost decreases as the signal space dimensions increase and that its efficiency is superior to that of any other multidimensional FFT algorithm.