Showing papers on "Prime-factor FFT algorithm published in 2001"
TL;DR: A generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph, that computes-either exactly or approximately-various marginal functions derived from the global function.
Abstract: Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.
6,637 citations
TL;DR: A new amending algorithm, poly-item cosine window interpolation, which is based on the interpolating algorithm proposed by V. Jain and T Grandke is presented, which improves the accuracy of the FFT, so it can be applied to the precision analysis for electrical harmonics.
Abstract: The fast Fourier transform (FFT) cannot be directly used in the harmonic analysis of an electric power system because of its higher errors, especially the phase error. This paper discusses the leakage phenomenon of FFT and presents a new amending algorithm, poly-item cosine window interpolation, which is based on the interpolating algorithm proposed by V. Jain and T Grandke. This new algorithm improves the accuracy of the FFT, so it can be applied to the precision analysis for electrical harmonics. The simulation result shows that applying different windows has different effects on the accuracy, and the Blackman-Harris window has the highest accuracy.
270 citations
TL;DR: An extended split-radix fast Fourier transform (FFT) algorithm is proposed that has the same asymptotic arithmetic complexity as the conventional split- Radix FFT algorithm but has the advantage of fewer loads and stores.
Abstract: An extended split-radix fast Fourier transform (FFT) algorithm is proposed. The extended split-radix FFT algorithm has the same asymptotic arithmetic complexity as the conventional split-radix FFT algorithm. Moreover, this algorithm has the advantage of fewer loads and stores than either the conventional split-radix FFT algorithm or the radix-4 FFT algorithm.
90 citations
TL;DR: The adaptation of an iterative Fourier transform algorithm for the calculation of theoretical spectral phase functions required for pulse shaping applications and is shown to converges much faster than both alternative methods.
Abstract: We demonstrate the adaptation of an iterative Fourier transform algorithm for the calculation of theoretical spectral phase functions required for pulse shaping applications. The algorithm is used to determine the phase functions necessary for the generation of different temporal intensity profiles. The performance of the algorithm is compared to two exemplary standard approaches. i.e. a Genetic Algorithm and a combination of a Simplex Downhill and a Simulated Annealing algorithm. It is shown that the iterative Fourier transform algorithm converges much faster than both alternative methods.
78 citations
01 May 2001
TL;DR: An enhanced FFT-based parametric (E-FFT) algorithm suitable for on-line harmonic analysis of electrical power systems is presented, able to provide simultaneous tracking of co-variations between integer and non-integer (sub) harmonics in a small number of iteration steps.
Abstract: An enhanced FFT-based parametric (E-FFT) algorithm suitable for on-line harmonic analysis of electrical power systems is presented. This E-FFT algorithm exploits its iteration loops in combination with the characteristic of steep-descent gradient search strategy, to limit the sensitiveness of the total harmonic distortion caused by changes in the number of parameters involved in distorted signal models. The E-FFT algorithm performs reasonably well with short data record length. Unlike most gradient-descent search algorithms for a global minimum point, the proposed E-FFT algorithm averts the risk of being trapped at any local minimum point in the search path. The E-FFT algorithm differs from other FFT and Kalman filter based tracking algorithms, in that it is able to provide simultaneous tracking of co-variations between integer and non-integer (sub) harmonics in a small number of iteration steps. Numerical illustrative examples demonstrating the operation of this E-FFT algorithm and its simulated performance results are also presented.
65 citations
TL;DR: Recursion relations in Fourier space together with fast Fourier transforms are presented which lead to a fast and accurate algorithm for solving Poisson problems within a unit disk.
29 citations
TL;DR: A fast algorithm for computing the modulated lapped transform (MLT) is proposed, based on the combination of a fast MLT via a type-IV discrete cosine transform (DCT-IV) algorithm and a fast DFT-based DCT- IV algorithm.
Abstract: A fast algorithm for computing the modulated lapped transform (MLT) is proposed. This method is based on the combination of a fast MLT via a type-IV discrete cosine transform (DCT-IV) algorithm and a fast DFT-based DCT-IV algorithm. It is achieved by defining a new data-shuffling scheme. The proposed algorithm is very suitable for efficient programmable logic device (PLD) implementation.
