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Journal articles on the topic 'Fast Fourier Transform(FFT)'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

Hu, Jiatu, Fuge Jia, and Wenzhe Liu. "Application of Fast Fourier Transform." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 590–97. http://dx.doi.org/10.54097/hset.v38i.5888.

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Fourier analysis is most frequently used as a univariate approach for either modeling or simplifying data. It may also be used as a method for multivariate data analysis. There are various connections between Fourier analysis and trend analysis. It takes a fresh look at how data sets are related. In the case of Fourier analysis, the technique clarifies the time dimension variable in the data set. The most fundamental kind of Fourier analysis works under the idea that many events have a periodic nature and that fluctuations in other variables brought on by this periodicity may be eliminated using Fourier transforms. By using the residual (i.e., time-independent) variance from other variables, Fourier-transformed data may be subjected to more powerful analysis.Based on differential matrices and semidiscrete Fourier transforms, this paper summarizes the key problems in Fourier analysis, FFT. Secondly, this paper points out the application of F FT in the field of modern science and technology and the main progress of current FFT research, and on this basis, the research prospects of FFT law are prospected.

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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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<span style="font-size: 9pt; font-family: 'Times New Roman', serif;" lang="EN-IN">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 <em>twiddle factors </em>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 G<sup>T</sup> algorithm. All these algorithms are implemented on FPGA (Spartan-3 XC3S4000l-4fg900) with XILINX 10.1 ISE.</span>

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3

Langs, D. A. "FAST: a compact general crystallographic fast Fourier transform (FFT)." Journal of Applied Crystallography 29, no. 4 (August 1, 1996): 481–83. http://dx.doi.org/10.1107/s0021889896003056.

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4

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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Chen, Yulin, You Lv, Xinyue Jiang, Haotian Huang, and Yuan Zhu. "Fast Fourier transform Ångström method for fast thermal measurements of microfibers." Review of Scientific Instruments 94, no. 1 (January 1, 2023): 014901. http://dx.doi.org/10.1063/5.0125726.

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The Ångström method is a promising thermal diffusivity measurement method for microfibers. Based on the heat-loss Ångström method and micro-Ångström method, the FFT (Fast Fourier Transform) Ångström method can be used to shorten the testing time and enhance the testing robustness of thermal conductivity. The FFT Ångström uses multi-frequency superimposed input signals and then uses the FFT for frequency division analysis. Since different frequencies are input at the same time, the measuring time is greatly reduced. Moreover, because different frequencies are input in the same environment, the random and environmental perturbations of the frequencies are the same, enhancing the fitting robustness. In contrast, the single feeding strategy is relatively time-consuming, and its measurement homogeneity for different frequencies cannot be guaranteed. By comparing the measurement results from a multi-frequency input and separated single-frequency input, the FFT shows good feasibility and robustness. It may also have great potential in other types of thermal wave measurements.

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Rufo, Montaña, Antonio Jiménez, Jesús M. Paniagua, and Alberto González-Mohíno. "Ultrasound Assessment of Honey Using Fast Fourier Transform." Sensors 21, no. 20 (October 11, 2021): 6748. http://dx.doi.org/10.3390/s21206748.

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Ultrasound inspection permits the characteristics of some foodstuffs to be determined easily and cheaply. This experimental study included the determination of various ultrasound parameters provided by the fast Fourier transform (FFT) which had not previously been considered in testing the physical properties of different varieties of honey. These parameters are practically independent of the criteria adopted for their calculation, unlike other ultrasound variables such as pulse velocity or attenuation whose determination can vary depending on those criteria. The study was carried out on four varieties of honey (Eucalyptus, Heather, Thyme, and Thousand Flowers) using 500-kHz transducers. A simultaneously performed honey texture analysis (Texture Profile Analysis-TPA) showed significant linear correlations between the ultrasound variables provided by FFT and the texture parameters. The FFT parameters distinguished between each of the four honey varieties studied.

