Showing papers on "Split-radix FFT algorithm published in 1995"
TL;DR: A fast digital Radon transform based on recursively defined digital straight lines is described, which has the sequential complexity of N^2 log N additions for an N x N image and is shown to be quite similar to the FFT algorithm for decimation in frequency.
108 citations
TL;DR: In this paper, the authors examined both methods and analyzes why the DFT is generally more efficient and easier to use than the FFT for FDTD time-to-frequency domain conversions.
Abstract: Although it is a time-domain method, the finite-difference time-domain (FDTD) method has been used extensively for calculating frequency domain parameters such as specific absorption rate, radar cross-section, and S-parameters. When a broad frequency band is of interest, using a broad-band pulsed excitation can provide this frequency response with a single FDTD simulation. The frequency domain data can be calculated from the time domain data using either a discrete Fourier transform (DFT) or a fast Fourier transform (FFT). This letter examines both methods and analyzes why the DFT is generally more efficient and easier to use than the FFT for FDTD time-to-frequency domain conversions. >
47 citations
TL;DR: A new composite filter-bank structure is presented for the efficient implementation of the recursive discrete transformation, based on a proper combination of the concepts of polyphase filtering and the fast Fourier transformation algorithm.
Abstract: A new composite filter-bank structure is presented for the efficient implementation of the recursive discrete transformation. This structure is based on a proper combination of the concepts of polyphase filtering and the fast Fourier transformation (FFT) algorithm. Its computational complexity is in direct correspondence with the FFT, and can be operated both in sliding and block-oriented modes. The inherent parallelism of this structure enables very high speed in practical implementations. >
46 citations
TL;DR: An algorithm is described that performs well on a Convex C4/XA vector supercomputer on large FFTs by using higher-radix kernels and moving the transpose step into the computational steps.
Abstract: Some implementations of a power-of-two one-dimensional fast Fourier transform (FFT) on vector computers use radix-4 Stockham autosort kernels with a separate transpose step. This paper describes an algorithm that performs well on a Convex C4/XA vector supercomputer on large FFTs by using higher-radix kernels and moving the transpose step into the computational steps. For short transforms a different algorithm is used that calculates the FFT without storing any intermediate results to memory. Performance results using these techniques are given.
31 citations
TL;DR: Fast Fourier transform, iteration, and least-squares fit are combined to form an image-processing system for the analysis of a carrier-coded fringe pattern and the algorithm offers an improvement over the Fourier-transform method reported in the literature.
Abstract: Fast Fourier transform (FFT), iteration, and least-squares fit are combined to form an image-processing system for the analysis of a carrier-coded fringe pattern. Only one coded fringe pattern is needed for extracting unambiguous information. The coded fringe pattern is first two-dimensionally FFT filtered to produce an initial coded phase with the carrier phase in it. Several phase iterations are carried out if necessary to improve the coded phase. The least-squares-fit technique is used to obtain a pure carrier phase. Then the carrier is removed by subtracting the pure carrier phase from the coded phase. The algorithm offers an improvement over the Fourier-transform method reported in the literature. A program is designed to execute the algorithm, and the processing is automated by a personal computer with an image board. Theory and applications of speckle interferometry and three-dimensional contouring are presented.
27 citations
TL;DR: Presents a very short, simple, easy to understand bit-reversal algorithm for radix-2 fast Fourier transform (FFT), which is, furthermore, easily extendable to Radix-M and Yong's technique, which is comparable to that of the fastest algorithms.
Abstract: Presents a very short, simple, easy to understand bit-reversal algorithm for radix-2 fast Fourier transform (FFT), which is, furthermore, easily extendable to radix-M. In addition, when implemented together with Yong's (see IEEE Trans. Acoust., Speech, Signal Processing, vol.39, no.1O, p.2365-7, 1991) technique, the computing time is comparable to that of the fastest algorithms. >
26 citations
TL;DR: A generalization of the sliding FFT, which introduces a wide class of orthogonal transforms that can be implemented with the order of N complexity is proposed.
