Journal articles: 'Fast Fourier Transform (Fft) Algorithm'

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Chandra Yadav, Subhash, Pradeep Juneja, and R. G. Varshney. "Optimization of Resource Utilization of Fast Fourier Transform." International Journal of Reconfigurable and Embedded Systems (IJRES) 6, no. 3 (May 28, 2018): 186. http://dx.doi.org/10.11591/ijres.v6.i3.pp186-190.

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This paper considers the optimization of resource utilization for three FFT algorithms, as it pertains not to the input samples or output modes, but to the twiddle factors that arise in Cooley-Tukey FFT algorithms. Twiddle factors are a set of complex roots of unity, fixed by the transform order for the particular algorithm. This paper shows the comparison between three known FFT algorithms, DIT-FFT, DIF-FFT and GT algorithm. All these algorithms are implemented on FPGA (Spartan-3 XC3S4000l-4fg900) with XILINX 10.1 ISE.

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Byun, Keun-Yung, Chun-Su Park, Jee-Young Sun, and Sung-Jea Ko. "Vector Radix 2 × 2 Sliding Fast Fourier Transform." Mathematical Problems in Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/2416286.

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The two-dimensional (2D) discrete Fourier transform (DFT) in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT) algorithm based on the vector radix (VR) 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.

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Philipov, Ph, and V. Lazarov. "Investigation of the Indirect Hypercube as Natural Architecture for Parallel Algorithms of a Transpose Type for FFT and Other Fourier-Related Transforms." Information Technologies and Control 11, no. 2 (October 2, 2014): 29–44. http://dx.doi.org/10.2478/itc-2013-0010.

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Abstract The natural architectures are architectures, derived from the signal graph of the corresponding algorithm. That is why they are considered to be the most appropriate architectures for parallel realization of this algorithm. For Fast Fourier Transform algorithm (FFT) two types of natural architectures are known – the direct and the indirect hypercube. The direct hypercube has been investigated and analyzed a long time ago. The development of the concept of Indirect Hypercube, although quite old, is too difficult, controversal and still unfinished. Fast Hartley transform (FHT)/Real-valued Fast Fourier transform (RFFT) algorithms are important Fourier-related transforms, because they lower twice the operational and memory requirements when the input data is real-valued. These types of algorithms, however, have an irregular computational structure, which makes their parallel implementation a very difficult task. The aim of this paper is, based on the results achieved so far, to present further development of the concept Indirect Hypercube. A method of parametric synthesis of an indirect hypercube is described as a model of parallel FFT algorithms of a transpose type with different granularity/radix. This method is generalized for relevant RFFT/FHT and FCT algorithms. Two types of SIMD array architectures are described (radix-2 and radix-4), based on the indirect hypercube concept. These architectures are implemented as fast FFT/RFFT/FHT processors for real time applications. The performance estimation, as well as the estimation of resource utilization is carried out.

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Andersson, Fredrik, and Johan Robertsson. "Fast τ-p transforms by chirp modulation." GEOPHYSICS 84, no. 1 (January 1, 2019): A13—A17. http://dx.doi.org/10.1190/geo2018-0380.1.

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We have developed simple, fast, and accurate algorithms for the linear Radon ([Formula: see text]-[Formula: see text]) transform and its inverse. The algorithms have an [Formula: see text] computational complexity in contrast to the [Formula: see text] cost of a direct implementation in 2D and an [Formula: see text] computational complexity compared to the [Formula: see text] cost of a direct implementation in 3D. The methods use Bluestein’s algorithm to evaluate discrete nonstandard Fourier sums, and they need, apart from the fast Fourier transform (FFT), only multiplication of chirp functions and their Fourier transforms. The computational cost and accuracy are thus reduced to that inherited by the FFT. Fully working algorithms can be implemented in a couple of lines of code. Moreover, we find that efficient graphics processing unit (GPU) implementations could achieve processing speeds of approximately [Formula: see text], implying that the algorithms are I/O bound rather than compute bound.

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HAMMERSLEY, ANDREW. "Parallelisation of a 2-D Fast Fourier Transform Algorithm." International Journal of Modern Physics C 02, no. 01 (March 1991): 363–66. http://dx.doi.org/10.1142/s0129183191000494.

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The calculation of two and higher-dimension Fast Fourier Transforms (FFT’s) are of great importance in many areas of data analysis and computational physics. The two-dimensional FFT is implemented for a parallel network using a master-slave approach. In-place performance is good, but the use of this technique as an “accelerator” is limited by the communications time between the host and the network. The total time is reduced by performing the host-master communications in parallel with the master-slave communications. Results for the calculation of the two-dimensional FFT of real-valued datasets are presented.

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Singhal, Akarshika, Anjana Goen, and Tanu Trushna Mohapatrara. "Design and Implementation of Fast Fourier Transform (FFT) using VHDL Code." International Journal of Emerging Research in Management and Technology 6, no. 8 (June 25, 2018): 268. http://dx.doi.org/10.23956/ijermt.v6i8.150.

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The Discrete Fourier Transform (DFT) can be implemented very fast using Fast Fourier Transform (FFT). It is one of the finest operation in the area of digital signal and image processing. FFT is a luxurious operation in terms of MAC. To achieve FFT calculation with a many points and with maximum number of samples the MACs requirement could not be matched by efficient hardware’s like DSP. A parallel and pipelined Fast Fourier Transform (FFT) processor for use in the Orthogonal Frequency division Multiplexer (OFDM) and WLAN, unlike being stored in the traditional ROM. The twiddle factors in our pipelined FFT processor can be accessed directly. In this paper, we present the implementation of fast algorithms for the DFT for evaluating their performance. The performance of this algorithm by implementing them on the Xillinx 9.2i Spartan 3E FPGAs by developing our own FFT processor architecture.

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Amannah and Bakpo. "SIMPLIFIED BLUESTEIN NUMERICAL FAST FOURIER TRANSFORMS ALGORITHM FOR DSP AND ASP." International Journal of Research -GRANTHAALAYAH 3, no. 11 (November 30, 2015): 153–63. http://dx.doi.org/10.29121/granthaalayah.v3.i11.2015.2925.