29 citations
31 Dec 2001
TL;DR: A new parallel radix-4 FFT algorithm based on the BSP model, which uses the group-cyclic distribution family, which makes it simple to understand and easy to implement and shows how to reduce the communication cost.
Abstract: We present a new parallel radix-4 FFT algorithm based on the BSP model. Our parallel algorithm uses the group-cyclic distribution family, which makes it simple to understand and easy to implement. We show how to reduce the communication cost of the algorithm by a factor of 3, in the case that the input/output vector is in the cyclic distribution. We also show how to reduce computation time on computers with a cache-based architecture. We present performance results on a Cray T3E with up to 64 processors, obtaining reasonable efficiency levels for local problem sizes as small as 256 and very good efficiency levels for local sizes larger than 2048.
22 citations
01 Jan 2001
TL;DR: The leakage of FFT is discussed briefly and the interpolation algorithm on Blackman Harris window is analyzed in detail, showing that the improved algorithm holds a very high precision when used for the unsynchronized sample sequence.
Abstract: The FFT has a higher error when used with a sample sequence which is not synchronized with the signal,which makes that the electric harmonic parameters can not be gotten accurately.To reduce the influence of an unsynchronized sample sequence on FFT and to improve the precision of harmonics in electric machine testing, This paper improves the algorithm by using windows and interpolation methods.This paper first discusses the leakage of FFT briefly and then analyzes the interpolation algorithm on Blackman Harris window in detail. With the new algorithm,we can get the accurate frequency offset and other accurate harmonic parameters by solving high order interpolation equation with the help of MATLAB language.After this,we make a little change to the interpolation formula,which can make the calculating accuracy be further improved on every condition especially for the severe leakage.An example of simulation is given and validates that the improved algorithm holds a very high precision when used for the unsynchronized sample sequence.
21 citations
26 Aug 2001
TL;DR: The architecture and the implementation of a 2K/4K/8K-point complex fast Fourier transform (FFT) processor for an OFDM system are presented and a new twiddle factor generation method is proposed for saving the size of ROM required for storing the twiddle factors.
Abstract: The architecture and the implementation of a 2K/4K/8K-point complex fast Fourier transform (FFT) processor for an OFDM system are presented. The processor can perform 8K-point FFT every 273 /spl mu/s, and 2K-point every 68.26 /spl mu/s at 30 MHz which is enough for the OFDM symbol rate. The architecture is based on the Cooley-Tukey (1965) algorithm for decomposing the long DFT into short length multi-dimensional DFTs. The transposition and shuffle memories are used for the implementation of multi-dimensional transforms. The CORDIC processor is employed for the twiddle factor multiplications in each dimension. A new twiddle factor generation method is also proposed for saving the size of ROM required for storing the twiddle factors.
20 citations
TL;DR: In this article, an efficient FFT algorithm is developed for discontinuous functions with both uniform and non-uniform sampled data, with O(Np+N log n) complexity, where N is the number of sampling points and p is the interpolation order.
Abstract: In the conjugate gradient–fast Fourier transform (CGFFT) method, the FFT is used to evaluate the convolution integrals. When the function to be transformed has discontinuities, the accuracy of the FFT results, and thus the CGFFT results, will degrade. In this letter, an efficient FFT algorithm is developed for discontinuous functions with both uniform and nonuniform sampled data, with O(Np+N log N) complexity, where N is the number of sampling points and p is the interpolation order. The algorithm is incorporated into the CGFFT method. Numerical results for slabs demonstrate the efficiency and accuracy of the new FFT and CGFFT algorithms. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 47–49, 2001.
TL;DR: This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of fast Fourier transform with precomputed twiddle factors and shows the strong influence of precomputation errors on the numerical stability of FFT.
Abstract: This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of fast Fourier transform (FFT) with precomputed twiddle factors and shows the strong influence of precomputation errors on the numerical stability of FFT. Numerical tests confirm the theoretical results.
07 May 2001
TL;DR: The concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fouriertransform is introduced and is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits.
Abstract: The concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has properties that it is an integer-to-integer mapping, power-adaptable and also reversible. A lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures. Split-radix FFT is used to illustrate the approach for the case of 2/sup N/-point FFT. The transform can be implemented by using only bit shifts and additions but no multiplication. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts.