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Alamsyah, Derry. "Maximum Likelihood Classification with Fast Fourier Transform Feature Extraction for Car Recognition." Jurnal Teknologi dan Sistem Komputer 6, no. 1 (January 31, 2018): 32–36. http://dx.doi.org/10.14710/jtsiskom.6.1.2018.32-36.

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The car recognition is part of the field of traffic surveillance on the image. In general, the car recognition using the form-based feature as a unique feature. Another feature in object recognition is the frequency feature. One feature of frequency is the Fourier feature, this feature is obtained by using Fast Fourier Transform (FFT) method. The object recognition can be done by determining the maximum value of likelihood and classifying it with Maximum Likelihood Classification (MLC). The use of FFT and MLC in the car object recognition has never been used. The results of both are in a good accuracy that is 76%.

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Ibrahim, Siti Nur Iqmal, John G. O'Hara, and Nick Constantinou. "Pricing Extendible Options Using the Fast Fourier Transform." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/831470.

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This paper applies the fast Fourier transform (FFT) approach, within the Black-Scholes framework, to the valuation of options whose time to maturity can be extended to a future date (extendible options). We determine the valuation of the extendible options as sums of expectations of indicator functions, leading to a semianalytic expression for the value of the options over a range of strikes. Compared to Monte Carlo simulation, numerical examples demonstrate that the FFT is both computationally more efficient and higher in accuracy.

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Mirfarshbafan, Seyed Hadi, Sueda Taner, and Christoph Studer. "SMUL-FFT: A Streaming Multiplierless Fast Fourier Transform." IEEE Transactions on Circuits and Systems II: Express Briefs 68, no. 5 (May 2021): 1715–19. http://dx.doi.org/10.1109/tcsii.2021.3064238.

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Kurnia, Rani, and Riki Mukhaiyar. "Pemantauan Flicker Tengangan Menggunakan Fast fourier transform (FFT)." Voteteknika (Vocational Teknik Elektronika dan Informatika) 9, no. 3 (September 1, 2021): 1. http://dx.doi.org/10.24036/voteteknika.v9i3.112034.

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Laju elektrifikasi Sumatera Barat 92,96%. Jumlah ini akan terus meningkat setiap tahun, dan dengan meningkatnya laju elektrifikasi di Sumatera Barat maka kualitas daya yang dibutuhkan akan meningkat. Di sisi lain, peningkatan kecepatan pengisian menyebabkan penurunan kualitas daya. Kualitas daya sistem tenaga dipengaruhi oleh gangguan. Dengan kata lain, sistem tenaga gagal, mengakibatkan kualitas daya yang buruk. Gangguan memanifestasikan dirinya dalam bentuk faktor eksternal dan internal. Faktor eksternal termasuk petir dan pohon tumbang, dan faktor internal termasuk pemadaman listrik sementara, fluktuasi tegangan, transien tegangan dan arus, serta kedipan tegangan. Kami akan fokus pada gangguan flicker tegangan yang disebabkan oleh gangguan ini. Kedipan tegangan memiliki berbagai efek seperti kegagalan relai pelindung, fluktuasi tegangan yang dapat menyebabkan lampu berkedip terang dan redup. Tujuan dari proyek akhir ini adalah membuat alat yang mendeteksi adanya tegangan jitter dengan metode Fast Fourier Transform (FFT), sehingga Anda dapat mengamati getaran akibat gelombang FFT pada aplikasi Matlab.Kata kunci : Monitoring, Voltage Flicker, Fast Fourier Transform

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Cormack, G. D., and J. O. Binder. "The extended function fast Fourier transform (EF-FFT)." IEEE Transactions on Instrumentation and Measurement 38, no. 3 (June 1989): 730–35. http://dx.doi.org/10.1109/19.32182.