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This research was designed to develop a simplified Bluestein numerical FFT algorithm necessary for the processing of digital signals. The simplified numerical algorithm developed in this study is abbreviated with SBNADSP. The methodology adopted in this work was iterative and incremental development design. The major technology used in this work is the Bluestein numerical FFT algorithm. The study set the pace for its goal by re-indexing, decomposing, and simplifying the default Fast Fourier Transform Algorithms (the Bluestein FFT Algorithm). The improved efficiency of the Bluestein FFT algorithm is accounted for by the obvious reduction in the number of operations and operators in the simplified Bluestein algorithms. The SBTNADSP is designed to have four products, and three exponentiations against the default Bluestein FFT algorithm which has six exponentiations and eight products. Since the increase in the number of operators increases the length of operation, it is therefore reasonable to infer that the algorithm with the less number of operators will run shorter execution time than the one with greater operators. In line with this, we conclude that SBNADSP is of greater efficiency than the Bluestein numerical algorithm.The result of this study showed that a faster numerical algorithm other than the Bluestein fftalgorithms is possible for the processing of digital signals.

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Powell, Harold R. "The Rossmann Fourier autoindexing algorithm inMOSFLM." Acta Crystallographica Section D Biological Crystallography 55, no. 10 (October 1, 1999): 1690–95. http://dx.doi.org/10.1107/s0907444999009506.

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The fast Fourier transform (FFT) autoindexing routines written by the Rossmann group at Purdue University have been incorporated inMOSFLM, providing a rapid and reliable method of indexing oscillation images. This is a procedure which extracts direct-space information about the unit cell from the FFT. The method and its implementation inMOSFLMare discussed.

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Raftery, J., L. Sawyer, and G. S. Pawley. "A fast Fourier transformation algorithm for parallel computers." Journal of Applied Crystallography 18, no. 6 (December 1, 1985): 424–29. http://dx.doi.org/10.1107/s0021889885010652.

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A new algorithm is presented for using the fast Fourier transform (FFT) in a very efficient mode. This algorithm is ideal for a parallel computer such as the ICL Distributed Array Processor (DAP), though it can be used with benefit on any serial computer. For a two- or three-dimensional electron density Fourier map the Fourier coefficients are arranged in a one-dimensional vector form of the chosen length and the whole map is obtained by a single FFT operation. To obtain a higher density of calculated points in the map a number of FFT operations is required, each entailing a phase modification of the one-dimensional Fourier coefficients. A three-dimensional map using 1429 crystal reflections and giving the density at 32768 points takes roughly 2 s in the ICL DAP.

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Peng, Yan Qing, Feng Wang, Ji Zhang, Jia Li, and Da Min Zhang. "Research of a New Power Quality Detection System Based on ARM." Applied Mechanics and Materials 568-570 (June 2014): 1825–33. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.1825.

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Based on the comparative analysis of the fast Fourier transform (FFT), the short-time Fourier transform (STFT), the wavelet transform (WT) and other power quality detection algorithms, this paper puts forward to a new power quality detection algorithm which combines the Fourier transform with the wavelet transform. The transient as well as the steady state signals are separated on the basis that the wavelet transform is sensitive to the singular signals. The presented algorithm detects a variety of harmonic parameters of the gird after the separation of steady state signals is finished by fast Fourier transform. A new power quality detection system is then designed based on the core chip of S3C2440A, and the algorithm which is ARM-9 based is transplanted into the embedded Linux operating system to carry out the experiments. Analysis of the experimental data shows the detection algorithm is reliable by Fourier transform and wavelet transform.

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Liu, Guibo, Dazu Huang, Dayong Luo, Wang Lei, Ying Guo, and Moonho Lee. "Fast Jacket-Haar Transform with Any Size." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/628642.

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Jacket-Haar transform has been recently generalized from Haar transform and Jacket transform, but, unfortunately, it is not available in a case where the lengthNis not a power of 2. In this paper, we have proposed an arbitrary-length Jacket-Haar transform which can be conveniently constructed from the 2-point generalized Haar transforms with the fast algorithm, and thus it can be constructed with any sizes. Moreover, it can be further extended with elegant structures, which result in the fast algorithms for decomposing. We show that this approach can be practically applied for the electrocardiogram (ECG) signal processing. Simulation results show that it is more efficient than the conventional fast Fourier transform (FFT) in signal processing.

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Noskov, Mikhail, Valeriy Tutatchikov, Mikhail Lapchik, Marina Ragulina, and Tatiana Yamskikh. "Application of parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for digital image processing of satellite data." E3S Web of Conferences 75 (2019): 01012. http://dx.doi.org/10.1051/e3sconf/20197501012.

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In modern systems of remote sensing two-dimensional fast Fourier transform (FFT) has been widely used for digital processing of satellite images and subsequent image filtering. This article provides a parallel version two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm and its implementation for processing the satellite image of Krasnoyarsk and its suburban areas.

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Liu, Shuangbiao, and Qian Wang. "Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm." Journal of Tribology 124, no. 1 (June 19, 2001): 36–45. http://dx.doi.org/10.1115/1.1401017.

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The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green’s function for the cases with known Green’s functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC-FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

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Fu, Chao, Qing Lv, and Hsiung-Cheng Lin. "Development of Deep Convolutional Neural Network with Adaptive Batch Normalization Algorithm for Bearing Fault Diagnosis." Shock and Vibration 2020 (September 18, 2020): 1–10. http://dx.doi.org/10.1155/2020/8837958.

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It is crucial to carry out the fault diagnosis of rotating machinery by extracting the features that contain fault information. Many previous works using a deep convolutional neural network (CNN) have achieved excellent performance in finding fault information from feature extraction of detected signals. They, however, may suffer from time-consuming and low versatility. In this paper, a CNN integrated with the adaptive batch normalization (ABN) algorithm (ABN-CNN) is developed to avoid high computing resource requirements of such complex networks. It uses a large-scale convolution kernel at the grassroots level and a multidimensional 3 × 1 small convolution nuclear. Therefore, a fast convergence and high recognition accuracy under noise and load variation environment can be achieved for bearing fault diagnosis. The performance results verify that the proposed model is superior to Support Vector Machine with Fast Fourier Transform (FFT-SVM) and Multilayer Perceptron with Fast Fourier Transform (FFT-MLP) models and Deep Neural Network with Fast Fourier Transform (FFT-DNN).