TL;DR: A new approach for computing the bit reversal is based upon a pseudo semi-group homomorphism property, which is believed to be the best with only O(N) operations and optimal constant, i.e. unity.
Abstract: In this correspondence, we present a new bit reversal algorithm that outperforms the existing ones The bit reversal technique is involved in the fast fourier transform (FFT) technique, which is widely used in computer-based numerical techniques for solving numerous problems The new approach for computing the bit reversal is based upon a pseudo semi-group homomorphism property The surprising thing is that this property is almost trivial to prove, but at the same time, it also leads to a very efficient algorithm, which we believe to be the best with only O(N) operations and optimal constant, ie unity
Patent•
05 Oct 2001TL;DR: In this paper, a fast Fourier transform (FFT) processor using a high speed area-efficient algorithm is described, which is embodied by using the algorithm including a radix-4 butterfly module for receiving four input signals, and performing a butterfly operation thereon.
Abstract: The present invention discloses a fast Fourier transform (FFT) processor using a high speed area-efficient algorithm. The FFT processor is embodied by using the algorithm including a radix-4 butterfly module for receiving four input signals, and performing a butterfly operation thereon, and a radix-2 butterfly module connected to the radix-4 butterfly module, for performing the butterfly operation on the output signals from the radix-4 butterfly module. As a result, a number of nontrivial complex multipliers is reduced, to perform the FFT in a high speed in a small area.
TL;DR: In this paper, the Hartley transform is used to avoid the Hermitian symmetry of the complex-valued Fourier transform, which causes computational redundancies in terms of the number of operations and memory requirements.
Abstract: Phase‐shift migration techniques that attempt to account for lateral velocity variations make substantial use of the fast Fourier transform (FFT). Generally, the Hermitian symmetry of the complex‐valued Fourier transform causes computational redundancies in terms of the number of operations and memory requirements. In practice a combination of the FFT with the well‐known real‐to‐complex Fourier transform is often used to avoid such complications. As an alternative means to the Fourier transform, we introduce the inherently real‐valued, non‐symmetric Hartley transform into phase‐shift migration techniques. By this we automatically avoid the Hermitian symmetry resulting in an optimized algorithm that is comparable in efficiency to algorithms based on the real‐to‐complex FFT. We derive the phase‐shift operator in the Hartley domain for migration in two and three dimensions and formulate phase shift plus interpolation, split‐step migration, and split‐step double‐square‐root prestack migration in terms of the ...
TL;DR: The proposed algorithm for the determination of the coefficients of an n -dimensional ( n -D) transfer function is theoretically attractive and computationally fast and it is based on the discrete Fourier transform (DFT).
Abstract: A new algorithm is presented for the determination of the coefficients of an n -dimensional ( n -D) transfer function. The n -D state-space system is described by the n -D Fornasini–Marchesini models. The proposed algorithm is theoretically attractive and computationally fast and it is based on the discrete Fourier transform (DFT). A step-by-step example is given to illustrate the application of the proposed algorithm.
Patent•
20 Jul 2001TL;DR: In this article, a semi-variogram is generated by taking the Fourier Transform of the spatial data in the space domain and computing the complex conjugate of FFT (FFT*), complex multiplying FFT and FFT* to produce a complex product, taking the inverse Fourier transform of the complex product to generate a space domain representation of complex product (IFFT), and subtracting IFFT from the zero lag covariance.
Abstract: A Semi-Variogram is generated by taking the Fourier Transform of ‘spatial data in the space domain’ thereby producing a frequency domain representation of the spatial data having a DC component (equivalent to a mean of the spatial data), removing the DC component to produce the frequency domain representation of the spatial data with zero mean (FFT), computing the complex conjugate of FFT (FFT*), complex multiplying FFT and FFT* to produce a complex product, taking the inverse Fourier Transform of the complex product to produce a space domain representation of the complex product (IFFT), and subtracting IFFT from the zero lag covariance to generate a Semi-Variogram. This Abstract is given for the sole purpose of allowing a patent searcher to easily determine the content of the disclosure in this specification.
25 Jun 2001
TL;DR: The block six-step FFT algorithm improves performance by effectively utilizing the cache memory and is presented as a blocking algorithm for computing large one-dimensional fast Fourier transform (FFT) on cache-based processors.