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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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Ponomareva, O. V., A. V. Ponomarev, and N. V. Smirnova. "Algorithms for Direct and Inverse Parametric Fast Fourier Transform." Informacionnye Tehnologii 28, no. 1 (January 17, 2022): 9–19. http://dx.doi.org/10.17587/it.28.9-19.

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Русский Main page New issue Archive of articles Editorial board For the authors Publishing house ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES". No. 1. Vol. 28. 2022 DOI: 10.17587/it.28.9-19 O. V. Ponomareva, Dr. Sc., Tech., Professor, A. V. Ponomarev, PhD, Econ., Associate Professor, Kalashnikov Izhevsk State Technical University, Izhevsk, 426069, Russian Federation, N. V. Smirnova, PhD, Tech., Associate Professor, Sevastopol State University, Sevastopol, 299053, Russian Federation Algorithms for Direct and Inverse Parametric Fast Fourier Transform Classical Fourier processing of finite information discrete signals (FID signals) is the most important method of digital analysis, modeling, optimization, improvement of control and decision making. The theoretical basis of classical Fourier processing of FID signals is the discrete Fourier transform (DFT). The practical basis of classical Fourier processing of FID signals is the Fast Fourier Transform (FFT). The practice of using classical Fourier processing of FID signals, having confirmed its effectiveness, revealed a number of negative effects inherent in this type of digital signal processing (DSP). The aliasing effect, scalloping effect, picket fence effect, significantly affect the effectiveness of analysis, modeling, optimization, improvement of management and decision making. To increase the efficiency of Fourier processing of FID signals, the authors of the paper have developed a generalization of DFT in the form of a parametric DFT (DFT-P). Since the direct application of parametric Fourier processing of FID signals (as well as the use of classical Fourier processing of FID signals) requires complex multiplications, fast procedures are required for the practical implementation of this type of FID signals. Purpose of the research is to develop algorithms for the fast parametric discrete Fourier transform (FFT-P). The work developed fast procedures for the implementation of DFT-P by time decimation. Parametric FFT-P with substitution (in place) and without substitution (no place) are proposed. The estimation of the efficiency of the FFT-P algorithms is given. The practical significance of the work is in the fact that developing algorithms for the parametric fast Fourier transform can reduce the computational costs of performing parametric discrete transformations by three or more orders of magnitude.

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He, Y., K. Hueske, J. Götze, and E. Coersmeier. "Matrix-Vector Based Fast Fourier Transformations on SDR Architectures." Advances in Radio Science 6 (May 26, 2008): 89–94. http://dx.doi.org/10.5194/ars-6-89-2008.

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Abstract. Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines. However, in face of the Software Defined Radio (SDR) development, more general (parallel) processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.

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Gritsutenko, Stanislav, and Nikolay Korovkin. "Applicability of a Fast Fourier Transform for a harmonic analysis." MATEC Web of Conferences 245 (2018): 10004. http://dx.doi.org/10.1051/matecconf/201824510004.

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Applicability for Fast Fourier Transform of signals with low entropy are discussed in this article. Firstly, FFT is studied for case of a harmonics set shifted relative to samples of FFT. A theoretical basis is analysed. A conclusion is that the error is goes down but it is high enough yet. Next, a method on a base of convolution with a harmonics spectrum neighbourhood and window’s spectrum is presented. A conclusion is that an amplitude error for harmonic measuring becomes good but a phase error continues to be bad one. Finally, a conclusion is that FFT concedes accuracy direct measuring methods. In case of accordance of characteristics of measure, FFT concedes in number of calculations.

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Mahmoud, Walid Amin. "Computation of Wavelet and Multiwavelet Transforms Using Fast Fourier Transform." Journal Port Science Research 4, no. 2 (December 8, 2021): 102–8. http://dx.doi.org/10.36371/port.2020.2.7.