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Dołęgowski, Michał, and Mirosław Szmajda. "A Novel Algorithm for Fast DC Electric Arc Detection." Energies 14, no. 2 (January 7, 2021): 288. http://dx.doi.org/10.3390/en14020288.

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Electric arcing is a common problem in DC power systems. To overcome this problem, the electric arc detection algorithm has been developed as a faster alternative to existing algorithms. The following issues are addressed in this paper: The calculation of the proposed algorithm of incremental decomposition of the signal over time; the computational complexity of Fast Fourier Transform (FFT) and the incremental decomposition; the test bench used to measure electric arcs at given parameters; the analysis of measurements using FFT; and the analysis of measurements using incremental decomposition. The parameters are the DC voltage, electric load, and width of the gap between electrodes. The results showed that the proposed algorithm allows for a faster calculation—about seven times faster than FFT—and cheaper implementation in electric arc detection devices than FFT.

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Dołęgowski, Michał, and Mirosław Szmajda. "A Novel Algorithm for Fast DC Electric Arc Detection." Energies 14, no. 2 (January 7, 2021): 288. http://dx.doi.org/10.3390/en14020288.

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Electric arcing is a common problem in DC power systems. To overcome this problem, the electric arc detection algorithm has been developed as a faster alternative to existing algorithms. The following issues are addressed in this paper: The calculation of the proposed algorithm of incremental decomposition of the signal over time; the computational complexity of Fast Fourier Transform (FFT) and the incremental decomposition; the test bench used to measure electric arcs at given parameters; the analysis of measurements using FFT; and the analysis of measurements using incremental decomposition. The parameters are the DC voltage, electric load, and width of the gap between electrodes. The results showed that the proposed algorithm allows for a faster calculation—about seven times faster than FFT—and cheaper implementation in electric arc detection devices than FFT.

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Reed, Michael J., Hung V. Nguyen, and Ronald E. Chambers. "Computing the Fourier transform in geophysics with the transform decomposition DFT." GEOPHYSICS 58, no. 11 (November 1993): 1707–9. http://dx.doi.org/10.1190/1.1443386.

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The Fourier transform and its computationally efficient discrete implementation, the fast Fourier transform (FFT), are omnipresent in geophysical processing. While a general implementation of the discrete Fourier transform (DFT) will take on the order [Formula: see text] operations to compute the transform of an N point sequence, the FFT algorithm accomplishes the DFT with an operation count proportional to [Formula: see text] When a large percentage of the output coefficients of the transform are not desired, or a majority of the inputs to the transform are zero, it is possible to further reduce the computation required to perform the DFT. Here, we review one possible approach to accomplishing this reduction and indicate its application to phase‐shift migration.

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Zhang, Wenji, Ahmad Hoorfar, and Christopher Thajudeen. "Two- and Three-Dimensional Fast Intrawall Imaging with Microwave Tomographic Algorithm." International Journal of Antennas and Propagation 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/7267601.

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A fast and efficient microwave tomographic algorithm is proposed for 2-D and 3-D real-time intrawall imaging. The exploding reflection model is utilized to simplify the imaging formulation, and the half-space Green’s function is expanded in the spectral domain to facilitate the easy implementation of the imaging algorithm with the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The linearization of the inversion scheme and employment of FFT/IFFT in the imaging formula make the algorithm suitable for various applications pertaining to the inspection of a large probed region and allow real-time processing. Representative numerical and experimental results are presented to show the effectiveness and efficiency of the proposed algorithm for real-time intrawall characterization.

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Kühl, Henning, Maurico D. Sacchi, and Jürgen Fertig. "The Hartley transform in seismic imaging." GEOPHYSICS 66, no. 4 (July 2001): 1251–57. http://dx.doi.org/10.1190/1.1487072.

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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 Hartley transform as examples. We test the Hartley phase‐shift operator for poststack and prestack migration using the SEG/EAGE salt model and the Marmousi data set, respectively.

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Farhan, Mhnd. "Glance on Parallelization of FFT Algorithms." Land Forces Academy Review 24, no. 1 (March 1, 2019): 77–82. http://dx.doi.org/10.2478/raft-2019-0009.

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Abstract This paper implores the parallelization of Fast Fourier Transform (FFT) algorithms and evaluates the resultant parallelized source codes. The FFT algorithm is considered to be among the most important algorithms in the digital era. There are various FFT algorithms but just a few are considered in this paper. The Cooley-Tukey FFT is the most widely known and used. With no exception, in this paper, the radix-2 Decimation in Time (DIT) and Decimation in Frequency (DIF) are studied and implemented. Another important FFT algorithm that is the Goertzel is also considered in this paper.

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Liu, R. H., Q. Zhang, and G. Yin. "Option pricing in a regime-switching model using the fast Fourier transform." Journal of Applied Mathematics and Stochastic Analysis 2006 (September 20, 2006): 1–22. http://dx.doi.org/10.1155/jamsa/2006/18109.

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This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black-Scholes formula. Finally, numerical results are reported.

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Langs, David A. "Elimination of minimal FFT grid-size limitations." Journal of Applied Crystallography 35, no. 4 (July 18, 2002): 505. http://dx.doi.org/10.1107/s0021889802008312.

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The fast Fourier transform (FFT) algorithm as normally formulated allows one to compute the Fourier transform of up toNcomplex structure factors,F(h),N/2 ≥h> −N/2, if the transform ρ(r) is computed on anN-point grid. Most crystallographic FFT programs test the ranges of the Miller indices of the input data to ensure that the total number of grid divisions in thex,yandzdirections of the cell is sufficiently large enough to perform the FFT. This note calls attention to a simple remedy whereby an FFT can be used to compute the transform on as coarse a grid as one desires without loss of precision.

