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Journal articles on the topic 'Fast Fourier Transform Analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Döhler, Michael, Stefan Kunis, and Daniel Potts. "Nonequispaced Hyperbolic Cross Fast Fourier Transform." SIAM Journal on Numerical Analysis 47, no. 6 (January 2010): 4415–28. http://dx.doi.org/10.1137/090754947.

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2

Adduri, Phani R., and Ravi C. Penmetsa. "Fast Fourier transform based system reliability analysis." International Journal of Reliability and Safety 1, no. 3 (2007): 239. http://dx.doi.org/10.1504/ijrs.2007.014964.

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3

Dishan, Huang. "Phase error in fast Fourier transform analysis." Mechanical Systems and Signal Processing 9, no. 2 (March 1995): 113–18. http://dx.doi.org/10.1006/mssp.1995.0009.

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4

Lin, Hsiung-Cheng, and Yu-Chen Ye. "Reviews of bearing vibration measurement using fast Fourier transform and enhanced fast Fourier transform algorithms." Advances in Mechanical Engineering 11, no. 1 (January 2019): 168781401881675. http://dx.doi.org/10.1177/1687814018816751.

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The rolling element bearing is one of the most critical components in a machine. Vibration signals resulting from these bearings imply important bearing defect information related to the machinery faults. Any defect in a bearing may cause a certain vibration with specific frequencies and amplitudes depending on the nature of the defect. Therefore, the vibration analysis plays a key role for fault detection, diagnosis, and prognosis to reach the reliability of the machines. Although fast Fourier transform for time–frequency analysis is still widely used in industry, it cannot extract enough frequencies without enough samples. If the real frequency does not match fast Fourier transform frequency grid exactly, the spectrum is spreading mostly among neighboring frequency bins. To resolve this drawback, the recent proposed enhanced fast Fourier transform algorithm was reported to improve this situation. This article reviews and compares both fast Fourier transform and enhanced fast Fourier transform for vibration signal analysis in both simulation and practical work. The comparative results verify that the enhanced fast Fourier transform can provide a better solution than traditional fast Fourier transform.

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5

SAKAMOTO, Jun, Yasuhiro MORI, and Takayoshi SEKIOKA. "PROBABILITY ANALYSIS METHOD BY DISCRETE FAST FOURIER TRANSFORM." Journal of Structural and Construction Engineering (Transactions of AIJ) 60, no. 472 (1995): 39–45. http://dx.doi.org/10.3130/aijs.60.39_2.

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6

TAKEKAWA, Satoru. "Analysis of Colonic Motility by Fast Fourier Transform." Journal of Smooth Muscle Research 32, no. 5 (1996): 203–12. http://dx.doi.org/10.1540/jsmr.32.203.

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7

Kasper, Peter K. "Structural acoustic analysis using the fast Fourier transform." Journal of the Acoustical Society of America 89, no. 4B (April 1991): 1922–23. http://dx.doi.org/10.1121/1.2029521.

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8

Fisher, Michal, Valery Bulatov, Salah Hasson, and Israel Schechter. "Fast Aerosol Analysis by Fourier Transform Imaging Fluorescence Microscopy." Analytical Chemistry 70, no. 11 (June 1998): 2409–14. http://dx.doi.org/10.1021/ac971355c.

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9

Wallace, John L. "Real‐time fast‐Fourier‐transform analysis ofM‐Hhysteresis loops." Journal of Applied Physics 73, no. 10 (May 15, 1993): 6849–51. http://dx.doi.org/10.1063/1.352459.

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10

Yutai Ma. "An accurate error analysis model for fast Fourier transform." IEEE Transactions on Signal Processing 45, no. 6 (June 1997): 1641–45. http://dx.doi.org/10.1109/78.600005.

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11

Nishiwaki, Seiji. "Calculations of optical field by fast Fourier transform analysis." Applied Optics 27, no. 16 (August 15, 1988): 3518. http://dx.doi.org/10.1364/ao.27.003518.