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A novel fast and efficient algorithm was proposed that uses the Fast Fourier Transform (FFT) as a tool to compute the Discrete Wavelet Transform (DWT) and Discrete Multiwavelet Transform. The Haar Wavelet Transform and the GHM system are shown to be a special case of the proposed algorithm, where the discrete linear convolution will adapt to achieve the desired approximation and detail coefficients. Assuming that no intermediate coefficients are canceled and no approximations are made, the algorithm will give the exact solution. Hence the proposed algorithm provides an efficient complexity verses accuracy tradeoff. The main advantages of the proposed algorithm is that high band and the low band coefficients can be exploited for several classes of signals resulting in very low computation.

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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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Kim, Chaewon, Chaelin Kim, Hanna Lee, Jeseol Yu, and Yunsik Jang. "Effects and Limitations of Separating Overlapped Fingerprints Using Fast Fourier Transform." Korean Security Science Review 61 (September 30, 2019): 377–400. http://dx.doi.org/10.36623/kssr.2019.61.16.

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Jang, Ju-Wook, Woo-Jin Han, Seon-Il Choi, Gokul Govindu, and Viktor K. Prasanna. "Energy-Efficient and Parameterized Designs for Fast Fourier Transform on FPGAs." KIPS Transactions:PartA 13A, no. 2 (April 1, 2006): 171–76. http://dx.doi.org/10.3745/kipsta.2006.13a.2.171.

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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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L. M. Hassan, S., N. Sulaiman, S. S. Shariffudin, and T. N. T. Yaakub. "Signal-to-noise Ratio Study on Pipelined Fast Fourier Transform Processor." Bulletin of Electrical Engineering and Informatics 7, no. 2 (June 1, 2018): 230–35. http://dx.doi.org/10.11591/eei.v7i2.1167.

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Fast Fourier transform (FFT) processor is a prevailing tool in converting signal in time domain to frequency domain. This paper provides signal-to-noise ratio (SNR) study on 16-point pipelined FFT processor implemented on field-programable gate array (FPGA). This processor can be used in vast digital signal applications such as wireless sensor network, digital video broadcasting and many more. These applications require accuracy in their data communication part, that is why SNR is an important analysis. SNR is a measure of signal strength relative to noise. The measurement is usually in decibles (dB). Previously, SNR studies have been carried out in software simulation, for example in Matlab. However, in this paper, pipelined FFT and SNR modules are developed in hardware form. SNR module is designed in Modelsim using Verilog code before implemented on FPGA board. The SNR module is connected directly to the output of the pipelined FFT module. Three different pipelined FFT with different architectures were studied. The result shows that SNR for radix-8 and R4SDC FFT architecture design are above 40dB, which represent a very excellent signal. SNR module on the FPGA and the SNR results of different pipelined FFT architecture can be consider as the novelty of this paper.

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Leng, Jian Wei, and Qiong Qiong Xu. "Realization of 1024 Points Fast Fourier Transform Based on FPGA IPCore." Applied Mechanics and Materials 496-500 (January 2014): 1885–88. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.1885.

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Requirement on signal processing of radar level system is higher and higher at present. Standards such as generalization, systematic and modular cannot be satisfied through traditional methods which were using software program, application specific integrated circuit (ASIC) to achieve fast flourier transform (FFT). Therefore taking advantage of field programmable gate array (FPGA) to complete FFT had been the choosing trend of most researchers. Based on arithmetic FFT raised by Cooley-Tukey, a new design scheme of base-4 FFT was put forward in this paper. The design flow of FFT was fairly simple for the rich resource and flexible intellectual property core (IP Core). Simulation and experiment results indicated that this method was easy and flexible, accuracy and reliable. And it can decrease the development period. The calculation speed was also improved greatly.

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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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Apsari, Made Sri Ayu, and I. Made Widiartha. "Classification of Women's Voices Using Fast Fourier Transform (FFT) Method." JELIKU (Jurnal Elektronik Ilmu Komputer Udayana) 10, no. 1 (August 6, 2021): 59. http://dx.doi.org/10.24843/jlk.2021.v10.i01.p08.