Abstract: Implementation of the transform domain adaptive filters is addressed. Recent results have shown that if the input data to a radix-2 fast Fourier transform (FFT) structure is sliding one sample at a time, only N-1 butterflies need to be calculated for updating the FFT structure. This is opposed to most of the previous reports that assume order of NlogN complexity for such implementation. In this correspondence, a generalization of the sliding FFT, which introduces a wide class of orthogonal transforms that can be implemented with the order of N complexity is proposed. >
20 citations
TL;DR: The RAFFT-GFP algorithm is superior for problem sizes larger than about 4000 components, in terms of both computation and CPU time for the examples studied in this paper.
Abstract: This paper presents the RAFFT-GFP (Recursively Applied Fast Fourier Transform for Generator Function Products) algorithm as a computationally superior algorithm for expressing and computing the reliability of k-out-of-n:G and k-to-l-out-of-n:G systems using the fast Fourier transform. Originally suggested by Barlow and Heidtmann (1984), generating functions provide a clear, concise method for computing the reliabilities of such systems. By recursively applying the FFT to computing generator function products, the RAFFT-GFP achieves an overall asymptotic computational complexity of O(n/spl middot/(log/sub 2/(n))/sup 2/) for computing system reliability. Algebraic manipulations suggested by Upadhyaya and Pham (1993) are reformulated in the context of generator functions to reduce the number of computations. The number of computations and the CPU time are used to compare the performance of the RAFFT-GFP algorithm to the best found in the literature. Due to larger overheads required, the RAFFT-GFP algorithm is superior for problem sizes larger than about 4000 components, in terms of both computation and CPU time for the examples studied in this paper. Lastly, studies of very large systems with unequal reliabilities indicate that the binomial distribution gives a good approximation for generating function coefficients, allowing algebraic solutions for system reliability. >
18 citations
11 Jan 1995
TL;DR: These algorithms get high speed FFT computation by combining the radix 4 FFT algorithm with the characteristics of the eight-neighbor processor array by estimating their processing time and comparing them with the conventional radix 2 FFT algorithms.
Abstract: Fast Fourier transform (FFT), which has wide and variety application areas, requires very high speed computation. Since parallel processing of FFT is very attractive for high speed FFT computation, many processor arrays and multiprocessor systems have been proposed with efficient FFT algorithms. As a result of the recent development of VLSI technology, several massively parallel computers have been implemented on commercial basis. The MasPar, which is one of the SIMD type massively parallel computers, consists of an eight-neighbor processor array. This paper discusses parallel 1-D FFT algorithms on an eight-neighbor processor array. We propose three algorithms according to various data allocation methods. Then we estimate and evaluate their processing time. With the number of processors N = N r × N r , processing time is estimated to be 2( N r − 2) t c + ( log 2 N r ) t b , where t c is the communication time between neighbor processors, and t b is the execution time for the radix 4 butterfly computation. We also compare these algorithms with the conventional radix 2 FFT algorithm implemented on a mesh processor array. It is shown that the radix 4 FFT algorithms are faster than the radix 2 algorithms. These algorithms get high speed FFT computation by combining the radix 4 FFT algorithm with the characteristics of the eight-neighbor processor array.
9 citations
TL;DR: A method for computing the inverse discrete Fourier transform (IDFT) by the in-place, in-order prime factor FFT algorithm (PFA) by modifying the input and the output index mapping equations.
Abstract: We present a method for computing the inverse discrete Fourier transform (IDFT) by the in-place, in-order prime factor FFT algorithm (PFA). This is achieved by modifying the input and the output index mapping equations. This approach does not result in any additional cost in terms of program length and computational time. >
TL;DR: This work proposes a parallel architecture that implements the SS radix r (r ≥ 2) algorithm, a highly efficient version of the fast Fourier transform, that is regular and modular, and presents constant geometry.
Patent•
NEC1
TL;DR: In this article, a speech coding system is shown, which comprises a linear transform unit 50 for executing linear transform on an input signal Si with a predetermined block length Sb and an FFT unit 10, 30 for executing Fast Fourier transform on the input signal S with two different block lengths, i.e., large and small, block lengths.