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12

Ohashi, Naoki, and Kanemasa Mizukoshi. "Analysis of Smooth Pursuit by the Fast Fourier Transform." Acta Oto-Laryngologica 111, sup481 (January 1991): 348–51. http://dx.doi.org/10.3109/00016489109131419.

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13

Gelb, Anne, and Guohui Song. "A Frame Theoretic Approach to the Nonuniform Fast Fourier Transform." SIAM Journal on Numerical Analysis 52, no. 3 (January 2014): 1222–42. http://dx.doi.org/10.1137/13092160x.

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14

He, Xuefei, Kian Meng Lim, and Siak Piang Lim. "A fast elastostatic solver based on fast Fourier transform on multipoles (FFTM)." International Journal for Numerical Methods in Engineering 76, no. 8 (November 19, 2008): 1231–49. http://dx.doi.org/10.1002/nme.2365.

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15

Kircheis, Melanie, and Daniel Potts. "Direct inversion of the nonequispaced fast Fourier transform." Linear Algebra and its Applications 575 (August 2019): 106–40. http://dx.doi.org/10.1016/j.laa.2019.03.028.

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16

Kim, Jin-Gyu, Seung Jo Yoo, Chang-Yeon Kim, and Hyeong-Tae Jou. "Circular Fast Fourier Transform Application: A Useful Script for Fast Fourier Transform Data Analysis of High-resolution Transmission Electron Microscopy Image." Applied Microscopy 44, no. 4 (December 30, 2014): 138–43. http://dx.doi.org/10.9729/am.2014.44.4.138.

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17

Agboje, Oboyerulu E., Olabode Babatunde Idowu-Bismark, and Augustus E. Ibhaze. "Comparative Analysis of Fast Fourier Transform and Discrete Wavelet Transform Based MIMO-OFDM." International Journal on Communications Antenna and Propagation (IRECAP) 7, no. 2 (April 30, 2017): 168. http://dx.doi.org/10.15866/irecap.v7i2.10803.

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18

Sun, Jichao, and Zhengping Zhang. "Generalized Orthogonal Discrete W Transform and Its Fast Algorithm." Discrete Dynamics in Nature and Society 2021 (January 11, 2021): 1–13. http://dx.doi.org/10.1155/2021/2529754.

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Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.

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19

Protsko, I. O., and D. V. Ostrovka. "ANALYSIS OF THE ERROR OF COMPUTATION FAST TRANSFORMS OF FOURIER CLASS BASED ON CYCLIC CONVOLUTIONS." Ukrainian Journal of Information Technology 2, no. 1 (2020): 52–56. http://dx.doi.org/10.23939/ujit2020.02.052.

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The features of the computational model of discrete transforms of Fourier class based on cyclic convolutions to determine the algorithmic calculation error are analyzed. Based on the approach of efficient computation of discrete transforms of Fourier class of arbitrary size N, using of a hashing array to transform a discrete basis matrix into a set of block-cyclic submatrices, the components of computational costs are considered. These components of computational costs depend on the type of transform, the size and the block-cycle structure of the transformation core. Examples of computational model and block-cyclic structure of matrices of simplified arguments of basis functions for mutually inverse discrete cosine transforms of types II, III are given. The computational model characterizes the accumulation of rounding errors at the stages of adding input data, computing cyclic convolutions, combining the results of convolutions. Discrete cyclic convolutions can be implemented using fast algorithms or a type of system that corresponds to digital filters with finite pulse characteristics. The possibility of parallel computation of the reduced number of cyclic convolutions makes the analysis of errors insensitive to rearrangement of their computations. The multiplication operations performed when computing the cyclic convolution uses a smaller number of basis coefficients equal to N/4 or N/2 depending on the size of transform. The formats of representation of real numbers in computer systems are considered, which also determine the magnitude of the computational error of transforms. The results of direct and fast computation of discrete cosine transform of type II based on cyclic convolutions with size N=58 in the format wit floating point of double precision and computation error between them are presented. The apriori process of studying the transform errors of the corresponding type and size by the method of mathematical modeling and computational experiment is approximate, which allows to predict the statistical averages of the accuracy of computing the discrete Fourier transform of arbitrary size based on cyclic convolutions.