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Everyone has a different kind of voice. Based on gender, voice type is divided into six parts, namely soprano, mezzo soprano, and alto for women; and tenor, baritone, and bass in men. Each type of sound has a different range and with different frequencies. This study classified the type of voice in women using the Fast Fourier Transform (FFT) method by recording the voices of each user which would then be processed using the FFT method to obtain the appropriate sound range. This research got results with an accuracy of up to 80%.The results obtained from this study are quite appropriate and it is proven that the FFT method can be used in digital signal processing.

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Kosheleva, Olga, Sergio D. Cabrera, Glenn A. Gibson, and Misha Koshelev. "Fast implementations of fuzzy arithmetic operations using fast Fourier transform (FFT)." Fuzzy Sets and Systems 91, no. 2 (October 1997): 269–77. http://dx.doi.org/10.1016/s0165-0114(97)00147-4.

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Deshmukh, Dr Suhas. "Low Cost Solution for FFT (Fast Fourier Transform) Analyser." International Journal for Research in Applied Science and Engineering Technology 9, no. 5 (May 31, 2021): 1738–43. http://dx.doi.org/10.22214/ijraset.2021.34664.

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Bansal, Rajneesh, Won Suk Lee, and Saumya Satish. "Green citrus detection using fast Fourier transform (FFT) leakage." Precision Agriculture 14, no. 1 (December 22, 2012): 59–70. http://dx.doi.org/10.1007/s11119-012-9292-3.

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Huang, Yin-Liang, Jian-Guo Liu, and Wei-Cheng Wang. "An FFT Based Fast Poisson Solver on Spherical Shells." Communications in Computational Physics 9, no. 3 (March 2011): 649–67. http://dx.doi.org/10.4208/cicp.060509.080609s.

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AbstractWe present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.

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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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MISHRA, SK. "On accelerating the FFT of Cooley and Tukey." MAUSAM 36, no. 2 (April 5, 2022): 167–72. http://dx.doi.org/10.54302/mausam.v36i2.1833.

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The efficient Fourier transform (EFT) and FFT algorithms are described and their computational efficiencies with respect to the direct method are discussed. An efficient procedure is proposed for the reordering of data set; the use of EFT algorithm for the initial Fourier transforms and restricting the size of final subsets to not less than 4 is also suggested for saving computation time in the FFT. It is found that on average the FFT with the proposed modifications is more than twice as fast as the original FFT. The amount of overhead operations involved in computer routine, based on the modified FFT is estimated.

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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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DEBBAL, S. M., F. BEREKSI-REGUIG, and A. MEZIANE TANI. "THE FAST FOURIER TRANSFORM AND THE CONTINUOUS WAVELET TRANSFORM ANALYSIS OF THE PHONOCARDIOGRAM SIGNAL." Journal of Mechanics in Medicine and Biology 04, no. 03 (September 2004): 257–72. http://dx.doi.org/10.1142/s0219519404001028.

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This paper is concerned with a synthesis study of the fast Fourier transform (FFT) and the continuous wavelet transform (CWT) in analysing the phonocardiogram signal (PCG). It is shown that the continuous wavelet transform provides enough features of the PCG signals that will help clinics to obtain qualitative and quantitative measurements of the time-frequency PCG signal characteristics and consequently aid to diagnosis. Similary, it is shown that the frequency content of such a signal can be determined by the FFT without difficulties.

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Hidayaturrohman, Umam, Erfiani Erfiani, and Farit M. Afendi. "IMPLEMENTASI TRANSFORMASI FOURIER UNTUK TRANSFORMASI DOMAIN WAKTU KE DOMAIN FREKUENSI PADA LUARAN PURWARUPA ALAT PENDETEKSIAN GULA DARAH SECARA NON-INVASIF." Indonesian Journal of Statistics and Its Applications 4, no. 2 (July 31, 2020): 234–44. http://dx.doi.org/10.29244/ijsa.v4i2.504.