Abstract: A speech coding system is shown, which comprises a linear transform unit 50 for executing linear transform on an input signal Si with a predetermined block length Sb and an FFT unit 10, 30 for executing Fast Fourier transform on the input signal Si with two different, i.e., large and small, block lengths, a block length setting unit 20 for calculating a predetermined block length Sb to be set in the linear transform unit 50 according to an FFT signal generated in the FFT unit 10, 30 and setting this block length in the linear transform unit 50, and a coding unit 80 for coding an intermediate signal Sm generated in the linear transform unit 50 to form and output a bit stream So. The FFT unit has a function of selecting a block length used for the Fast Fourier transform among two, i.e., large and small, block lengths according to a continuous portion of the input signal Si.
TL;DR: In this paper, the frequency-domain signal-to-noise (S/N) ratio due to windowing by the function of sinα(X) and quantization with finite bit-length A/D converters is derived, and the relationship equation between the frequency error and the S/N ratio is derived.
Abstract: Interpolation formulas for the apodized magnitude-mode fast Fourier transformed (FFT) spectra determine accurately the frequency, damping constant, and amplitude of time-domain damped signals. However, additive noise causes a large amount of error in interpolation. In this paper, we obtain, theoretically, the frequency-domain signal-to-noise (S/N) ratio due to windowing by the function of sinα(X) and quantization with finite bit-length analog-to-digital (A/D) converters. Then, with the use of the squared ratios between three magnitudes nearest to the peak maximum on the apodized FFT spectrum, we derive the relationship equation between the frequency error and the S/N ratio. The results obtained by computer simulation of experimental conditions (i.e., sampling, quantization, windowing, FFT, and interpolation) for the Hanning window (α = 2) agree well with the theoretical calculations; the frequency errors decrease with increasing bit-length of the A/D converter. These observed errors are unavoidable because A/D converters are indispensable for measurements with Fourier transform spectrometers. Furthermore, as shown theoretically, the observed accuracy of interpolation is inversely proportional to the S/N ratio, provided that the S/N ratio is below the value due to quantization and windowing.
TL;DR: In this article, two computationally efficient Fourier transform methods, namely, the mixed radix Fast Fourier Transform (FFTA) and the Winograd Fourier Transformer (WFTA), were used to evaluate the reliability of the IEEE reliability test system.
TL;DR: It is demonstrated that this method outperforms the FFT with and without Hamming weighting both in estimating the magnitudes and phases of the spectral components of a time series and in resolving frequency to a fraction of an FFT frequency resolution cell.
Abstract: The fast Fourier transform (FFT) signature of a finite duration, constant frequency, time signal displays sidebands which are a sampling artifact. An analytical expression is derived which precisely predicts artifact behavior. Using this expression, a precise spectral estimate (PSE) is derived. It is demonstrated that this method outperforms the FFT with and without Hamming weighting both in estimating the magnitudes and phases of the spectral components of a time series. Furthermore, PSE is capable of resolving frequency to a fraction of an FFT frequency resolution cell.
15 May 1995
TL;DR: In this article, the authors combine the strengths of the FFT, CZT (chirp Z transform), and DFT (discrete Fourier transform) in a composite algorithm called the "variable search method".
Abstract: Power quality issues often are related to the presence of harmonic and nonharmonic frequencies. The authors have developed a more efficient and accurate solution than traditional FFT (fast Fourier transform) approaches. The approach combines the strengths of the FFT, CZT (chirp Z transform), and DFT (discrete Fourier transform) in a composite algorithm called the "variable search method".
TL;DR: The use of fast algorithms for evaluation of discrete Fourier transform-inverse transform pairs with uniformly spaced input data but with output data required only at exponentially spaced intervals is investigated.
Abstract: The use of fast algorithms for evaluation of discrete Fourier transform-inverse transform pairs with uniformly spaced input data but with output data required only at exponentially spaced intervals is investigated. The algorithms require order (N) arithmetic operations, rather than the order (N log(N)) required for the full FFT algorithm.