Abstract: In this paper, we propose a blocking algorithm for computing large one-dimensional fast Fourier transform (FFT) on cache-based processors Our proposed FFT algorithm is based on the six-step FFT algorithm We show that the block six-step FFT algorithm improves performance by effectively utilizing the cache memory Performance results of one-dimensional FFTs on the Sun Ultra 10 and PentiumIII PC are reported We succeeded in obtaining performance of about 108MFLOPS on the Sun Ultra 10 (UltraSPARC-IIi 333MHz) and about 247MFLOPS on the 1GHz PentiumIII PC for 220-point FFT
01 Jan 2001
TL;DR: An approximate fast Hartley transform (FHT) based method to compute the discrete Fourier transform (DFT) coefficients approximately is proposed and it is found that the proposed method is computationally superior to both the radix 2 fast Fouriers transform (FFT) and also the radIX 2 approximate FFT algorithms.
Abstract: We propose an approximate fast Hartley transform (FHT) based method to compute the discrete Fourier transform (DFT) coefficients approximately. The approximate FHT is implemented using a periodic discrete wavelet transform (DWT). We find that the proposed method is computationally superior to both the radix 2 fast Fourier transform (FFT) and also the radix 2 approximate FFT algorithms.
01 Jul 2001
TL;DR: A general design and analysis approach for all fast unitary transforms relies on fundamental linear algebra methods coupled with associated dual space representations that are natural descriptions of real parity values.
Abstract: Discrete fast unitary transform algorithms, of which the fast Fourier transform (FFT) and fast discrete Cosine transform (DCT) are practical examples, are highly susceptible to temporary calculation failures because of their interconnected computational flows. Many error detection techniques for FFT algorithms have been reported, but fault tolerance issues for other important transforms have not been addressed as vigorously. A general design and analysis approach for all fast unitary transforms is presented. It relies on fundamental linear algebra methods coupled with associated dual space representations that are natural descriptions of real parity values. Basic output error patterns from single computational errors are used to define an equal-sized group of dual space basis vectors on which practical parity weighting functions may be evaluated. An iterative design approach leads to complete single error detection capabilities. FFT and fast DCT examples are given.
08 Jul 2001
TL;DR: A new fast Fourier transform (FFT)-based algorithm to expedite matrix-vector multiplies involving multilevel block-Toeplitz (BT), or T/sub f/ /sup M/ matrices, which has a similar purpose to that of Goodman, Draine and Flatau (1991), but uses less memory and is more general in implementation.
Abstract: We describe a new fast Fourier transform (FFT)-based algorithm to expedite matrix-vector multiplies involving multilevel block-Toeplitz (BT), or T/sub f/ /sup M/ matrices. Matrices of this class often occur in electromagnetic scattering applications because of the convolutional nature of the Green's function. Multilevel BT matrices are also associated with the autocorrelation of a 2-D discrete random process and with many problems involving symmetries based on cubic meshes. The algorithm presented here applies to multilevel BT matrices with blocks and sub-blocks which are themselves BT and in general asymmetric. The algorithm also provides for the last, M/sup th/ level sub-block to be a square, dense, not necessarily Toeplitz matrix. This method has a similar purpose to that of Goodman, Draine and Flatau (1991), but uses less memory and is more general in implementation.
Patent•
31 Aug 2001
TL;DR: In this paper, the authors propose a system and method of implementing a Fast Fourier Transform (FFT) function in a high data rate communication network, employing technology such as VDSL and DMT or FDM.
Abstract: A system and method of implementing a Fast Fourier Transform (FFT) function in a high data rate communication network. The communication network, employing technology such as VDSL and DMT or FDM, frequently implements a FFT at a transmitter to transfer frequency domain modulated signals into time domain signals. An IFFT is implemented at the receiver to obtain the original signal. The present system divides the channel bandwidth into sub-bands and performs the FFT function with multiple FFTs in order to reduce chip size and computation time.
01 Jan 2001
TL;DR: A novel structure for a radix-4 type FFT is proposed which can process frames of 16-bit complex samples at a rate of one output sample per 100 MHz clock cycle, thus performing a 1024-point transform in approximately 10 /spl mu/s.