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Diabetes mellitus is the result of changes in the body caused by a decrease of insulin performance which is characterized by an increase of blood sugar level. Detection of blood sugar can be done with Invasive methods or non-invasive methods. However, non-invasive methods are considered better because they can check early, faster and accurate. The prototype output is values of intensity in the time domain, thus fourier transformation is very much needed to transform into the frequency domain. In this study, Fourier transformation methods used are Discrete Fourier Transform (DFT), Fast Fourier Transform Radix-2, and Fast Fourier Transform Radix-4. Evaluation for the best method is done by comparing the processing speed of each method. The FFT Radix-4 method is more effective to perform the transformation into the frequency domain. The average processing speed with the FFT Radix-4 method reaches 2.67×105 nanoseconds, and this is much faster 5.06×106 nanoseconds than the FFT Radix-2 method and 2.40×107 nanoseconds faster than the DFT method.

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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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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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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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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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Mosier-Boss, P. A., S. H. Lieberman, and R. Newbery. "Fluorescence Rejection in Raman Spectroscopy by Shifted-Spectra, Edge Detection, and FFT Filtering Techniques." Applied Spectroscopy 49, no. 5 (May 1995): 630–38. http://dx.doi.org/10.1366/0003702953964039.

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The use of shifted-spectra, first-derivative spectroscopy (or edge detection), and fast Fourier transform filtering techniques for fluorescence rejection in Raman spectra is demonstrated. These techniques take advantage of the fact that Raman signals are very narrow in comparison to fluorescence bands in order to discriminate between the two. None of these techniques require modification of existing instrumentation. Fast Fourier transform filtering and deconvolution techniques also provide a means of improving spectral resolution and the signal-to-noise ratio.

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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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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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SO, TAKEHIKO. "Analysis by fast Fourier transform (FFT) of cardiac electrotransmission characteristics." Japanese Journal of Electrocardiology 10, no. 6 (1990): 759–67. http://dx.doi.org/10.5105/jse.10.759.

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Muhlisin, Iip, and Rusman Rusyadi. "Vibration Analysis on Rotating Machines using Fast Fourier Transform (FFT)." ACMIT Proceedings 3, no. 1 (March 18, 2019): 67–75. http://dx.doi.org/10.33555/acmit.v3i1.28.

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The history has record that heavy industries face major problems that causes by variant types of mechanical failures came from rotating machines. The Vibrations in rotating machine almost fond in everywhere, due to unbalances, misalignments and imperfect part, analytical approaches has shown that vibration monitoring has great capability in detecting and addressing the defect particular part in the machine line .The vibration velocities and vibration load will be measured at different speeds using The Time-frequency analysis at initial condition. The result of vibration readings spectrum analysis and phase analysis can be determining the figure of vibrations character, and the causes of height vibration will be found. By reading the spectrum unbalance will be identified. When the unbalanced part was balanced then we found that the vibration was decrease. The Vibration experimental frequency spectrum test will be conduct for both balanced and unbalanced condition and also in different speed conditions. To full fill the vibration analysis test, in this experimental research a prototype of vibration monitoring system was constructed. The vibration can be generated and the system performance can be monitored. In this prototype the signal from load cell and velocity sensor will be processed in microcontroller and send to computer where FFT will processed the signal to create spectrum in the computer display. The actual final result of Vibration analysis test will be provide after finish the vibrations analysis test that will be done latter, therefore the chart result on this paper is based on theoretical only.

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Listyalina, Latifah, Evrita Lusiana Utari, and Mario Warran Wizando. "IMPLEMENTATION OF FAST FOURIER TRANSFORM (FFT) FOR INFANT CRYING DETECTION." Indonesian Applied Physics Letters 4, no. 1 (August 14, 2023): 1–8. http://dx.doi.org/10.20473/iapl.v4i1.46916.