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Diao, Jie Tao, Jing Guo, Nan Li, Wei Yi, Sen Liu, Qiang Li, and Hui Xu. "The Research and Improvement of APFFT Algorithm." Advanced Materials Research 532-533 (June 2012): 1841–45. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.1841.

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Discrete Fourier Transform (DFT) is widely used in spectrum analysis. All Phase Fast Fourier Transform (APFFT) is proposed to improve FFT. It has merits such as phase invariance and small spectral leakage. But APFFT is a concrete algorithm. There are no parameters to adjust the result. The paper researches APFFT by changing the length of the overlapping data segments of APFFT. This change gives APFFT some new characteristic and some meaningful results are got.

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Konguvel, Elango, and Muniandi Kannan. "A Survey on FFT/IFFT Processors for Next Generation Telecommunication Systems." Journal of Circuits, Systems and Computers 27, no. 03 (October 30, 2017): 1830001. http://dx.doi.org/10.1142/s0218126618300015.

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The Fast Fourier Transform and Inverse Fast Fourier Transform (FFT/IFFT) are the most significant digital signal processing (DSP) techniques used in Orthogonal Frequency Division Multiplexing (OFDM)-based applications which include day-to-day wired/wireless communications, broadband access, and information sharing. The advancements in telecommunication technologies require an efficient FFT/IFFT processing device to meet the necessary specifications which depend on the particular application. A real-time implementation of high-speed FFT/IFFT processor with less area that operates in minimal power consumption is essential in designing an OFDM integrated chip. A comparative study of efficient algorithms and architectures for FFT chip design is presented in this paper. It is also recommended that mixed-radix/higher-radix algorithm combined with Single-path Delay Commutator (SDC) architecture is appropriate for massive MIMO in 5G, optical OFDM, cooperative MIMO and multi-user MIMO-based applications.

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Wan, Zhou, Zhang, Chen, and Yu. "Efficient Algorithm for SAR Refocusing of Ground Fast-Maneuvering Targets." Remote Sensing 11, no. 19 (September 22, 2019): 2214. http://dx.doi.org/10.3390/rs11192214.

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The synthetic aperture radar (SAR) image of moving targets will defocus due to the unknown motion parameters. For fast-maneuvering targets, the range cell migration (RCM), Doppler frequency migration and Doppler ambiguity are complex problems. As a result, focusing of fast-maneuvering targets is difficult. In this work, an efficient SAR refocusing algorithm is proposed for fast-maneuvering targets. The proposed algorithm mainly contains three steps. Firstly, the RCM is corrected using sequence reversing, matrix complex multiplication and an improved second-order RCM correction function. Secondly, a 1D scaled Fourier transform is introduced to estimate the remaining chirp rate. Thirdly, a matched filter based on the estimated chirp rate is proposed to focus the maneuvering target in the range–azimuth time domain. The proposed method is computationally efficient because it can be implemented by the fast Fourier transform (FFT), inverse FFT and non-uniform FFT. A new deramp function is proposed to further address the serious problem of Doppler ambiguity. A spurious peak recognition procedure is proposed on the basis of the cross-term analysis. Simulated and real data processing results demonstrate the validity of the proposed target focusing algorithm and spurious peak recognition procedure.

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Sapper, André, Guilherme Paim, Eduardo Antônio César Da Costa, and Sergio Bampi. "Exploring the CORDIC Algorithm and Clock-Gating for Power-Efficient Fast Fourier Transform Hardware Architectures." Journal of Integrated Circuits and Systems 16, no. 2 (August 15, 2021): 1–11. http://dx.doi.org/10.29292/jics.v16i2.226.

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This work explores hardware-oriented optimizations for the CORDIC (COordinate Rotation Digital Computer) algorithm investigating the power-efficiency improvements employing N-point Fast Fourier Transform (FFT) hardware architectures. We introduced three hardware-oriented optimizations for the CORDIC: (a) improving the signal extension, (b) removing the angle accumulation and (c) eliminating the redundancies in the iterations, both unnecessary when processing the FFT processing. Fully sequential FFT architectures of 32, 64, 128, and 256 points were synthesized employing ST 65 nm standard cell libraries. The results show up to 38% of power savings on average when using our best CORDIC optimization proposal to the FFT architecture comparing to the explicit multiply-based butterfly version. Moreover, when combining our best CORDIC optimization with the clock-gating technique, the power savings rises to 78.5% on average for N-point FFT.

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AL NA'MNEH, RAMI, W. DAVID PAN, and SEONG-MOO YOO. "TWO PARALLEL 1-D FFT ALGORITHMS WITHOUT ALL-TO-ALL COMMUNICATION." Parallel Processing Letters 16, no. 02 (June 2006): 153–64. http://dx.doi.org/10.1142/s012962640600254x.

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Computing the 1-D Fast Fourier Transform (FFT) using the conventional six-step FFT algorithm on parallel computers requires intensive all-to-all communication due to the necessity of matrix transpose in three steps. This all-to-all communication is a limiting factor in improving the performance of FFT in its parallel implementations. In this paper, we present two parallel algorithms for implementing the 1-D FFT without all-to-all communication between processors, at the expense of increased inner-processor computation as compared to the conventional six-step FFT algorithm. Our analysis reveals the advantage of these two algorithms over the six-step FFT algorithm in parallel systems where the cost of inter-processor communication outweighs the cost of inner-processor computation. As a case study, we choose a 32-node Beowulf cluster with fast processors (running at 2 GHz) but relatively slow inter-processor communication (over a 100 Mbit/s switch). Simulation results on this cluster demonstrate that the proposed no-communication FFT algorithms can achieve a speedup ranging from 1.1 to 1.5 over the six-step FFT algorithm.

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Chen, Shu-Wen, Feng Lu, and Yao Ma. "Fitting Green’s Function FFT Acceleration Applied to Anisotropic Dielectric Scattering Problems." International Journal of Antennas and Propagation 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/123739.