Abstract: The fast Fourier transform (FFT) and its inverse (IFFT) are two of the most widely used building blocks in digital signal processing designs. A novel structure for a radix-4 type FFT is proposed which can process frames of 16-bit complex samples at a rate of one output sample per 100 MHz clock cycle, thus performing a 1024-point transform in approximately 10 /spl mu/s. The dedicated, parallel multiplier and distributed block memory features of the Virtex/sup /spl reg//-II FPGA family provide the designer with a single chip solution where external components such as memory are not required.
19 Aug 2001
TL;DR: An efficient FFT (fast Fourier transform) algorithm for OFDM (orthogonal frequency division multiplexing) modulation, named "radix-4/2", which reduces the number of non-trivial multiplications compared to the radix-2/sup 3/ FFT algorithm, and has twice the processing rate.
Abstract: We propose an efficient FFT (fast Fourier transform) algorithm for OFDM (orthogonal frequency division multiplexing) modulation, named "radix-4/2". This algorithm, based on the radix-4 butterfly operator reduces the number of non-trivial multiplications compared to the radix-2/sup 3/ FFT algorithm, and it has twice the processing rate as the radix-2/sup 3/ FFT algorithm. With 64-point and pipeline architecture, the proposed radix-4/2 algorithm reduces the number of non-trivial multiplications to the ratio of 3 to 2 compared with the radix-4 algorithm, and it has twice the processing rate as the radix-2/sup 3/ algorithm.
TL;DR: A prime factor fast algorithm for the computation of the multidimensional forward and inverse discrete cosine transform (DCT) and an efficient method for input/output mapping is reported to substantially reduce the computational overhead associated with the prime factor algorithm.
Abstract: 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.
01 Jan 2001
TL;DR: Based on this analysis, a new algorithm for efficient and accurate computation of FRFT is given, which needs not to consider the match between eigenvalues and eigenvectors.
Abstract: The definition of the Fractional Fourier Transform (FRFT) has been presented in the paper.Several fast algorithms of discrete FRFT have been reviewed.The performances of these algorithms have been analyzed briefly.Based on this analysis,a new algorithm for efficient and accurate computation of FRFT is given.This algorithm needs not to consider the match between eigenvalues and eigenvectors.There are some advantages such as easily understanding and implementing with excellent effect.And if the rotational angle is changed,only a diagonal matrix should be recomputed.A few simulation results for some typical signals are provided to compare with previous ones by other methods in the end.
27 Jul 2001
TL;DR: This work develops a parallel algorithm for FFT and implements it to price options and discusses the performance of the algorithm and the results from FFT algorithm and binomial tree algorithm developed and implemented for the same/similar problem.
Abstract: Pricing of derivatives is one of the central problems in Computational Finance. Since the theory of derivative pricing is highly mathematical, numerical techniques such as lattice approach, finite-difference and finite-element techniques among others have been resorted in the past. Recently Fast Fourier Transform (FFT) have been used for such applications as derivative pricing. In the current work, we develop a parallel algorithm for FFT and implement it to price options. Our main aim is to study the performance of this algorithm. For a data size of N and P processors, a blocked data distribution for the algorithm in general produces log(N) - log(P) iterations of local communications and log(P) iterations of remote communications. Therefore, the algorithm is divided into two parts: local and remote. In the local algorithm, the processors perform the computations on their locally partitioned data elements without any communications. In the case of remote algorithm, the processors perform the computation on the local data elements with remote communications. In this paper we focus on the remote communication and computation aspect of the algorithm. We discuss the performance of our algorithm and the results (in general terms) from FFT algorithm and binomial tree algorithm developed and implemented for the same/similar problem. We make some general observation on these two algorithms.
23 Oct 2001
TL;DR: This paper shows how to implement the wavelet transform and the Fast Fourier Transform (FFT) with a Field Programmed Gate Array (FPGA).
Abstract: This paper shows how to implement the wavelet transform and the Fast Fourier Transform (FFT) with a Field Programmed Gate Array (FPGA). First, it introduces the implementation of the wavelet transform with lattice filters and achieves the FFT with the Coordinate Rotational Digital Computation (CORDIC). Then, the emulation data of the Daubechies D4 & D6 wavelet transforms and the FFT with 16 points are given, and their performances are analyzed. The results prove this to be a novel and effective method to implement the wavelet transform and the FFT with FPGA.