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20

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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21

MA JIAN-GUO, GUO YING-HUAN, and WANG YUN-YU. "ANALYSIS OF POSITRON ANNIHILATION LIFETIME SPECTRUM BY FAST FOURIER TRANSFORM." Acta Physica Sinica 43, no. 4 (1994): 547. http://dx.doi.org/10.7498/aps.43.547.

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22

Sakamoto, J., Y. Mori, and T. Sekioka. "Probability analysis method using Fast Fourier transform and its application." Structural Safety 19, no. 1 (January 1997): 21–36. http://dx.doi.org/10.1016/s0167-4730(96)00032-x.

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23

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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24

Pyrda, L. "Application of Fast Fourier Transform in thermo-magnetic convection analysis." Journal of Physics: Conference Series 530 (August 22, 2014): 012060. http://dx.doi.org/10.1088/1742-6596/530/1/012060.

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25

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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26

Yust, Charles S. "Fast Fourier Transform Analysis of Computer-Acquired Friction Data©." Tribology Transactions 37, no. 1 (January 1994): 201–5. http://dx.doi.org/10.1080/10402009408983285.

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27

Park, Cheong Hee, and Haesun Park. "Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis." Pattern Recognition 38, no. 4 (April 2005): 495–503. http://dx.doi.org/10.1016/j.patcog.2004.08.013.

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28

Calvetti, Daniela. "A stochastic roundoff error analysis for the fast Fourier transform." Mathematics of Computation 56, no. 194 (May 1, 1991): 755. http://dx.doi.org/10.1090/s0025-5718-1991-1068824-0.

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29

Wang, Yan-xue, Li-xuan Chen, Yan-song Li, Yun Zhang, Ken Hsiao, and Yung-Jui Lee. "43-3: Image Sticking Evaluation Using Fast Fourier Transform Analysis." SID Symposium Digest of Technical Papers 47, no. 1 (May 2016): 585–87. http://dx.doi.org/10.1002/sdtp.10743.

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30

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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31

Hendriks, Harrie. "Application of fast spherical Fourier transform to density estimation." Journal of Multivariate Analysis 84, no. 2 (February 2003): 209–21. http://dx.doi.org/10.1016/s0047-259x(02)00041-6.

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32

Chakravarty, Lopamudra, and Amal Krishna Halder. "Comparative study of Fourier transform and an approach of fast Fourier transform in solving the boundary value problem of PDE." Journal of Interdisciplinary Mathematics 13, no. 6 (December 2010): 649–59. http://dx.doi.org/10.1080/09720502.2010.10700725.

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33

Wicht, Daniel, Matti Schneider, and Thomas Böhlke. "On Quasi‐Newton methods in fast Fourier transform‐based micromechanics." International Journal for Numerical Methods in Engineering 121, no. 8 (December 23, 2019): 1665–94. http://dx.doi.org/10.1002/nme.6283.

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34

Mahdi, Jinan F. "Frequency analyses of human voice using fast Fourier transform." Iraqi Journal of Physics (IJP) 13, no. 27 (February 4, 2019): 174–81. http://dx.doi.org/10.30723/ijp.v13i27.276.