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A volume integral equation based fast algorithm using the Fast Fourier Transform of fitting Green’s function (FG-FFT) is proposed in this paper for analysis of electromagnetic scattering from 3D anisotropic dielectric objects. For the anisotropic VIE model, geometric discretization is still implemented by tetrahedron cells and the Schaubert-Wilton-Glisson (SWG) basis functions are also used to represent the electric flux density vectors. Compared with other Fast Fourier Transform based fast methods, using fitting Green’s function technique has higher accuracy and can be applied to a relatively coarse grid, so the Fast Fourier Transform of fitting Green’s function is selected to accelerate anisotropic dielectric model of volume integral equation for solving electromagnetic scattering problems. Besides, the near-field matrix elements in this method are used to construct preconditioner, which has been proved to be effective. At last, several representative numerical experiments proved the validity and efficiency of the proposed method.

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Zamiri, Farshad, and Abdolreza Nabavi. "A modified Fresnel-based algorithm for 3D microwave imaging of metal objects." International Journal of Microwave and Wireless Technologies 11, no. 4 (September 12, 2018): 313–25. http://dx.doi.org/10.1017/s175907871800123x.

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AbstractMicrowave holography technique reconstructs a target image using recorded amplitudes and phases of the signals reflected from the target with Fast Fourier Transform (FFT)-based algorithms. The reconstruction algorithms have two or more steps of two- and three-dimensional Fourier transforms, which have a high computational load. In this paper, by neglecting the impact of target depth on image reconstruction, an efficient Fresnel-based algorithm is proposed, involving only one-step FFT for both single- and multi-frequency microwave imaging. Numerous tests have been performed to show the effectiveness of the proposed algorithm including planar and non-planar targets, using the raw data gathered by means of a scanner operating in X-band. Finally, a low-cost and high-speed hardware architecture based on fixed-point arithmetic is introduced which reconstructs the planar targets. This pipeline architecture was tested on field programmable gate arrays operating at 200 MHz clock frequency, which illustrates more than 30 times improvement in computation time compared with a computer.

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Kong, Wei, Xiao Yang, Feng Zhou, Jia Xie, Chuan Chen, Na Li, and Wen Yang. "Fast Analysis of Broadband Electromagnetic Scattering Characteristics of Electrically Large Targets using Precorrected Fast Fourier Transform Algorithm based on Near Field Matrix Interpolation Method." Applied Computational Electromagnetics Society 36, no. 7 (August 19, 2021): 928–34. http://dx.doi.org/10.47037/2021.aces.j.360716.

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In this paper, a new method is proposed to analyze the broadband electromagnetic characteristics of electrically large targets by combining the precorrected-FFT algorithm (P-FFT) with the near-field matrix interpolation technique. The proposed method uses the precorrected-FFT algorithm to reduce the storage and accelerate the matrix vector product of the far field. In order to make the precorrected-FFT algorithm can calculate the broadband characteristics of electrically large targets more quickly, the matrix interpolation method is used to interpolate the near-field matrix of the precorrected-FFT algorithm to improve the efficiency of calculation. The numerical results obtained validate the proposed method and its implementation in terms of accuracy and runtime performance.

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Pham, Giao N., Anh N. Bui, Binh A. Nguyen, Tung V. Nguyen, and Hai T. Nguyen. "Fast IQ Amplitude Approximation Method for ASIC Digital System." International Journal of Emerging Technology and Advanced Engineering 11, no. 8 (August 19, 2021): 19–22. http://dx.doi.org/10.46338/ijetae0821_03.

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In some modules of digital systems, such as Fast Fourier Transform (FFT), Discrete Fourier transform (DFT), IQ (in-phase and quadrature components) modulation/ demodulation, the outputs use the complex data formed , and the calculation of its magnitude value √ are required. In software digital signal processing platform, the multiplication and square root operations are executed by using its math library; however, in Application specific integrated circuit (ASIC) digital system design, the implementation of those operators via Coordinate Rotation Digital Computer (CORDIC) algorithm requires the numerous resources and delays. So, in this paper, we present a fast approximation method for above problem which takes a small delay but acceptable accuracy for AISC digital system design. Keywords—ASIC, Digital system design, FFT, DFT, Fast amplitude approximation, Max-Min approximation.

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Gauss, Jürgen, and Eric J. Heller. "A time-dependent semiclassical wavepacket method using a fast Fourier transform (FFT) algorithm." Computer Physics Communications 63, no. 1-3 (February 1991): 375–88. http://dx.doi.org/10.1016/0010-4655(91)90264-l.

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Shiu, Peter. "The whole can be very much less than the sum of its parts." Mathematical Gazette 103, no. 556 (February 14, 2019): 117–27. http://dx.doi.org/10.1017/mag.2019.14.

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This Article is on the discrete Fourier transform (DFT) and the fast Fourier transform (FFT). As we shall see, FFT is a slight misnomer, causing confusion to beginners. The idiosyncratic title will be clarified in §4.Computing machines are highly efficient nowadays, and much of the efficiency is based on the use of the FFT to speed up calculations in ultrahigh precision arithmetic. The algorithm is now an indispensable tool for solving problems that involve a large amount of computation, resulting in many useful and important applications: for example, in signal processing, data compression and photo-images in general, and WiFi, mobile phones, CT scanners and MR imaging in particular.

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Yang, Hua, Jun Wu, and Lei Meng Cheng. "Research and Design about a System of Harmonic Detection Based on ARM and HHT." Applied Mechanics and Materials 333-335 (July 2013): 487–91. http://dx.doi.org/10.4028/www.scientific.net/amm.333-335.487.

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As we all know FFT(Fast Fourier Transform) can be used analyze and calculate linear and stationary signals, while signals in reality are always nonlinear and transient, so we use HHT(Hilbert-Huang Transform) to detect them. In the past,scholars detect harmonics by applying ARM accompany with FFT. In this article, we use the development board S3C6410-as hardware platform. our processor is ARM, while the main algorithm is HHT.

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Pointon, C. T., and R. A. Carrasco. "A Transputer Processing System Interface for The Evaluation of Digital Signal Processing Algorithms." International Journal of Electrical Engineering & Education 31, no. 1 (January 1994): 54–65. http://dx.doi.org/10.1177/002072099403100106.