01 Mar 1995
TL;DR: The performance of a segmented FFT algorithm which allows the out-of-core computation of the Fourier transform of a very large mass storage data array is presented and the use of tunable parameters allows optimization of the algorithm on machines with different configurations.
Abstract: The performance of a segmented FFT algorithm which allows the out-of-core computation of the Fourier transform of a very large mass storage data array is presented. The code is particularly optimized for vector computers. Tests performed mainly on a CONVEX C210 vector computer showed that, for very long transforms, tuning of the main parameters involved leads to computation speed and global efficiency better than for FFTs performed in-core. The use of tunable parameters allows optimization of the algorithm on machines with different configurations.
28 Apr 1995
TL;DR: This work presents a new MD FFT algorithm capable of saving computation in front of general signal's symmetries, and can take advantage of even and odd parity's asymmetries for reducing the computation.
Abstract: Symmetric signals are defined by subsets of their support which depend on the specific symmetry. Depending on the symmetry, the cardinality of these subsets may be much smaller than that of the supports. The DFT of the symmetric signals enjoys symmetries related to the input symmetry, by which the DFT is defined by subsets the same as those defining the input signal. In principle, the computation of the DFT of symmetric signal can only use the input subset sufficient for defining the signal. In practice, all known MD FFT algorithms can only take advantage of even and odd parity's symmetries, and cannot exploit general signal symmetries for reducing the computation. This work presents a new MD FFT algorithm capable of saving computation in front of general signal's symmetries.
Journal Article•
TL;DR: The developed method enables one to obtain high resolution for low frequencies by increasing the density of sampling of the analyzed signal and has been tested both on the model data and on the real signal records.
Abstract: Realization of the discrete Fourier transform (DFT) as the fast Fourier transform (FFT) has a widespread application in practice There are, however, such problems in technology where the application of the FFT method does not justify satisfactory results Such problems comprise eg the analysis of short sections of fast decaying vibrations or the analysis of instantaneous values of nonstationary signal parameters Solving the problems arising in this type of signals analysis has contributed to development of the algorithm of the DFT fast computing for transient vibrations The developed method enables one to obtain high resolution for low frequencies by increasing the density of sampling of the analyzed signal The algorithm in terms of the computer program (Lenort (1989)) has been tested both on the model data and on the real signal records
22 May 1995
TL;DR: In this paper the fast Hartley transform (FHT) approach for computing the one-dimensional discrete pseudo-Wigner distribution (1D DPWD) is extended to compute the two-dimensional (2-D) DPWD and a new fast algorithm is presented for computing it entirely in the real domain.
Abstract: Wigner distribution (WD) is useful in analyzing and processing nonstationary signals. In this paper the fast Hartley transform (FHT) approach for computing the one-dimensional discrete pseudo-Wigner distribution (1D DPWD) is extended to compute the two-dimensional (2-D) DPWD and a new fast algorithm is presented for computing the 2-D DPWD by the 2-D FHT entirely in the real domain. First, the original 2-D real signal is converted into its complex analytic version. A fast algorithm is proposed to compute the 2-D discrete Hilbert transform using the 2-D FHT instead of the 2-D complex FFT with a reduced number of real operations. Then, the algorithm formulae are derived for computing the 2-D DPWD of the analytic signal by the 2-D FHT. Compared with the conventional FFT approach, the proposed algorithm is performed entirely in the real domain, and the computational complexity is greatly reduced from 3 2-D complex FFT's to 3 2-D real FHT's.
TL;DR: A hardware structure for fast Fourier transform computation thai that provides significant hardware savings on the requirements of data memory and multipliers and efficient data format conversions between different number systems is described.
Abstract: This paper describes a hardware structure for fast Fourier transform (FFT) computation thai is particularly suited to input data presented sequentially. The algorithm allows different representations of complex numbers to be used in the same processing system so that the FFT can be computed by using multiplication-free butterfly elements based on the radix numbers of 2, 3, 4 and 6. In comparison with previous designs in the literature, the new algorithm provides significant hardware savings on the requirements of data memory and multipliers. Furthermore, the FFT size N, which is usually a composite number of 2 or 4, can be more flexible. Efficient data format conversions between different number systems are also provided.