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Quantitative analysis of human voice has been subject of interest and the subject gained momentum when human voice was identified as a modality for human authentication and identification. The main organ responsible for production of sound is larynx and the structure of larynx along with its physical properties and modes of vibration determine the nature and quality of sound produced. There has been lot of work from the point of view of fundamental frequency of sound and its characteristics. With the introduction of additional applications of human voice interest grew in other characteristics of sound and possibility of extracting useful features from human voice. We conducted a study using Fast Fourier Transform (FFT) technique to analyze human voice to identify different frequencies present in the voice with their relative proportion while pronouncing selected words like numbers. Details of findings are presented

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35

Ong, E. T., K. H. Lee, and K. M. Lim. "A fast algorithm for three-dimensional electrostatics analysis: fast Fourier transform on multipoles(FFTM)." International Journal for Numerical Methods in Engineering 61, no. 5 (September 21, 2004): 633–56. http://dx.doi.org/10.1002/nme.1081.

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36

Ghani, Hadhrami Ab, Mohamad Razwan Abdul Malek, Muhammad Fadzli Kamarul Azmi, Muhammad Jefri Muril, and Azizul Azizan. "A review on sparse fast fourier transform applications in image processing." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 2 (April 1, 2020): 1346. http://dx.doi.org/10.11591/ijece.v10i2.pp1346-1351.

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Fast Fourier Transform has long been established as an essential tool in signal processing. To address the computational issues while helping the analysis work for multi-dimensional signals in image processing, sparse Fast Fourier Transform model is reviewed here when applied in different applications such as lithography optimization, cancer detection, evolutionary arts and wasterwater treatment. As the demand for higher dimensional signals in various applications especially multimedia appplications, the need for sparse Fast Fourier Transform grows higher.

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37

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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38

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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39

Soares, Antonio Henrique Germano, Breno Quintella Farah, Gabriel Grizzo Cucato, Carmelo José Albanez Bastos-Filho, Diego Giulliano Destro Christofaro, Luiz Carlos Marques Vanderlei, Aluísio Henrique Rodrigues de Andrade Lima, and Raphael Mendes Ritti-Dias. "Is the algorithm used to process heart rate variability data clinically relevant? Analysis in male adolescents." Einstein (São Paulo) 14, no. 2 (June 2016): 196–201. http://dx.doi.org/10.1590/s1679-45082016ao3683.

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ABSTRACT Objective To analyze whether the algorithm used for the heart rate variability assessment (fast Fourier transform versus autoregressive methods) influenced its association with cardiovascular risk factors in male adolescents. Methods This cross-sectional study included 1,152 male adolescents (aged 14 to 19 years). The low frequency, high frequency components (absolute numbers and normalized units), low frequency/high frequency ratio, and total power of heart rate variability parameters were obtained using the fast Fourier transform and autoregressive methods, while the adolescents were resting in a supine position. Results All heart rate variability parameters calculated from both methods were different (p<0.05). However, a low effect size (<0.1) was found for all parameters. The intra-class correlation between methods ranged from 0.96 to 0.99, whereas the variation coefficient ranged from 7.4 to 14.8%. Furthermore, waist circumference was negatively associated with high frequency, and positively associated with low frequency and sympatovagal balance (p<0.001 for both fast Fourier transform and autoregressive methods in all associations). Systolic blood pressure was negatively associated with total power and high frequency, whereas it was positively associated with low frequency and sympatovagal balance (p<0.001 for both fast Fourier transform and autoregressive methods in all associations). Body mass index was negatively associated with high frequency, while it was positively associated with low frequency and sympatovagal balance (p values ranged from <0.001 to 0.007). Conclusion There are significant differences in heart rate variability parameters obtained with the fast Fourier transform and autoregressive methods in male adolescent; however, these differences are not clinically significant.

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40

Zhang, Qing Xin, Jin Li, Hai Bin Li, and Chong Liu. "Motor Fault Diagnosis Based on Wavelet Analysis and Fast Fourier Transform." Advanced Materials Research 301-303 (July 2011): 1401–5. http://dx.doi.org/10.4028/www.scientific.net/amr.301-303.1401.