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A transputer processing system interface for the evaluation of digital signal processing algorithms The design and construction of a low-cost transputer processing system input/output (I/O) interface for the acquisition and retrieval of data, and its use in the evaluation of the computational performance characteristics of discrete convolution in the time domain, and fast convolution, using a non-look-up table fast Fourier transform (FFT) algorithm, is presented.

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Jin, Lin, and Qiu Lei Du. "The Systematic Study of Music Spectrum Display Based on FFT." Advanced Materials Research 945-949 (June 2014): 1764–67. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.1764.

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Spectrum analysis is the superposition signal intodifferent frequency component and the imaginary indexcomponent, the analysis of signal from the frequency point of view. It is widely used in voice processing, image processing, digital audio, seismic exploration. The FFT algorithm, provides an effective solution forreal-time processing of frequency domain analysis. Music display system based on FFT spectrum, the main work is as follows:First, the fast Fourier transform ideas a brief description, and combined with the specific hardware and software implementations of the algorithm of the system used by the fast Fourier transform is described in detail. Then, describes the main hardware devices used in the system, including STC12C5A60S2 chips, display principle Principle 32 * 64LED dot matrix screen, use 74LS595 and 74LS164's. The system is simple, easy to use, you can use STC12C5A60S2 SCM data processing functions of the sound signal spectrum analysis.

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Morello, V., E. D. Barr, B. W. Stappers, E. F. Keane, and A. G. Lyne. "Optimal periodicity searching: revisiting the fast folding algorithm for large-scale pulsar surveys." Monthly Notices of the Royal Astronomical Society 497, no. 4 (August 6, 2020): 4654–71. http://dx.doi.org/10.1093/mnras/staa2291.

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ABSTRACT The fast folding algorithm (FFA) is a phase-coherent search technique for periodic signals. It has rarely been used in radio pulsar searches, having been historically supplanted by the less computationally expensive fast fourier transform (FFT) with incoherent harmonic summing (IHS). Here, we derive from first principles that an FFA search closely approaches the theoretical optimum sensitivity to all periodic signals; it is analytically shown to be significantly more sensitive than the standard FFT+IHS method, regardless of pulse period and duty cycle. A portion of the pulsar phase space has thus been systematically underexplored for decades; pulsar surveys aiming to fully sample the pulsar population should include an FFA search as part of their data analysis. We have developed an FFA software package, riptide, fast enough to process radio observations on a large scale; riptide has already discovered sources undetectable using existing FFT+IHS implementations. Our sensitivity comparison between search techniques also shows that a more realistic radiometer equation is needed, which includes an additional term: the search efficiency. We derive the theoretical efficiencies of both the FFA and the FFT+IHS methods and discuss how excluding this term has consequences for pulsar population synthesis studies.

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Eskola, Sisko Maria, and Folke Stenman. "Interpolation of Spectral Data Using the Shift Theorem of the Discrete Fourier Transform." Applied Spectroscopy 51, no. 8 (August 1997): 1179–84. http://dx.doi.org/10.1366/0003702971941719.

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We present a method for interpolating discrete spectral data using the shift theorem of the discrete Fourier transform. The advantages of the method as compared to ordinary curve fitting and similar direct interpolation methods are that, being based on the discrete Fourier transform, our method is also very fast for large sample volumes if used with the fast Fourier transform (FFT) algorithm. In contrast to direct interpolation methods in spectral space, our method does not modify the modulus of the inverse Fourier transform of the shifted profile, so that the spectral content of the signal is preserved. The basis of the method also makes it suitable for analyzing hot-band structures in vibrational spectra. The method is illustrated with two examples.

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Hsu, J. T., and J. S. Dranoff. "Numerical inversion of certain laplace transforms by the direct application of fast fourier transform (FFT) algorithm." Computers & Chemical Engineering 11, no. 2 (January 1987): 101–10. http://dx.doi.org/10.1016/0098-1354(87)80011-x.

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Abdulzhraa AL-Sagheer, Radhwan Hussein, K. I. Mohammed, Alaa Abdul Hussein Mezher, and Karrar Abdullah Mohammed Habeeban. "Impact of Crack Length into Pipe Conveying Fluid Utilizing Fast Fourier transform Computer Algorithm." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 4 (August 1, 2019): 2541. http://dx.doi.org/10.11591/ijece.v9i4.pp2541-2547.

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One of the most prominent problems experienced by the oil facilities is leakage of oil from the pipes. This problem caused 55% of oil refineries to be shut off. Oil leakage is a common problem that often results in oil waste, damage, and hazard to public health. Therefore, it is necessary to use Modern technologies to reduce this phenomenon and avoid them in advance. Pipes that convey fluids have many uses in various industries and living facilities. Risk increases when the fluid inside the pipe is flammable. In this work, main case that cause damage to the pipe, longitudinal crack is investigate.This work presents a new experimental model based on computer applications with a Fast Fourier transform (FFT) algorithm for testing the effect of longitudinal crack length by frequency and ultrasonic measurements to measure fluid velocity. The method is used for plastic pipe with 2 cm internal diameter, 3 cm external diameter, and 1 m length. The modulus of elasticity of the material is 800 N/mm2 according to the ISO 178 test method. The pipe conveys oil with simply supported ends. The results show that FFT model shows better features compared with other ways that depends on visual inspection or localized measurements which gave an external perception of pipeline damage. FFT model offers a reliable and cheap style for ensuring pipeline integrity and warning the risks before its occurrence. From the observations made the fundamental natural frequency (FNF) decreases by increasing of crack length in the pipe that conveys fluid

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Hoffmann, Alexandre, Valérie Perrier, and Sergei Grudinin. "A novel fast Fourier transform accelerated off-grid exhaustive search method for cryo-electron microscopy fitting." Journal of Applied Crystallography 50, no. 4 (June 26, 2017): 1036–47. http://dx.doi.org/10.1107/s1600576717008172.