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Babies cry based on the discomfort felt by the baby which is a reflex such as when a hungry baby will suck his hand and then he will start crying, hunger can be interpreted from the baby's crying. At each of the baby's cries, when each crying pattern was responded to with the solution applied to the previous baby, each baby would stop crying. For this reason, to carry out this solution, a research was carried out to identify the pattern recognition of the sound of a baby's cry using the fast fourier transform (FFT) method with several different frequency ranges. The voice recording process is stored in digital form in the form of frequency-based sound spectrum waves, where signals that were previously in the time domain will be changed in the frequency domain. The sounds that will be distinguished in this study include the sounds of crying babies, adults, and colliding objects. This can be obtained through several stages, namely sound sample recording, sampling, signal cutting, frame blocking, final normalization, hamming window, and finally the FFT calculation process. From these series of stages, the results of the frequency range of baby crying are 101-1863 Hz, for adults the frequency range is 101-1376 Hz and for the sound of colliding objects 101-2233 Hz.

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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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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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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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Martínez, Manuel Sandoval, Janette Moreno Sandoval, Claudia Morales Barrón, and Luz Elba Castillo Izquierdo. "Outbreaks Predictions of Covid19 in Tabasco, Mexico, using Fast Fourier Transform." International Journal of Engineering and Applied Computer Science 04, no. 04 (June 3, 2022): 36–40. http://dx.doi.org/10.24032/ijeacs/0404/012.

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Results of analysis carried out on data of Covid19, in Tabasco State, are presented, from March 2020 to February 2022. The procedure named 7 day´s moving average was applied to smooth the original graph and, in this way, analyze the data more easily. Fast Fourier transform (FFT) was applied to find the frequency that allows us to detect the period (in weeks) of generation of greater Covid19 infections. FFT allows us to determine that for a period of 14n weeks (n=1,3,5,7) there will be a new outbreak. The analysis of data reveals, during the first wave, the week with the highest number of infections was July 7-12 (2751 cases), that is in week 14 ( n=1). FFT indicates that the second wave of infection would be in week 42 with n=3, the maximum was obtained at week 40 (2122 cases). The next prediction (variant Delta) was for week 70 (n=5), where there would be a high number of cases (thrid wave); real data indicates that it was reached in week 73 (7,023 cases). The four-wave (Omicron) is predicted for week 98, however, it was reached in week 94 (12,834 cases). It should be noted that due to the high transmissibility of Omicron, the number of infection grew fast during January 2022, so in this case, the difference between the prediction and the reality, present a difference of four week, however, for week 94 number of cases remains very high (1265 cases). FFT has turned out to be an adequate tool to make predictions of four waves that have occurred in Tabasco.

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Kumar Bansal, Dr Ashwani. "A Study on the Fast Fourier Transform Applications." Asian Journal of Basic Science & Research 05, no. 02 (2023): 29–39. http://dx.doi.org/10.38177/ajbsr.2023.5203.

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A fundamental issue in many branches of mathematics, science, and engineering is polynomial evaluation. Numerous applications, such as cryptography, banking, and the fields of economic analysis, numerical analysis, and sign processing, can advantage considerably from the use of environment friendly polynomial contrast algorithms. We seemed at some of the most famous polynomial comparison methods in this topic, which includes Horner's approach, Newton-Raphson method, and Lagrange interpolation method. We additionally reviewed extra state-of-the-art strategies that can consider polynomials extra correctly in some situations, such as the Fast Fourier Transform (FFT) and Fast Multipoint Evaluation (FME). The preference of algorithm will matter on the specific hassle and software at hand as every algorithm has benefits and cons of its own. It is indispensable to take computational complexity into account.

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Schneider, Matti. "A review of nonlinear FFT-based computational homogenization methods." Acta Mechanica 232, no. 6 (March 24, 2021): 2051–100. http://dx.doi.org/10.1007/s00707-021-02962-1.

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AbstractSince their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.

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