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For the detection of the broken-bar fault of rotor in motors, a traditional method is frequency spectrum analysis for the stator current. However, the frequency components representative of the rotor fault can be easily submerged by the fundamental frequency, so that the detections results are inaccurate. In this paper, the stator current will be decomposed and reconstructed, after that the fast Fourier transform can be applied to the frequency spectrum analysis. It eliminates the influence that the fault characteristic components are flooded by the basic frequency components. The experiment result shows that the existence of a slight fault in rotor can be detected. The method has a good theoretical and engineering application.

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41

Bécares, Eloy, and Antonio J. García-Olivares. "CHARACTERIZATION OF INDUSTRIAL WASTEWATER TREATMENT DYNAMICS USING FAST FOURIER TRANSFORM ANALYSIS." Water Science and Technology 30, no. 2 (July 1, 1994): 229–32. http://dx.doi.org/10.2166/wst.1994.0047.

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Fast Fourier transform analysis has been applied to decompose the variance of some temporal series from an A + B industrial wastewater treatment system, as well as to discriminate which frequencies are basically contributing to parameter variability. The basic oscillations of the effluents, evaluated by means of the total COD, are shown to be mainly dependent on the internal dynamics of the reactors, whose design and control features are the generating forces for the final effluent fluctuations. Owing to the shorter retention time in the first reactor, the output signal was more complex than the input one. Although the second reactor reduces system complexity, it does not have an important effect on the final total COD.

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42

Zhong Hu and Honghui Wan. "A novel generic fast Fourier transform pruning technique and complexity analysis." IEEE Transactions on Signal Processing 53, no. 1 (January 2005): 274–82. http://dx.doi.org/10.1109/tsp.2004.838925.

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43

Taniwaki, Mitsuru, and Kaoru Kohyama. "Fast Fourier transform analysis of sounds made while swallowing various foods." Journal of the Acoustical Society of America 132, no. 4 (October 2012): 2478–82. http://dx.doi.org/10.1121/1.4750491.

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44

Mingsheng Zhang, Bingcu Cai, Xiaolin Zhao, and Zongguang Wang. "Three-dimensional magnetic field analysis of micromotor by fast Fourier transform." IEEE Transactions on Magnetics 35, no. 5 (1999): 3685–87. http://dx.doi.org/10.1109/20.800631.

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45

Deng, F. W., J. H. Cushman, and J. W. Delleur. "A Fast Fourier transform stochastic analysis of the contaminant transport problem." Water Resources Research 29, no. 9 (September 1993): 3241–47. http://dx.doi.org/10.1029/93wr01236.

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46

Rao, B. N., and Rajib Chowdhury. "Probabilistic Analysis Using High Dimensional Model Representation and Fast Fourier Transform." International Journal for Computational Methods in Engineering Science and Mechanics 9, no. 6 (September 30, 2008): 342–57. http://dx.doi.org/10.1080/15502280802363035.

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47

Pitas, I., and M. G. Strintzis. "Floating point error analysis of two-dimensional, fast Fourier transform algorithms." IEEE Transactions on Circuits and Systems 35, no. 1 (1988): 112–15. http://dx.doi.org/10.1109/31.1706.

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48

Lin, Hsiung-Cheng, Yu-Chen Ye, Bo-Jyun Huang, and Jia-Lun Su. "Bearing vibration detection and analysis using enhanced fast Fourier transform algorithm." Advances in Mechanical Engineering 8, no. 10 (October 2016): 168781401667508. http://dx.doi.org/10.1177/1687814016675080.

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49

Rust, B., and D. Donnelly. "The Fast Fourier Transform for Experimentalists Part III: Classical Spectral Analysis." Computing in Science and Engineering 7, no. 5 (September 2005): 74–78. http://dx.doi.org/10.1109/mcse.2005.103.

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50

Rust, B., and D. Donnelly. "The Fast Fourier Transform for Experimentalists, Part IV: Autoregressive Spectral Analysis." Computing in Science and Engineering 7, no. 6 (November 2005): 85–90. http://dx.doi.org/10.1109/mcse.2005.126.

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