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This paper presents a novel fast Fourier transform (FFT)-based exhaustive search method extended to off-grid translational and rotational degrees of freedom. The method combines the advantages of the FFT-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique that guarantees to find the nearest optimal off-grid conformation. The method is demonstrated on a fitting problem and can be readily applied to a docking problem. The algorithm first samples a scoring function on a six-dimensional grid of sizeN6using the FFT. This operation has an asymptotic complexity ofO(N6logN). Then, the method performs the off-grid search using a local quadratic approximation of the cost function and the trust-region optimization algorithm. The computation of the quadratic approximation is also accelerated by FFT at the same additional asymptotic cost ofO(N6logN). The method is demonstrated by fitting atomic protein models into several simulated and experimental maps from cryo-electron microscopy. The method is available at https://team.inria.fr/nano-d/software/offgridfit.

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Antonijević, Siniša. "An Improved Algorithm for Indirect Time domain Analysis of Thin Wire Structures." Journal of Communications Software and Systems 8, no. 1 (March 22, 2012): 12. http://dx.doi.org/10.24138/jcomss.v8i1.172.

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The algorithm for an indirect time domain (TD) analysis using arbitrary frequency domain method is presented.In previous work, an optimized version of the indirect timedomain method based on adaptive sampling iterative algorithm used in combination with inverse Fast Fourier Transform (FFT) was presented. In this paper, the algorithm is further improved by circumventing the use of inverse FFT altogether, and using the simple formula based on the analytical inverse Fourier transform. The proposed approach is simpler and more convenient for use with the underlying iterative optimization method, as only a part of the frequency domain (FD) signal has to be transformed to the time domain during each iteration procedure, the frequency domain discretisation does not have to be uniform, and the time domain discretisation does not have to be performed. These advantages can also lead to the reduced computational time cost of the frequency to time domain transformation when compared with the standard inverse FFT.

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Bertie, John E., and Shuliang L. Zhang. "Infrared intensities of liquids. IX. The Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 520–31. http://dx.doi.org/10.1139/v92-074.

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It is well known that the infinite Kramers–Kronig transform is equivalent to the infinite Hilbert transform, which is equivalent to the allied Fourier integrals. The Hilbert transform can thus be implemented using fast Fourier transform routines. Such implementation is usually some 60 times faster than the Kramers–Kronig transform for a data file containing about 7 points. This paper reports that, for transformations between the real and imaginary refractive indices, [Formula: see text] and [Formula: see text] in [Formula: see text], the FFT-based Hilbert transform can be much less accurate than, or as accurate as, the Kramers–Kronig transform, depending on the algorithm used. The Kramers–Kronig transform, incorporating Mclaurin's formula for finding the principal value of the integral, transforms [Formula: see text] spectra into [Formula: see text] spectra that are accurate to about 0.05%. Some Hilbert transform algorithms in the literature yield only about 4% accuracy. The BZ algorithm for the Hilbert transform is presented, for use on a laboratory computer running under DOS, that yields [Formula: see text] spectra accurate to 0.05%. For the transform from [Formula: see text] to [Formula: see text], the BZ algorithm gives [Formula: see text] accurate to about −0.2% of the largest k value in the spectrum. This compares with an accuracy of 0.5% for the Kramers–Kronig transform. In cases where the [Formula: see text] spectrum is truncated at low wavenumbers, a simple method is presented that improves by a factor of ~10 the accuracy at low wavenumber of the [Formula: see text] spectrum obtained by Hilbert or Kramers–Kronig transforms of the [Formula: see text] spectrum. Keywords: infrared intensities, complex refractive indices, Kramers–Kronig transform, Hilbert transform, optical constants.

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Oruganti, Venkata Subrahmanya Raghavendra Varaprasad, Venkata Sesha Samba Siva Sarma Dhanikonda, Helmo Kelis Morales Paredes, and Marcelo Godoy Simões. "Enhanced Dual-Spectrum Line Interpolated FFT with Four-Term Minimal Sidelobe Cosine Window for Real-Time Harmonic Estimation in Synchrophasor Smart-Grid Technology." Electronics 8, no. 2 (February 6, 2019): 191. http://dx.doi.org/10.3390/electronics8020191.

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The proliferation of nonlinear loads and integration of renewable energy sources require attention for accurate harmonic estimation along with estimation of fundamental amplitude, phase, and frequency for protection, improving power quality, and managing power effectively in a smart distribution grid. There are currently different Windowed Interpolated Fast Fourier Transform (WIFFT) algorithms for harmonic voltage estimation, but estimation of current harmonics using WIFFT is not explored sufficiently. The existing WIFFT algorithms, when used for current harmonic estimation result in low accuracy due to spectral leakage and picket fence effect. On the other hand, Interpolated Discrete Fourier Transform (DFT) is used for synchrophasor quality metrics, but it is effective only when there are no harmonics and the fundamental frequency is constant. This paper proposes a unified solution, comprising of peak location index search (PLIS)-based Dual-Spectrum Line Interpolated Fast Fourier Transform (DSLIFFT) algorithm with 4-Term Minimal Sidelobe Cosine Window (4MSCW) for estimating both low-amplitude voltage or current harmonics and synchrophasor under variable frequency conditions for high-penetration renewable energy utility grids. The effectiveness of the proposed algorithm is validated by simulation studies and real-time experimentation using the National Instruments reconfigurable embedded system under nonlinear loading conditions.

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Kliwati, Sri. "ALGORITMA DETEKSI FREKUENSI DTMF MENGGUNAKAN KORELASI SILANG UNTUK TELEKOMANDO WAHANA TERBANG." Jurnal Teknologi Dirgantara 14, no. 1 (July 22, 2016): 1. http://dx.doi.org/10.30536/j.jtd.2016.v14.a2562.