TL;DR: This chapter presents a discussion on group invariant Fourier transform algorithms, which fully use data invariance with respect to subgroups of the affine group of data indexing sets.
Abstract: Publisher Summary The design of algorithms for computing the crystallographic Fourier transform is a subject in applied group theory. This chapter presents a discussion on group invariant Fourier transform algorithms. Finite abelian groups serve as data indexing sets. A class of affine group fast Fourier transform (FFT) algorithms is introduced, which fully use data invariance with respect to subgroups of the affine group of data indexing sets. The chapter reviews all the necessary group theory. The affine group of a finite abelian group is defined. Constructs related to the action of affine subgroups on data indexing sets are introduced in the chapter. The chapter defines the Fourier transform of an abelian group and discussed its fundamental role in interchanging periodization and decimation operations (duality). The reduced transform (RT), Cooley–Tukey algorithm (CT), FFT, and Good–Thomas (GT) algorithms are presented as applications of this duality to different global decomposition strategies. Affine group FFT algorithms based on the RT algorithm are discussed, while those coming from the application of the affine group CT, FFT are introduced. The chapter describes a method of incorporating one-dimensional (1D) symmetry into FFT computations, which calls on lower order existing FFT routines using the symmetry condition. The chapter presents many examples to reflect both the theory and experience and others, over several years in writing code for the three-dimensional (3D) crystallographic FT.
05 Sep 1995
TL;DR: The parallel implementation of a modified, high radix fast Fourier transform (FFT) together with a Jacobi-based algorithm for matrix factorization to compute the singular value decomposition (SVD) of a 16384/spl times/16384 projection normal matrix arising from probability measure estimation in positron emission tomography (PET).
Abstract: We describe in this paper the parallel implementation of a modified, high radix fast Fourier transform (FFT) together with a Jacobi-based algorithm for matrix factorization to compute the singular value decomposition (SVD) of a 16384/spl times/16384 projection normal matrix arising from probability measure estimation in positron emission tomography (PET) We simplify the analysis significantly by working with block matrices and the Kronecker products because the symmetries built into the orthogonal decompositions allow the computation of the various factorizations of interest
Patent•
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NEC1
TL;DR: In this paper, a speech coding system is presented, which comprises a linear transform unit (50) for executing linear transform on an input signal (Si) with a predetermined block length (Sb) and an FFT unit (10, 30) with two different, i.e., large and small, block lengths.
Abstract: A speech coding system is shown, which comprises a linear transform unit (50) for executing linear transform on an input signal (Si) with a predetermined block length (Sb) and an FFT unit (10, 30) for executing Fast Fourier transform on the input signal (Si) with two different, i.e., large and small, block lengths, a block length setting unit (20) for calculating a predetermined block length (Sb) to be set in the linear transform unit (50) according to an FFT signal generated in the FFT unit (10, 30) and setting this block length in the linear transform unit (50), and a coding unit (80) for coding an intermediate signal (Sm) generated in the linear transfom unit (50) to form and output a bit stream (So). The FFT unit has a function of selecting a block length used for the Fast Fourier transform among two, i.e., large and small, block lengths according to a continuous portion of the input signal (Si).
TL;DR: In this paper, a new adaptive control algorithm in frequency domain was proposed, which corresponds to the ordinary filtered-x least mean square (LMS) algorithm in discrete time domain.
Abstract: A new adaptive control algorithm in frequency domain was proposed. This frequency domain approach corresponds to the ordinary filtered-x least mean square (LMS) algorithm in discrete time domain. In this approach, the fast Fourier transform (FFT) was used for converting signals between frequency domain and discrete time domain. Since the computaion processes in these two domains are almost independent with each other, this algorithm can be realized effectively by using two processors. Computer simulations were carried out for investigating convergence characteristics of this approach. As the result of these simulations, it was shown that this algorithm has faster convergence with less computation comparing to the ordinary filtered-x LMS algorithm.