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In general, the frequency DTMF detection algorithm using FFT (Fast Fourier Transform) and Goertzel Algorithm. However, in certain circumstances a more suitable signal detected by the other algorithms. For example in a non-periodic signal as the measurement sensors for flight vehicle. The purpose of this study is to develop a system telecommand for flight vehicle. And this paper discusses the frequency DTMF (Dual Tone Multi Frequency) detection method using cross correlation algorithm and data-base DTMF. The simulation results show the frequency detection successfully carried out in accordance with the accuracy of the data-base created (1 Hz) to change the frequency of zero to 1700 Hz (DTMF frequency limit). Abstrak Deteksi frekuensi DTMF secara umum menggunakan algoritma Fast Fourier Transform (FFT) dan Goertzel Algorithm. Akan tetapi pada kondisi tertentu sebuah sinyal lebih cocok dideteksi dengan algoritma yang lain. Misalnya pada sinyal yang non-periodik seperti pada pengukuran sensor-sensor wahana terbang. Tujuan penelitian ini adalah membangun sistem telekomando untuk wahana terbang. Dan tulisan ini membahas metode deteksi frekuensi Dual Tone Multi Frequency (DTMF) dengan menggunakan algoritma korelasi silang dan data-base DTMF. Hasil simulasi menunjukkan deteksi frekuensi berhasil dilakukan sesuai dengan akurasi database yang dibuat (1 Hz) untuk perubahan frekuensi antara nol hingga 1700 Hz (batas frekuensi DTMF).

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Kliwati, Sri. "ALGORITMA DETEKSI FREKUENSI DTMF MENGGUNAKAN KORELASI SILANG UNTUK TELEKOMANDO WAHANA TERBANG (DTMF FREQUENCY DETECTION ALGORITHM USING CROSSCORRELATION FOR VEHICLE TELECOMMAND)." Jurnal Teknologi Dirgantara 14, no. 1 (March 19, 2018): 1. http://dx.doi.org/10.30536/j.jtd.2016.v14.a2942.

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In general, the frequency DTMF detection algorithm using FFT (Fast Fourier Transform) and Goertzel Algorithm. However, in certain circumstances a more suitable signal detected by the other algorithms. For example in a non-periodic signal as the measurement sensors for flight vehicle. The purpose of this study is to develop a system telecommand for flight vehicle. And this paper discusses the frequency DTMF (Dual Tone Multi Frequency) detection method using cross correlation algorithm and data-base DTMF. The simulation results show the frequency detection successfully carried out in accordance with the accuracy of the data-base created (1 Hz) to change the frequency of zero to 1700 Hz (DTMF frequency limit). ABSTRAKDeteksi frekuensi DTMF secara umum menggunakan algoritma Fast Fourier Transform (FFT) dan Goertzel Algorithm. Akan tetapi pada kondisi tertentu sebuah sinyal lebih cocok dideteksi dengan algoritma yang lain. Misalnya pada sinyal yang non-periodik seperti pada pengukuran sensor-sensor wahana terbang. Tujuan penelitian ini adalah membangun sistem telekomando untuk wahana terbang. Dan tulisan ini membahas metode deteksi frekuensi Dual Tone Multi Frequency (DTMF) dengan menggunakan algoritma korelasi silang dan data-base DTMF. Hasil simulasi menunjukkan deteksi frekuensi berhasil dilakukan sesuai dengan akurasi database yang dibuat (1 Hz) untuk perubahan frekuensi antara nol hingga 1700 Hz (batas frekuensi DTMF).

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Hosseinzadegan, Samar, Andreas Fhager, Mikael Persson, and Paul Meaney. "A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging." International Journal of Antennas and Propagation 2019 (July 17, 2019): 1–12. http://dx.doi.org/10.1155/2019/9014969.

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We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.

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Wang, L. L., D. G. Fang, and W. X. Sheng. "Combination of genetic algorithm (GA) and fast fourier transform (FFT) for synthesis of arrays." Microwave and Optical Technology Letters 37, no. 1 (February 24, 2003): 56–59. http://dx.doi.org/10.1002/mop.10823.

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STOEV, STILIAN, and MURAD S. TAQQU. "SIMULATION METHODS FOR LINEAR FRACTIONAL STABLE MOTION AND FARIMA USING THE FAST FOURIER TRANSFORM." Fractals 12, no. 01 (March 2004): 95–121. http://dx.doi.org/10.1142/s0218348x04002379.

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We present efficient methods for simulation, using the Fast Fourier Transform (FFT) algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely, (i) the linear fractional stable motion (LFSM) process and (ii) the fractional autoregressive moving average (FARIMA) time series with SαS innovations. These two types of heavy-tailed processes have infinite variances and long-range dependence and they can be used in modeling the traffic of modern computer telecommunication networks. We generate paths of the LFSM process by using Riemann-sum approximations of its SαS stochastic integral representation and paths of the FARIMA time series by truncating their moving average representation. In both the LFSM and FARIMA cases, we compute the involved sums efficiently by using the Fast Fourier Transform algorithm and provide bounds and/or estimates of the approximation error. We discuss different choices of the discretization and truncation parameters involved in our algorithms and illustrate our method. We include MATLAB implementations of these simulation algorithms and indicate how the practitioner can use them.

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Berbenni, Stéphane, and Vincent Taupin. "Fast Fourier transform-based micromechanics of interfacial line defects in crystalline materials." Journal of Micromechanics and Molecular Physics 03, no. 03n04 (September 2018): 1840007. http://dx.doi.org/10.1142/s2424913018400076.

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Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics community. The present contribution addresses the critical question of determining local mechanical fields using the FFT method in the presence of interfacial defects. Precisely, the present work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of disclinations, i.e., rotational discontinuities, and inhomogeneities. A centered finite difference scheme for differential rules are first used for numerically solving the Poisson-type equations in the Fourier space to get the incompatible elastic fields due to disclinations and dislocations. Second, centered finite differences on a rotated grid are chosen for the computation of the modified Fourier-Green’s operator in the Lippmann–Schwinger–Dyson type equation for heterogeneous media. Elastic fields of disclination dipole distributions interacting with inhomogeneities of varying stiffnesses, grain boundaries seen as DSUM (Disclination Structural Unit Model), grain boundary disconnection defects and phase boundary “terraces” in anisotropic bi-materials are numerically computed as applications of the method.

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Journal articles on the topic 'Fast Fourier Transform (Fft) Algorithm'

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